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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Big Data</journal-id>
<journal-title>Frontiers in Big Data</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Big Data</abbrev-journal-title>
<issn pub-type="epub">2624-909X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fdata.2023.1114796</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Big Data</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Sustainable energy policies from a complexity perspective</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Acevedo-Rueda</surname> <given-names>Rub&#x000E9;n Alexander</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="corresp" rid="c002"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/2230612/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Ram&#x000ED;rez-Pisco</surname> <given-names>Rodrigo</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
</contrib>
<contrib contrib-type="author">
<name><surname>V&#x000E1;squez Stanescu</surname> <given-names>Carmen Luisa</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1893144/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Torres Cruz</surname> <given-names>Ennodio Jos&#x000E9;</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
</contrib>
<contrib contrib-type="author">
<name><surname>G&#x000F3;mez-Caicedo</surname> <given-names>Melva In&#x000E9;s</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1861492/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Gait&#x000E1;n-Angulo</surname> <given-names>Mercedes</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1746457/overview"/>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>Doctorado en Ciencias de la Ingenier&#x000ED;a menci&#x000F3;n Productividad, Universidad Nacional Experimental Polit&#x000E9;cnica Antonio Jos&#x000E9; de Sucre</institution>, <addr-line>Barquisimeto</addr-line>, <country>Venezuela</country></aff>
<aff id="aff2"><sup>2</sup><institution>Universitat Carlemany</institution>, <addr-line>Sant Juli&#x000E0; de L&#x000F2;ria</addr-line>, <country>Andorra</country></aff>
<aff id="aff3"><sup>3</sup><institution>Facultad de Ciencias Econ&#x000F3;micas, Administrativas y Contables, Fundaci&#x000F3;n Universitaria los Libertadores</institution>, <addr-line>Bogot&#x000E1;</addr-line>, <country>Colombia</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Manuela Tvaronaviciene, Vilnius Gediminas Technical University, Lithuania</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Jainendra Pathak, Institute of Science, Banaras Hindu University, India; Luis Manuel Navas, University of Valladolid, Spain</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Mercedes Gait&#x000E1;n-Angulo <email>mercedes.gaitana&#x00040;konradlorenz.edu.co</email></corresp>
<corresp id="c002">Rub&#x000E9;n Alexander Acevedo-Rueda <email>ruben.a.acevedo&#x00040;gmail.com</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>05</day>
<month>05</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>6</volume>
<elocation-id>1114796</elocation-id>
<history>
<date date-type="received">
<day>02</day>
<month>12</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>10</day>
<month>04</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2023 Acevedo-Rueda, Ram&#x000ED;rez-Pisco, V&#x000E1;squez Stanescu, Torres Cruz, G&#x000F3;mez-Caicedo and Gait&#x000E1;n-Angulo.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Acevedo-Rueda, Ram&#x000ED;rez-Pisco, V&#x000E1;squez Stanescu, Torres Cruz, G&#x000F3;mez-Caicedo and Gait&#x000E1;n-Angulo</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p></license> </permissions>
<abstract>
<p>The energy policies of the countries have become a key aspect of development. They must be formulated to guarantee economic and social development, state security and compliance with the objectives of sustainable development. In this framework, generation technologies must be considered not only in terms of available natural resources but also in terms of possible contingency scenarios. The purpose of this article is to prioritize technologies by applying a fuzzy inference model and uncertainty model and to address the principles of complex thinking to a case study. The methodology considers the integral vision of the dimensions under the systemic, feedback, autonomy/dependence, holographic and recursive principles, the assignment of weights for the dimension of sustainable development and, finally, the formulation of contingent scenarios. These scenarios consider: exhaustion of a primary source and change of technology with negative or positive impact. As a result, priority is given to the development of wind technology among renewable sources, followed by hydropower and geothermal. In the field of conventional energy, natural gas remains in the first place, since it also reinforces the security and fairness of the system. It is concluded that the process of formulating energy policies based on economic variables and the incorporation of sustainability, in terms of restrictions and linearity in the study models. This must be complemented with the adaptation of the legal and institutional framework that allows the fulfillment of the objectives that are expected to be achieved. Finally, it is necessary to keep constantly updated on changes and improvements in technology, which can modify the variables under study, in order to adapt strategies to new conditions.</p></abstract>
<kwd-group>
<kwd>energy</kwd>
<kwd>sustainability</kwd>
<kwd>uncertainty models</kwd>
<kwd>complexity</kwd>
<kwd>model</kwd>
</kwd-group>
<contract-sponsor id="cn001">Fundaci&#x000F3;n Universia<named-content content-type="fundref-id">10.13039/501100019161</named-content></contract-sponsor>
<counts>
<fig-count count="5"/>
<table-count count="9"/>
<equation-count count="19"/>
<ref-count count="30"/>
<page-count count="13"/>
<word-count count="5917"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Data Analytics for Social Impact</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1. Introduction</title>
<p>According to DeTombe and van Dijkum (<xref ref-type="bibr" rid="B6">2014</xref>), energy is of fundamental importance for humanity, considering that access to energy has become one of the main challenges to guarantee the development and security of the state, the eradication of poverty, social and economic transformation (Mulugetta et al., <xref ref-type="bibr" rid="B16">2019</xref>; Wahlund and Palm, <xref ref-type="bibr" rid="B27">2022</xref>). The formulation of policies in this area is aimed at supporting the sustainable development of countries and regions and is a process that merits a detailed analysis regarding in terms the applicable tools and models, as well as their particularities. According to OLADE (<xref ref-type="bibr" rid="B20">1997</xref>), these should be based mainly on temporary objectives rather than actions. These actions should be flexible as knowledge of your applications deepens and should be based on feedback.</p>
<p>The fight against poverty (Guzowski et al., <xref ref-type="bibr" rid="B9">2021</xref>), social transformations and economic development (Orde&#x000F1;ana et al., <xref ref-type="bibr" rid="B21">2022</xref>; Vardar et al., <xref ref-type="bibr" rid="B26">2022</xref>), the needs of modern society for a quality energy supply (Mercado-Bautista et al., <xref ref-type="bibr" rid="B15">2022</xref>; Wahlund and Palm, <xref ref-type="bibr" rid="B27">2022</xref>; Wierzbicka, <xref ref-type="bibr" rid="B30">2022</xref>) and guarantee the security of the state (Gaspar, <xref ref-type="bibr" rid="B8">2022</xref>; Steffen and Patt, <xref ref-type="bibr" rid="B23">2022</xref>) and, finally, move toward low-carbon generation sources (Lawrence et al., <xref ref-type="bibr" rid="B14">2022</xref>), among other reasons, to frame what today is considered as energy policies sustainable (Nilsson, <xref ref-type="bibr" rid="B18">2005</xref>).</p>
<p>According to the World Energy Council (WEC, <xref ref-type="bibr" rid="B29">2011</xref>) energy sustainability is defined in three (3) dimensions:</p>
<list list-type="bullet">
<list-item><p><bold>Energy security</bold>. For both importers and net exporters of energy, it includes effective management of primary energy supply from internal and external resources; the reliability of the energy infrastructure; and the ability of participating energy companies to meet current and future demands. In countries that are net exporters of energy, it also refers to the ability to maintain income from sales to foreign markets.</p></list-item>
<list-item><p><bold>Social equity</bold>. It refers to the accessibility and affordability of energy supply for the population.</p></list-item>
<list-item><p><bold>Reducing of environmental impact</bold>. It means efficiency in energy supply and demand, as well as in the development of energy supply from renewable resources and other low-carbon sources.</p></list-item>
</list>
<p>One of the problems presented by the concept of sustainable development is the measurement of compliance with its dimensions, an issue that has been the subject of studies and proposals, such as the one proposed by Bluszcz (<xref ref-type="bibr" rid="B3">2016</xref>). This author points out that its multidimensionality makes it difficult to accurately and exhaustively measure its social, economic and environmental components. This makes it necessary to use composite indicators (also called synthetic), which allow the aggregation of individual indicators with different units of measurement and even of a qualitative nature.</p>
<p>The indicators used by WEC (<xref ref-type="bibr" rid="B29">2011</xref>) are classified into the three (3) Human/Social, Ecological/Environmental and Economic dimensions and, within these, are grouped in turn by subcategory: Basic Needs, Personal Development and Health, Social Equity, Natural Resources, Climate and Energy and, finally, Transition and Economy.</p>
<p>Szopik-Depczy&#x00144;ska et al. (<xref ref-type="bibr" rid="B25">2018</xref>) point out that innovation initiatives within the framework of the indicators presented in the UN 2030 agenda have motivated companies to make investments in new technologies or modernization of existing assets, which could result in a decrease in energy expenditure and use of natural resources. In this sense, energy policy makers are forced to collaborate with their colleagues in other areas and governance structures are established to activate and maintain such coordination (Nerini et al., <xref ref-type="bibr" rid="B17">2018</xref>).</p>
<p>It is proposed that in order to understand the application of the principles of complex thinking, proposed by Edgar Morin, to the formulation of energy policies, it is necessary to approach the study from the principles: Subject/Object, Systemic, Feedback, Autonomy/Dependence, Recursivity, Holographic, Uncertainty, Fuzzy, Situational, and Chaordic Strategy (Acevedo Rueda et al., <xref ref-type="bibr" rid="B1">2020</xref>). The purpose of this article is to establish the prioritization of technologies by applying an uncertainty and fuzzy inference model that addresses the principles of complex thinking to a case study.</p>
</sec>
<sec id="s2">
<title>2. Sustainable energy policies</title>
<p>Energy systems are strongly identified and related to the different spheres of economic and environmental development. The ECLAC (<xref ref-type="bibr" rid="B7">2003</xref>) highlights the following considerations:</p>
<list list-type="bullet">
<list-item><p>Energy is an essential element for the quality of life of human beings; it is a widely used input in all productive activities.</p></list-item>
<list-item><p>The availability of energy has played a central role in the process of human development.</p></list-item>
<list-item><p>The great technological revolutions, which affected production and consumption activities, are intimately linked to the substitution between primary energy sources. Energy production and consumption have strong interactions with the natural environment. In addition to the possibility of depletion or degradation of energy resources, there are multiple negative impacts on the soil and, ultimately, on the water and the aerial environment, derived from production, transformation and use.</p></list-item>
</list>
<p>Sustainable energy is understood as the provision of an affordable, accessible and reliable service that meets economic and social needs, with attention to environmental aspects. It is a broad context that encompasses resource consumption, existing energy infrastructure, and development needs (Oxilia and Blanco, <xref ref-type="bibr" rid="B22">2016</xref>).</p>
<p>Energy sustainability indicators have been addressed by the World Energy Council (WEC), applying a methodology called Energy Trilemma, which considers 32 indicators in each of the dimensions. In addition, it is also presented as a tool to support the formulation of energy policies (Imio and Fonseca-Prieto, <xref ref-type="bibr" rid="B10">2022</xref>).</p>
<p>From a theoretical perspective, energy sustainability is the capacity of an organization or political community (State or Community of States) to cover the energy demand of its society, without affecting its environment to such an extent that it could break the continuity of this capacity in the future. The theoretical construction of this capacity complies with the principles of complex thought. On the other hand, from a methodological perspective, it is a measure that assigns a real value to the resulting set of variables considered for the problem in the Economic, Human/Social, Ecological/Environmental and Political/Institutional dimensions. Finally, from a theoretical-methodological perspective, it is the measure of capacity, which shows the expected value for a particular event, this event is a discrete condition, in a specific time horizon or instant, resulting from the combination of variables considered in the process under study, as an effect of the decisions (causes) assumed. The event of interest is the condition in which the system is sustainable, vs. the unsustainable condition.</p>
</sec>
<sec id="s3">
<title>3. Materials and methods</title>
<p>Fuzzy logic has found a place in different disciplines as a tool to handle the complexity of human language and sensory perception. It is common in decision-making processes or modeling and control of systems that present difficulties in their representation in classical logic (Klir and Yuan, <xref ref-type="bibr" rid="B13">1995</xref>) and as a tool for decision-making under conditions of uncertainty (Ayyub, <xref ref-type="bibr" rid="B2">2005</xref>). In addition, it has been applied in the control and optimization of variables associated with renewable energy systems, obtaining realistic estimates that justify the complexity of this approach, which moves away from the approximations and linearizations of traditional methods (Suganthi et al., <xref ref-type="bibr" rid="B24">2015</xref>).</p>
<p><xref ref-type="fig" rid="F1">Figure 1</xref> describes the proposed methodology for the application of the model considering the principles of uncertainty and fuzzy. For this, the principles of complex thinking are incorporated (Acevedo Rueda et al., <xref ref-type="bibr" rid="B1">2020</xref>) and the following considerations were considered:</p>
<list list-type="bullet">
<list-item><p><bold>Assignment of weighted weights for each dimension of sustainable development</bold>. Based on the indicators proposed by the Energy Trilemma (WEC, <xref ref-type="bibr" rid="B28">2019</xref>) and their weightings, the subject/object principle is addressed by assigning a contribution from each of the subjects in the decision-making process.</p></list-item>
<list-item><p><bold>Comprehensive vision of all dimensions</bold>. The model contemplates decision making based on the relational evaluation of indicators of all dimensions of sustainable development, considering the impact that each of the decision alternatives has on the global indicators over time, as well as the impact of the current environmental conditions on the evaluation of alternatives. In this way, the principles of systemic, feedback, autonomy/dependence, holography and recursion are addressed.</p></list-item>
<list-item><p><bold>Formulation of contingent scenarios</bold>. The principles of uncertainty, situational and chaordic strategy are incorporated with the formulation of probable, possible and desirable scenarios to make decisions and establish contingency plans, considering the possibility of generating Fuzzy Energy Events (FEE), typified as Creative Fuzzy Energy Events (C) or Destructive Fuzzy Energy Events (D).</p></list-item>
</list>
<fig id="F1" position="float">
<label>Figure 1</label>
<caption><p>Methodology used to apply the principles of complex thinking. Source: Self made.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fdata-06-1114796-g0001.tif"/>
</fig>
<p>For the formulation of the contingent scenarios, the methodology described below is used:</p>
<list list-type="simple">
<list-item><p>1. Evaluation of generation technologies:</p></list-item>
</list>
<list list-type="simple">
<list-item><p>a. Evaluation of impact indicators in the dimensions of sustainable development.</p></list-item>
<list-item><p>b. Identification of the linguistic scale for the weighting of the criteria.</p></list-item>
<list-item><p>c. Construction of the comparative matrix and fusion of the criteria.</p></list-item>
</list>
<list list-type="simple">
<list-item><p>2. Evaluation of environmental conditions:</p></list-item>
</list>
<list list-type="simple">
<list-item><p>a. Evaluation of the indicators present in the dimensions of sustainable development.</p></list-item>
<list-item><p>b. Identification of the linguistic scale for the weighting of the criteria.</p></list-item>
<list-item><p>c. Construction of the comparative matrix and fusion of the criteria.</p></list-item>
<list-item><p>d. Identification of risks in environmental conditions.</p></list-item>
</list>
<list list-type="simple">
<list-item><p>3. Formulation of fuzzy rules:</p></list-item>
</list>
<list list-type="simple">
<list-item><p>a. Analysis of the relationships between variables.</p></list-item>
<list-item><p>b. Identification of the linguistic scale for the weight of relationships.</p></list-item>
<list-item><p>c. Incorporation of probable EEDs.</p></list-item>
</list>
<list list-type="simple">
<list-item><p>4. Obtaining the results:</p></list-item>
</list>
<list list-type="simple">
<list-item><p>a. Selection of the defuzzification method.</p></list-item>
<list-item><p>b. Application of fuzzy rules for each probable EED (contingent scenario).</p></list-item>
<list-item><p>c. Defuzzification of results.</p></list-item>
</list>
<list list-type="simple">
<list-item><p>5. Presentation of alternatives:</p></list-item>
</list>
<list list-type="simple">
<list-item><p>a. Analysis of each contingent scenario with identification of EEDsC and EEDsD.</p></list-item>
<list-item><p>b. Formulation of recommendations for the follow-up and monitoring of results.</p></list-item>
</list>
</sec>
<sec id="s4">
<title>4. Description of the analysis variables</title>
<p>Decision making in the formulation of energy policies from the perspective of complexity requires evaluating the impact of the alternatives on the selected indicators. Carlberg (<xref ref-type="bibr" rid="B4">2013</xref>) presents the rating system of the Electric Power Research Institute (EPRI) which develops a reference table for the evaluation of generation technologies, including renewables, natural gas, coal and nuclear, in terms of their relative impact on specific areas, as presented in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>Figure 2</label>
<caption><p>EPRI reference table of generation technologies (Carlberg, <xref ref-type="bibr" rid="B4">2013</xref>).</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fdata-06-1114796-g0002.tif"/>
</fig>
<p>In this aspect, the available electricity generation technologies are considered, with the characteristics developed in the literature (IRENA, <xref ref-type="bibr" rid="B11">2018</xref>, <xref ref-type="bibr" rid="B12">2020</xref>; CNE, <xref ref-type="bibr" rid="B5">2020</xref>; NREL, <xref ref-type="bibr" rid="B19">2020</xref>). The values are weighted according to the maximums in each variable and, based on what is presented in <xref ref-type="fig" rid="F2">Figure 2</xref>, the values not available in the references are estimated, under the following considerations:</p>
<list list-type="bullet">
<list-item><p>The generation technologies evaluated are Coal, Diesel, Natural Gas, Hydraulic, Wind, Biomass, Geothermal and Solar Photovoltaic.</p></list-item>
<list-item><p>The Emissions variable is defined, encompassing CO<sub>2</sub> and non-CO<sub>2</sub>.</p></list-item>
<list-item><p>The variables take values proportional to their maximum, between 0.01 and 1.00. Where 1.00 represents the maximum value in the set of technologies evaluated and the others correspond to the proportion with respect to this.</p></list-item>
</list>
<p><xref ref-type="table" rid="T1">Table 1</xref> presents the weighted variables for the classification of power generation technologies in the proposed fuzzy model.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Variables for the fuzzy model for classifying power generation technologies.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th/>
<th/>
<th valign="top" align="left" colspan="8"><bold>Technology</bold></th>
</tr>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Variable</bold></th>
<th valign="top" align="left"><bold>Description</bold></th>
<th valign="top" align="left"><bold>Coal</bold></th>
<th valign="top" align="left"><bold>Diesel</bold></th>
<th valign="top" align="left"><bold>Natural</bold></th>
<th valign="top" align="left"><bold>Hydro</bold></th>
<th valign="top" align="left"><bold>Wind</bold></th>
<th valign="top" align="left"><bold>Biomass</bold></th>
<th valign="top" align="left"><bold>Geothermal</bold></th>
<th valign="top" align="left"><bold>Solar photovoltaic</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">I1</td>
<td valign="top" align="left">Construction cost</td>
<td valign="top" align="left">0.48</td>
<td valign="top" align="left">0.35</td>
<td valign="top" align="left">0.28</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">0.22</td>
<td valign="top" align="left">0.56</td>
<td valign="top" align="left">0.71</td>
<td valign="top" align="left">0.68</td>
</tr> <tr>
<td valign="top" align="left">I2</td>
<td valign="top" align="left">Cost of electricity</td>
<td valign="top" align="left">0.37</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">0.55</td>
<td valign="top" align="left">0.35</td>
<td valign="top" align="left">0.20</td>
<td valign="top" align="left">0.82</td>
<td valign="top" align="left">0.46</td>
<td valign="top" align="left">0.25</td>
</tr> <tr>
<td valign="top" align="left">I3</td>
<td valign="top" align="left">Land use</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.10</td>
<td valign="top" align="left">0.10</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">0.40</td>
<td valign="top" align="left">0.85</td>
</tr> <tr>
<td valign="top" align="left">I4</td>
<td valign="top" align="left">Water requirements</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.10</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">0.65</td>
<td valign="top" align="left">0.10</td>
</tr> <tr>
<td valign="top" align="left">I5</td>
<td valign="top" align="left">Pollution</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">1.00</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.10</td>
<td valign="top" align="left">0.10</td>
<td valign="top" align="left">0.30</td>
<td valign="top" align="left">0.30</td>
<td valign="top" align="left">0.10</td>
</tr> <tr>
<td valign="top" align="left">I6</td>
<td valign="top" align="left">Availability</td>
<td valign="top" align="left">0.80</td>
<td valign="top" align="left">0.80</td>
<td valign="top" align="left">0.90</td>
<td valign="top" align="left">0.65</td>
<td valign="top" align="left">0.30</td>
<td valign="top" align="left">0.75</td>
<td valign="top" align="left">0.75</td>
<td valign="top" align="left">0.25</td>
</tr> <tr>
<td valign="top" align="left">I7</td>
<td valign="top" align="left">Flexibility</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.70</td>
<td valign="top" align="left">0.90</td>
<td valign="top" align="left">0.90</td>
<td valign="top" align="left">0.15</td>
<td valign="top" align="left">0.50</td>
<td valign="top" align="left">0.20</td>
<td valign="top" align="left">0.15</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>Source: Own elaboration with information from Carlberg (<xref ref-type="bibr" rid="B4">2013</xref>), IRENA (<xref ref-type="bibr" rid="B11">2018</xref>), CNE (<xref ref-type="bibr" rid="B5">2020</xref>), IRENA (<xref ref-type="bibr" rid="B12">2020</xref>), and NREL (<xref ref-type="bibr" rid="B19">2020</xref>).</p>
</table-wrap-foot>
</table-wrap>
<p>For decision making, the impact of the alternatives on the selected indicators will be evaluated and the development of installations of these technologies will be prioritized.</p>
<sec>
<title>4.1. Evaluation of environmental conditions</title>
<p>For the evaluation variables of the environmental conditions, the rating of the energy trilemma index is taken, in each of its dimensions. This has a percentage weighting that can also be projected to values between zero (0) and one (1), with zero (0) corresponding to 0% and one (1) to 100%. The variable installed capacity by technology is included in these dimensions, to incorporate the diversity of the energy resource in the analysis, with values between zero (0) and one (1). Where zero (0) indicates that there is no installed capacity of a certain technology and one (1) represents the use of a single technology to cover the total energy requirement. The variables considered for the evaluation of environmental conditions in the fuzzy model are presented in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Environmental conditions assessment variables for the fuzzy model.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Variable</bold></th>
<th valign="top" align="left"><bold>Description</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">C1</td>
<td valign="top" align="left">Energy security</td>
</tr> <tr>
<td valign="top" align="left">C2</td>
<td valign="top" align="left">Energy equity</td>
</tr> <tr>
<td valign="top" align="left">C3</td>
<td valign="top" align="left">Environmental sustainability of energy systems</td>
</tr> <tr>
<td valign="top" align="left">C4</td>
<td valign="top" align="left">Installed capacity by technology</td>
</tr></tbody>
</table>
</table-wrap>
</sec>
<sec>
<title>4.2. Variable fusion</title>
<p>Both the variables that represent the impact of each alternative and the environment variables were characterized in the set [0,1] and the membership functions are modeled considering the sets Low (B), Medium (M), and High (A), so:</p>
<p>Membership function to the set Under &#x003BC;<sub><italic>B</italic></sub>(<italic>x</italic>) of type L, function Equation (1).</p>
<disp-formula id="E1"><label>(1)</label><mml:math id="M1"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>Set membership function of the set Medium &#x003BC;<sub><italic>M</italic></sub>(<italic>x</italic>) of type Triangular Equation (2).</p>
<disp-formula id="E2"><label>(2)</label><mml:math id="M2"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mi>c</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>High set membership function &#x003BC;<sub><italic>A</italic></sub>(<italic>x</italic>) of type Gamma Linear Equation (3).</p>
<disp-formula id="E3"><label>(3)</label><mml:math id="M3"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>For the variable C1, corresponding to the security condition of the energy trilemma index, given that the results presented for the group of qualified countries are between 30 and 79%, the following is assigned (<italic>a</italic>; <italic>b</italic>; <italic>c</italic>) = (0.50; 0.60; 0.65). Thus, the membership functions are defined as Equations (4)&#x02013;(6).</p>
<disp-formula id="E4"><label>(4)</label><mml:math id="M4"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>60</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E5"><label>(5)</label><mml:math id="M5"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>50</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>65</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>05</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E6"><label>(6)</label><mml:math id="M6"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>60</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>05</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>For the other variables, we assign (<italic>a</italic>; <italic>b</italic>; <italic>c</italic>) = (0.25; 0.5; 1) to the other variables, distributing the range of values evenly. Thus, the membership functions are defined as Equations (7)&#x02013;(9).</p>
<disp-formula id="E7"><label>(7)</label><mml:math id="M7"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>25</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>25</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E8"><label>(8)</label><mml:math id="M8"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>25</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>25</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>75</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>25</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E9"><label>(9)</label><mml:math id="M9"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>5</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>25</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>To reduce the effect of conscious ignorance due to imprecision (Ayyub, <xref ref-type="bibr" rid="B2">2005</xref>) further fine- tuning the output with the sets Very Low (MB), Low (B), Medium (M), High (A), Very High (MA), as follows:</p>
<list list-type="bullet">
<list-item><p>Very Low set membership function &#x003BC;<sub>B</sub>(<italic>x</italic>) of type L Equation (10).</p></list-item>
</list>
<disp-formula id="E10"><label>(10)</label><mml:math id="M10"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<list list-type="bullet">
<list-item><p>Set membership function Low &#x003BC;<sub>A</sub>(<italic>x</italic>) of type Triangular Equation (11)</p></list-item>
</list>
<disp-formula id="E11"><label>(11)</label><mml:math id="M11"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mo>-</mml:mo><mml:mi>a</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mi>c</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<list list-type="bullet">
<list-item><p>Membership function of the set Medium &#x003BC;<sub><italic>M</italic></sub>(<italic>x</italic>) of type Triangular Equation (12).</p></list-item>
</list>
<disp-formula id="E12"><label>(12)</label><mml:math id="M12"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mo>-</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<list list-type="bullet">
<list-item><p>Very High set membership function &#x003BC;<sub><italic>A</italic></sub>(<italic>x</italic>) of Triangular type Equation (13).</p></list-item>
</list>
<disp-formula id="E13"><label>(13)</label><mml:math id="M13"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mo>-</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mi>e</mml:mi><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:mo>-</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>High set membership function &#x003BC;<sub><italic>A</italic></sub>(<italic>x</italic>) of type Gamma Linear Equation (14).</p>
<disp-formula id="E14"><label>(14)</label><mml:math id="M14"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:mo>-</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>It is assigned (<italic>a</italic>; <italic>b</italic>; <italic>c</italic>; <italic>d</italic>; <italic>e</italic>) = (0.19; 0.38; 0.57; 0.76; 0.95) to evenly distribute the range of values. Thus, the membership functions are defined as Equations (15)&#x02013;(19).</p>
<disp-formula id="E15"><label>(15)</label><mml:math id="M15"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>38</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E16"><label>(16)</label><mml:math id="M16"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>57</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E17"><label>(17)</label><mml:math id="M17"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>38</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>76</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E18"><label>(18)</label><mml:math id="M18"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>M</mml:mi><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>57</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mfrac><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>95</mml:mn><mml:mo>-</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E19"><label>(19)</label><mml:math id="M19"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mo class="qopname">max</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>76</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>19</mml:mn></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p><xref ref-type="fig" rid="F3">Figure 3</xref> shows the graphs of membership functions for a set of variables.</p>
<fig id="F3" position="float">
<label>Figure 3</label>
<caption><p>Belonging functions.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fdata-06-1114796-g0003.tif"/>
</fig>
</sec>
<sec>
<title>4.3. Formulation of fuzzy rules</title>
<p>To formulate the fuzzy rules, it is necessary to identify and classify the variables according to their impact on the energy sustainability index. In this way, the benefit offered by each alternative on the corresponding dimensions can be obtained as a result, to finally obtain a categorization of the technologies evaluated under the existing environmental conditions. This benefit is also set in a range from zero (0) to one (1) and is modeled considering the sets Low (B), Medium (M), High (A), with the same parameters and membership functions used for the model variables. <xref ref-type="fig" rid="F4">Figure 4</xref> presents the classification of the variables according to their impact on the energy trilemma index.</p>
<fig id="F4" position="float">
<label>Figure 4</label>
<caption><p>Ranking of variables by impact on the energy sustainability index.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fdata-06-1114796-g0004.tif"/>
</fig>
<p>By incorporating the rating of the energy trilemma index as environmental conditions, fuzzy rules allow higher priority to be given to technologies that offer greater benefits to the dimensions that require it most. As a rule of thumb, they are formulated as follows:</p>
<p><bold>IF</bold> [Environment Variable is (A, M, B)] <bold>AND</bold> [Variable is (A, M, B)] <bold>THEN</bold> Benefit is (MA, M, B, MB).</p>
<p>Where the notation (U is V) denotes the intersection of the conditions for the variables considered, i.e., [Variable is (A, M, B)] = I1 is A <bold>AND</bold> I2 is M <bold>AND</bold> I3 is B.</p>
<p>With this classification of the variables, a total of 243 rules are obtained, distributed in three groups of 81 rules each. <xref ref-type="fig" rid="F5">Figure 5</xref> shows a graphical representation of the fuzzy surfaces for three (3) variables in each domain.</p>
<fig id="F5" position="float">
<label>Figure 5</label>
<caption><p>Fuzzy rule surfaces.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fdata-06-1114796-g0005.tif"/>
</fig>
<p>The results obtained after defuzzification in each group will be added to obtain the final benefit of each evaluated technology. This provides valuable information for decision-making in the formulation of energy policies.</p>
</sec>
<sec>
<title>4.4. Probable diffuse energy events</title>
<p>To identify likely diffuse Energy Events, one must maintain an expert understanding of what variable relationship factors or perturbations can change, which can alter the dynamics of the system. For this work, events with the following characteristics will be considered in particular:</p>
<list list-type="bullet">
<list-item><p>Depletion of a primary energy source. This can be caused by technical, legal, political or environmental restrictions that prevent the exploitation of a certain resource. In the case of fuel-importing countries, it could be due to a breakdown in relations with suppliers; in other cases, it could be due to the inability to meet water or land use requirements.</p></list-item>
<list-item><p>Negative change in the impact of a technology. This can be caused by technical, legal, political or environmental conditions that increase the costs of exploiting a certain resource, such as taxes or goods.</p></list-item>
<list-item><p>Technological improvements that change the relationship in one or more variables, with positive impact.</p></list-item>
</list>
<p>In this phase, the alternatives for the base case and the cases of the contingent scenario are evaluated, corresponding to the occurrence of the probable EEDs identified.</p>
</sec>
</sec>
<sec id="s5">
<title>5. Results</title>
<p>In this phase, the alternatives for the base case and the cases of the contingent scenario are evaluated, corresponding to the occurrence of the probable EEDs identified, and the centroid method is used to defuzzify the result. The result presents a score for each technology in the dimensions of safety, equity and environmental sustainability, which are then consolidated as a summation into a single indicator.</p>
<p>As a test example, we work with a hypothetical case that presents a result of 68, 61, and 48% in safety, equity and environmental sustainability, respectively, and an installed capacity per technology, as shown in <xref ref-type="table" rid="T3">Table 3</xref>. In addition, primary sources are assumed to be available for all technologies under evaluation.</p>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>Categorization of installed capacity by technology.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Coal</bold></th>
<th valign="top" align="center"><bold>Diesel</bold></th>
<th valign="top" align="center"><bold>Natural gas</bold></th>
<th valign="top" align="center"><bold>Hydro</bold></th>
<th valign="top" align="center"><bold>Wind</bold></th>
<th valign="top" align="center"><bold>Biomass</bold></th>
<th valign="top" align="center"><bold>Geothermal</bold></th>
<th valign="top" align="center"><bold>Solar photovoltaic</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">0.70</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.95</td>
<td valign="top" align="center">0.25</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.15</td>
</tr></tbody>
</table>
</table-wrap>
<sec>
<title>5.1. Base case</title>
<p>Applying the fuzzy model to these values yields the results presented in <xref ref-type="table" rid="T4">Table 4</xref>.</p>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Priorities base case.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Technology</bold></th>
<th valign="top" align="center"><bold>Security</bold></th>
<th valign="top" align="center"><bold>Equity</bold></th>
<th valign="top" align="center"><bold>Sust. medioamb</bold>.</th>
<th valign="top" align="center"><bold>Total</bold></th>
<th valign="top" align="center"><bold>Priority</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Coal</td>
<td valign="top" align="center">0.414</td>
<td valign="top" align="center">0.668</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">1.222</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Diesel</td>
<td valign="top" align="center">0.594</td>
<td valign="top" align="center">0.369</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">1.102</td>
<td valign="top" align="center">8</td>
</tr> <tr>
<td valign="top" align="left">Natural gas</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.647</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.977</td>
<td valign="top" align="center">1</td>
</tr> <tr>
<td valign="top" align="left">Hydro</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.719</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Wind</td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.808</td>
<td valign="top" align="center">1.759</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Biomass</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.150</td>
<td valign="top" align="center">0.325</td>
<td valign="top" align="center">1.234</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Geothermal</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.491</td>
<td valign="top" align="center">0.636</td>
<td valign="top" align="center">1.697</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Solar photovoltaic</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">0.428</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.328</td>
<td valign="top" align="center">5</td>
</tr></tbody>
</table>
</table-wrap>
</sec>
<sec>
<title>5.2. Contingent scenario 1. Primary source depletion</title>
<p>When considering the EED of depletion of primary sources, the technologies that require it are eliminated. The prioritization among the remaining alternatives is maintained. As a hypothetical case, the joint case of decarbonization of the energy matrix due to political provisions and the depletion of hydroelectric resources due to the lack of suitable spaces for the construction of new dams is considered. Under these assumptions, the prioritization would be as shown in <xref ref-type="table" rid="T5">Table 5</xref>.</p>
<table-wrap position="float" id="T5">
<label>Table 5</label>
<caption><p>Priorities contingent scenario 1.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Technology</bold></th>
<th valign="top" align="center"><bold>Security</bold></th>
<th valign="top" align="center"><bold>Equity</bold></th>
<th valign="top" align="center"><bold>Sust. medioamb</bold>.</th>
<th valign="top" align="center"><bold>Total</bold></th>
<th valign="top" align="center"><bold>Priority</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Coal</td>
<td valign="top" align="center">0.414</td>
<td valign="top" align="center">0.668</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">1.222</td>
<td valign="top" align="center">-</td>
</tr> <tr>
<td valign="top" align="left">Diesel</td>
<td valign="top" align="center">0.594</td>
<td valign="top" align="center">0.369</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">1.102</td>
<td valign="top" align="center">-</td>
</tr> <tr>
<td valign="top" align="left">Natural gas</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.647</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.977</td>
<td valign="top" align="center">1</td>
</tr> <tr>
<td valign="top" align="left">Hydro</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.719</td>
<td valign="top" align="center">-</td>
</tr> <tr>
<td valign="top" align="left">Wind</td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.808</td>
<td valign="top" align="center">1.759</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Biomass</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.150</td>
<td valign="top" align="center">0.325</td>
<td valign="top" align="center">1.234</td>
<td valign="top" align="center">5</td>
</tr> <tr>
<td valign="top" align="left">Geothermal</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.491</td>
<td valign="top" align="center">0.636</td>
<td valign="top" align="center">1.697</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Solar photovoltaic</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">0.428</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.328</td>
<td/>
</tr></tbody>
</table>
</table-wrap>
</sec>
<sec>
<title>5.3. Contingent scenario 2. Negative change in the impact of an alternative</title>
<p>When considering the EED of negative change in the impact of an alternative, the values in the matrix of variables by technology are modified and the fuzzy model is applied again to obtain the prioritization for this contingent scenario. As a hypothetical case, the application of taxes on emissions and construction permits, and policies restricting the dispatch of non-renewable technologies, which modify the values as shown in <xref ref-type="table" rid="T6">Table 6</xref>, are considered. Under these assumptions, the prioritization would be as presented in <xref ref-type="table" rid="T7">Table 7</xref>.</p>
<table-wrap position="float" id="T6">
<label>Table 6</label>
<caption><p>Variables for the fuzzy model contingent scenario 2.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th/>
<th/>
<th valign="top" align="center" colspan="8"><bold>Technology</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<td valign="top" align="left"><bold>Variable</bold></td>
<td valign="top" align="center"><bold>Description</bold></td>
<td valign="top" align="center"><bold>Coal</bold></td>
<td valign="top" align="center"><bold>Diesel</bold></td>
<td valign="top" align="center"><bold>Natural gas</bold></td>
<td valign="top" align="center"><bold>Hydro</bold></td>
<td valign="top" align="center"><bold>Wind</bold></td>
<td valign="top" align="center"><bold>Biomass</bold></td>
<td valign="top" align="center"><bold>Geothermal</bold></td>
<td valign="top" align="center"><bold>Solar photovoltaic</bold></td>
</tr> <tr>
<td valign="top" align="left">I1</td>
<td valign="top" align="center">Construction cost</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.95</td>
<td valign="top" align="center">0.48</td>
<td valign="top" align="center">0.80</td>
<td valign="top" align="center">0.12</td>
<td valign="top" align="center">0.45</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">0.52</td>
</tr> <tr>
<td valign="top" align="left">I2</td>
<td valign="top" align="center">Cost of electricity</td>
<td valign="top" align="center">0.45</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">0.35</td>
<td valign="top" align="center">0.20</td>
<td valign="top" align="center">0.85</td>
<td valign="top" align="center">0.46</td>
<td valign="top" align="center">0.25</td>
</tr> <tr>
<td valign="top" align="left">I3</td>
<td valign="top" align="center">Land use</td>
<td valign="top" align="center">0.64</td>
<td valign="top" align="center">0.25</td>
<td valign="top" align="center">0.23</td>
<td valign="top" align="center">0.62</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.40</td>
<td valign="top" align="center">0.85</td>
</tr> <tr>
<td valign="top" align="left">I4</td>
<td valign="top" align="center">Water requirements</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.64</td>
<td valign="top" align="center">0.54</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">0.10</td>
</tr> <tr>
<td valign="top" align="left">I5</td>
<td valign="top" align="center">Pollution</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.58</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.45</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.10</td>
</tr> <tr>
<td valign="top" align="left">I6</td>
<td valign="top" align="center">Availability</td>
<td valign="top" align="center">0.70</td>
<td valign="top" align="center">0.75</td>
<td valign="top" align="center">0.80</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.75</td>
<td valign="top" align="center">0.75</td>
<td valign="top" align="center">0.25</td>
</tr> <tr>
<td valign="top" align="left">I7</td>
<td valign="top" align="center">Flexibility</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.70</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">0.15</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.20</td>
<td valign="top" align="center">0.15</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>Source: Own elaboration with information from Carlberg (<xref ref-type="bibr" rid="B4">2013</xref>); IRENA (<xref ref-type="bibr" rid="B11">2018</xref>, <xref ref-type="bibr" rid="B12">2020</xref>); CNE (<xref ref-type="bibr" rid="B5">2020</xref>), and NREL (<xref ref-type="bibr" rid="B19">2020</xref>).</p>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="T7">
<label>Table 7</label>
<caption><p>Priorities contingent scenario 2.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Technology</bold></th>
<th valign="top" align="center"><bold>Security</bold></th>
<th valign="top" align="center"><bold>Equity</bold></th>
<th valign="top" align="center"><bold>Sust. medioamb</bold>.</th>
<th valign="top" align="center"><bold>Total</bold></th>
<th valign="top" align="center"><bold>Priority</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Coal</td>
<td valign="top" align="center">0.370</td>
<td valign="top" align="center">0.420</td>
<td valign="top" align="center">0.159</td>
<td valign="top" align="center">0.949</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Diesel</td>
<td valign="top" align="center">0.594</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">0.873</td>
<td valign="top" align="center">8</td>
</tr> <tr>
<td valign="top" align="left">Natural gas</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.531</td>
<td valign="top" align="center">0.462</td>
<td valign="top" align="center">1.563</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Hydro</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.467</td>
<td valign="top" align="center">0.619</td>
<td valign="top" align="center">1.565</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Wind</td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.808</td>
<td valign="top" align="center">1.759</td>
<td valign="top" align="center">1</td>
</tr> <tr>
<td valign="top" align="left">Biomass</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.148</td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">1.098</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Geothermal</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.534</td>
<td valign="top" align="center">0.636</td>
<td valign="top" align="center">1.741</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Solar photovoltaic</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">0.545</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.445</td>
<td valign="top" align="center">5</td>
</tr></tbody>
</table>
</table-wrap>
</sec>
<sec>
<title>5.4. Contingent scenario 3. Technological improvements</title>
<p>When considering the EED of technological improvements, the values of the matrix of variables by technology are modified in favor of an alternative and the fuzzy model is applied again to obtain the prioritization for this contingent scenario. As a hypothetical case, the case of photovoltaic solar technology is considered, with the incorporation of storage equipment that improves availability, improvements in inverters and panels, which increase flexibility, reduce construction costs and land use, which modifies the values as shown in <xref ref-type="table" rid="T8">Table 8</xref>. Under these assumptions, the prioritization would be as shown in <xref ref-type="table" rid="T9">Table 9</xref>.</p>
<table-wrap position="float" id="T8">
<label>Table 8</label>
<caption><p>Variables for the fuzzy model contingent scenario 3.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th/>
<th/>
<th valign="top" align="center" colspan="8"><bold>Technology</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<td valign="top" align="left"><bold>Variable</bold></td>
<td valign="top" align="center"><bold>Description</bold></td>
<td valign="top" align="center"><bold>Coal</bold></td>
<td valign="top" align="center"><bold>Diesel</bold></td>
<td valign="top" align="center"><bold>Natural gas</bold></td>
<td valign="top" align="center"><bold>Hydro</bold></td>
<td valign="top" align="center"><bold>Wind</bold></td>
<td valign="top" align="center"><bold>Biomass</bold></td>
<td valign="top" align="center"><bold>Geothermal</bold></td>
<td valign="top" align="center"><bold>Solar photovoltaic</bold></td>
</tr> <tr>
<td valign="top" align="left">I1</td>
<td valign="top" align="center">Construction cost</td>
<td valign="top" align="center">0.48</td>
<td valign="top" align="center">0.35</td>
<td valign="top" align="center">0.28</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.22</td>
<td valign="top" align="center">0.56</td>
<td valign="top" align="center">0.71</td>
<td valign="top" align="center">0.35</td>
</tr> <tr>
<td valign="top" align="left">I2</td>
<td valign="top" align="center">Cost of electricity</td>
<td valign="top" align="center">0.37</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.55</td>
<td valign="top" align="center">0.35</td>
<td valign="top" align="center">0.20</td>
<td valign="top" align="center">0.82</td>
<td valign="top" align="center">0.46</td>
<td valign="top" align="center">0.25</td>
</tr> <tr>
<td valign="top" align="left">I3</td>
<td valign="top" align="center">Land use</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.40</td>
<td valign="top" align="center">0.60</td>
</tr> <tr>
<td valign="top" align="left">I4</td>
<td valign="top" align="center">Water requirements</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">0.10</td>
</tr> <tr>
<td valign="top" align="left">I5</td>
<td valign="top" align="center">Pollution</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.10</td>
</tr> <tr>
<td valign="top" align="left">I6</td>
<td valign="top" align="center">Availability</td>
<td valign="top" align="center">0.80</td>
<td valign="top" align="center">0.80</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">0.65</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.75</td>
<td valign="top" align="center">0.75</td>
<td valign="top" align="center">0.45</td>
</tr> <tr>
<td valign="top" align="left">I7</td>
<td valign="top" align="center">Flexibility</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.70</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">0.15</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.20</td>
<td valign="top" align="center">0.25</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>Source: Own elaboration with information from Carlberg (<xref ref-type="bibr" rid="B4">2013</xref>), IRENA (<xref ref-type="bibr" rid="B11">2018</xref>), CNE (<xref ref-type="bibr" rid="B5">2020</xref>), IRENA (<xref ref-type="bibr" rid="B12">2020</xref>), and NREL (<xref ref-type="bibr" rid="B19">2020</xref>).</p>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="T9">
<label>Table 9</label>
<caption><p>Priorities contingency scenario 3.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Technology</bold></th>
<th valign="top" align="center"><bold>Security</bold></th>
<th valign="top" align="center"><bold>Equity</bold></th>
<th valign="top" align="center"><bold>Sust. medioamb</bold>.</th>
<th valign="top" align="center"><bold>Total</bold></th>
<th valign="top" align="center"><bold>Priority</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Coal</td>
<td valign="top" align="center">0.414</td>
<td valign="top" align="center">0.668</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">1.222</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Diesel</td>
<td valign="top" align="center">0.594</td>
<td valign="top" align="center">0.369</td>
<td valign="top" align="center">0.140</td>
<td valign="top" align="center">1.102</td>
<td valign="top" align="center">8</td>
</tr> <tr>
<td valign="top" align="left">Natural gas</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.647</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.977</td>
<td valign="top" align="center">1</td>
</tr> <tr>
<td valign="top" align="left">Hydro</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.479</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">1.719</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Wind</td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.808</td>
<td valign="top" align="center">1.759</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Biomass</td>
<td valign="top" align="center">0.760</td>
<td valign="top" align="center">0.150</td>
<td valign="top" align="center">0.325</td>
<td valign="top" align="center">1.234</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Geothermal</td>
<td valign="top" align="center">0.570</td>
<td valign="top" align="center">0.491</td>
<td valign="top" align="center">0.636</td>
<td valign="top" align="center">1.697</td>
<td valign="top" align="center">5</td>
</tr> <tr>
<td valign="top" align="left">Solar photovoltaic</td>
<td valign="top" align="center">0.325</td>
<td valign="top" align="center">0.680</td>
<td valign="top" align="center">0.788</td>
<td valign="top" align="center">1.793</td>
<td/>
</tr></tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s6">
<title>6. Analysis of results</title>
<p>The results obtained show the priority given to the development of projects with wind technology in renewable energies, which remains in first place among these technologies in all scenarios, in addition to hydraulic and geothermal. Solar photovoltaic does not reach the first places, which is explained by the low availability and flexibility, in addition to the extensive use of land assigned in the evaluation, but in the scenario of improving of its technology, it reaches the first place in the renewable priorities. In the conventional energy category, natural gas remains in first place, while coal and diesel follow in second and third place, respectively.</p>
<p>Considering the availability of all primary resources for exploitation, in these scenarios the development of natural gas projects is recommended to strengthen security and equity. For the security indicator, biomass offers the best result, which is explained by its low presence in the energy matrix and the good level of availability and flexibility it offers. Wind and solar photovoltaic technology offer improvements in equity and environmental sustainability indicators, so their use is also considered favorable. It is necessary to keep constantly updated on changes and improvements in technology, which can modify the variables under study, in order to adapt strategies to new conditions.</p>
<p>The contingent scenarios, as analyzed, constitute CGEsC that allow for the diversification of the energy matrix, with the incorporation of priorities to non-conventional technologies. If contingent scenario 1 occurs as a total depletion, due to disasters or conflicts that completely interrupt the supply of the primary resource or cause the destruction of the existing infrastructure, it would be a CGED that would collapse the energy system, reinforcing the recommendation to develop technological projects that increase safety through the diversification of electricity generation.</p>
<p>This must be complemented with the revision of economic policies that favor investment in the technologies of interest, as well as the adaptation of the legal and institutional framework that allows the fulfillment of the objectives that are expected to be achieved. In this sense, the evaluation of the dimensions in the fuzzy model can include weights or incentives that adjust priorities.</p>
</sec>
<sec id="s7">
<title>7. Conclusions</title>
<p>This paper presents a model based on fuzzy logic to prioritize the development of electricity generation technologies, with a formulation of contingent scenarios, to address the principles of complex thinking, especially the principles of uncertainty and situational strategy, for a case study with availability of primary resources for the technologies considered: coal, diesel, natural gas, hydraulic, wind, biomass, geothermal and solar photovoltaic as the primary source of generation.</p>
<p>The problem was approached with a comprehensive vision of the dimensions under the systemic, feedback, autonomy/dependence, holographic and recursive principles; weights were assigned for the dimension of sustainable development, including 11 analysis variables based on the trilemma of electrical safety, energy, equity and environmental sustainability. Finally, contingent scenarios were formulated. These scenarios considered: exhaustion of a primary source and change technology with negative or positive impact.</p>
<p>As a result, wind power technology was found to be the most important renewable energy source in the case study, followed by hydropower and geothermal power. In the field of conventional energy, natural gas remains in the first place, since it also reinforces the security and fairness of the system.</p>
<p>It is concluded that the process of formulating energy policies based on economic variables and the incorporation of sustainability, in terms of restrictions and linearity in the study models. This must be complemented with the adaptation of the legal and institutional framework that allows the fulfillment of the objectives that are expected to be achieved. Finally, it is necessary to constantly update the model, based on changes and improvements in technology, which can modify the variables under study, strategies to the new conditions of the environment.</p>
</sec>
<sec sec-type="data-availability" id="s8">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="supplementary-material" rid="SM1">Supplementary material</xref>, further inquiries can be directed to the corresponding authors.</p>
</sec>
<sec sec-type="author-contributions" id="s9">
<title>Author contributions</title>
<p>All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.</p>
</sec>
</body>
<back>
<sec sec-type="funding-information" id="s10">
<title>Funding</title>
<p>This study was funded by Fundaci&#x000F3;n Universitat Carlemany.</p>
</sec>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x00027;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="s12">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fdata.2023.1114796/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fdata.2023.1114796/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="Data_Sheet_1.pdf" id="SM1" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
<supplementary-material xlink:href="Data_Sheet_2.pdf" id="SM2" mimetype="application/pdf" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
<fn-group>
<title>Abbreviations</title>
<fn fn-type="abbr"><p>ECLAC, Economic Commission for Latin America and the Caribbean; EED, Diffuse Energy Events; EEDC, Creative Fuzzy Energy Events; EEDD, Diffuse Destructive Energetic Events; EPRI, Power Electricity Research Institute; GHG, Green House Gases; OLADE, Latin American Energy Organization; UN, United Nations; WEC, World Energy Council.</p></fn></fn-group>
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