ORIGINAL RESEARCH article

Front. Artif. Intell., 18 June 2025

Sec. AI in Business

Volume 8 - 2025 | https://doi.org/10.3389/frai.2025.1599334

This article is part of the Research TopicSoft Computing and Artificial Intelligence Techniques in Decision Making, Management and EngineeringView all 3 articles

The evaluation of performance for agroecological greenhouse tomato strategies by the CRITIC-OWA model

  • 1Economic and Financial Department, Miguel Hernández University, Elche, Spain
  • 2Institute for Agri-Food and Agro-Environmental Research and Innovation, CIAGRO, Miguel Hernández University, Orihuela, Spain

Introduction: Modern agriculture must begin to use production strategies that are increasingly sustainable. To help in decision-making, the present work analyzes the sustainability of greenhouse tomato production with different agroecological strategies: shading (conventional fixed mesh and mobile photovoltaic shading), grafting and deficit irrigation, based on economic, social, and environmental criteria.

Methods: For the ranking of the different strategies, the use of an extension of the CRiteria Importance Through Inter-criteria Correlation (CRITIC) is proposed, in which the correlation between the criteria is obtained through the Pearson-OWA, where the aggregation of the quadratic differences between criteria is carried out considering the attitudinal character of the decision-maker, that is, using Ordered Weighted Averaging (OWA), in addition to induced variables, with the Induced Probabilistic OWA CRITIC (IPOWA CRITIC). Three extensions are considered based on this model depending on the way the multicriteria score is calculated: i) the ranking is carried out on the relative score (S) of each alternative (IPOWA-S-CRITIC), ii) on the weighting vector (W) (IPOWA-W-CRITIC), or iii) on both (IPOWA-S-W-CRITIC).

Results: The results of the classifications conducted indicate that the use of mobile photovoltaic mesh is a sustainable production strategy, due to its effect on production and quality of the crop, CO2 fixation, and irrigation water savings.

Discussion: The use of mobile photovoltaic shades is compatible with tomato cultivation in a greenhouse if the management of the installation is performed considering the needs of the plants in most of the rankings.

1 Introduction

Presently, climate perturbations include extreme temperature values that increase the evapotranspiration of plants and irrigation needs, compromising agricultural production, especially of crops in Mediterranean climate areas, due to the scarce quantity and quality of the water available (Giordano et al., 2021). Tomatoes (Solanum lycopersicum L.) are the second most-cultivated crop in the world after potatoes, with approximately 187 million tons and 5 Mha in 2021, according to the statistical results from the Food and Agriculture Organization of the United Nations (FAOSTAT, 2025). This crop has high water and nutritional demands and is also sensitive to the reduction in photosynthesis due to photoinhibition, so it is strongly affected by climate change (Mutale-Joan et al., 2020).

In tomato cultivation, grafts are one of the most utilized agroecological techniques. This technique was originally used for controlling pathogens (Louws, 2012), and it is currently used to improve production and quality (Turhan et al., 2011), or to favor the crop's adaptation to conditions of abiotic stress, such as drought, salinity, and high temperatures (Kumar et al., 2017). Shading limits the effect of solar radiation on crops, reducing transpiration and the associated consumption of irrigation water and fertilizers, as well as the leaching of nutrients (Ghoulem et al., 2019). In addition, it improves the homogeneity of the climate and increases productivity and the quality of crops that are especially sensitive to photoinhibition, such as tomatoes (Briassoulis et al., 2007). Photovoltaic technologies directly convert sunlight into electrical energy, thanks to the photoelectric effect. Agrovoltaic applications in open-air crops and greenhouses have been investigated since the start of the 21st century (Magadley et al., 2020). Specifically for tomato, the recommendation is for the modules not to exceed 20% of shading, and it is estimated that shading the entire surface of the crop reduces solar radiation by 80%, which leads to a decrease in production of 70% (Cossu et al., 2018; Kumar et al., 2022). In recent years, there has been a growing number of investigations for possible solutions that make short-term forecasts and identify an unrecognized evaluation standard (Moreno et al., 2025).

A cost–benefit study will allow farmers and growers to make advances in the optimization of agricultural production (Cámara-Zapata et al., 2019). However, assessing the sustainability of different agricultural production strategies requires a multicriteria hierarchical analysis, considering agronomic, economic, environmental, and social criteria (Brotons-Martínez et al., 2024). In this way, it is possible to rank different production strategies considering the result of this analysis. Among the methods utilized, the Monte Carlo analysis, the determination of accumulated probabilities, and polling experts, stand out. However, all of these lack the objectivity necessary to make a decision about the adequacy of the strategies analyzed. Thus, it is necessary to use new ranking methodologies that contribute toward consolidating the motivation of the decisions to be made.

The Criteria Importance Through Inter-Criteria Correlation (CRITIC) method was introduced by Diakoulaki et al. (1995). Its objective is to rank a set of alternatives based on a series of criteria. This method uses the information available and objectively assigns weights to the different criteria through an analytical investigation of the evaluation matrix, quantifying the intrinsic information of each assessment criterion through the value of its standard deviation and the relative discrepancy between the values of each criterion, measured through Pearson's correlation. According to Luo et al. (2024), the estimation of the indicator weight, based on the intensity of comparison, that is, the standard deviation, and the conflict between the evaluation indicators, is used as an objective assignment. To introduce the degree of optimism or pessimism of decision-makers, the combination of this method with a very common aggregation method, the ordered weighted averaging (OWA) operator introduced by Yager (1988), is proposed. The OWA operator considers an aggregation process, providing the maximum, the minimum, and the average. A generalization in the variance and the covariance, allowing for a wide range of scenarios from the minimum to the maximum, that is, from the most optimistic to the most pessimistic scenario, can be followed in Yager (1996a) and Merigó (2011). The OWA linear regression (LR) was introduced by Yager and Beliakov (2010). Flores-Sosa et al. (2020) present an application that uses simple linear regression and the Induced OWA operator in the same formulation.

The CRITIC method and the OWA operator and its extensions have been used in a wide range of applications (Peng and Huang, 2020; Diakoulaki et al., 1995; Merigó and Casanovas, 2011; Yager, 1996b). Although some published studies have combined both concepts (Luo et al., 2024; Xing et al., 2022), they have been presented as two independent methods. Some studies have introduced the OWA in aggregating relative scores (Brotons-Martínez et al., 2024). The CRITIC method has been proposed for several applications in agriculture, such as the evaluation of irrigation systems (Hezam et al., 2024), the selection of suitable reference evapotranspiration (ETo) models (Islam et al., 2020), or for selecting the best alternative for using reclaimed water in India (Narayanamoorthy et al., 2019). The main advantage of the CRITIC method is that it computes the conflict and variability of the criteria by calculating their weights objectively, by analyzing their variability and inter-correlation. The CRITIC method not only avoids the interference of subjective factors but also considers the contrast intensity and conflict between indicators to determine the weight (Anwar, 2021).

Some studies use CRITIC combined with other methodologies, such as the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) in multicriteria decision-making (Liu et al., 2024), the gray relational analysis (Xu et al., 2020; Mishra and Muhuri, 2021), the Analytic Hierarchy Process (AHP) (Zhao et al., 2022), the AHP combined with multicriteria optimization and compromise solution (VIKOR) (Feng et al., 2021), a gray multicriteria decision-making combined compromise solution (Yazdani et al., 2024), the qualitative flexible multiple criteria (QUALIFLEX) method (Liu et al., 2022), the Extended Distance from the Average Solution (EDAS) under a mixture Z-number environment (Sun et al., 2022), the entropy weight method (EWM) (Yuan et al., 2024), the neutrosophic linguistic MCDM (MultiCriteria Decision-Making) algorithm based Combined Compromise Solution (CoCoSo) (Peng and Huang, 2020), or with the Taxonomy method extended to the intuitionistic fuzzy numbers (Xiao et al., 2020). All of these studies deal with methodological combinations that try to improve the CRITIC method, but without considering the attitudinal characteristic of the decision-maker.

The aim of the study is to obtain a CRITIC method where the conflict and variability of the criteria could be considered for estimating the weights according to a degree of optimism to obtain different forecast scenarios. Moreover, by using the Induced OWA (IOWA) and Induced Probabilistic OWA (IPOWA) operators, the decision-maker can under- or over-estimate the information according to a complex attitude that includes the degree of optimism and the psychological and competitive factors (Flores-Sosa et al., 2020). Thus, using induced operators helps us work with complex variables for which the greatest benefit is not always the best solution. For example, this may occur depending on the results that competitors obtain or some personal opinions about the alternatives.

The main novelty of the study is the introduction of the OWA in the analysis of the correlation among different criteria. Using extensions such as the Pearson-POWA allows combining the attitudinal character with the probability of commercial implementation of each treatment. Finally, the Pearson-OWA makes it possible to assign the importance of each sum of the correlation coefficients as a function of an induced variable, the sum of the normalized values of the different criteria for each treatment.

The manuscript is structured in the following manner: first, the basic concepts of the OWA, variance-OWA, and covariance-OWA are described. Next, the Pearson-POWA and Pearson-IPOWA are defined and added to the CRITIC methodology. Furthermore, the IPOWA CRITIC and the extensions IPOWA-OWA-S-CRITIC, IPOWA-OWA-W-CRITIC, and IPOWA-OWA-S-W-CRITIC are proposed to obtain the multicriteria score. The study is concluded with an empirical application, and the results are discussed to assess the applicability of this strategy. Finally, the main conclusions obtained are presented.

2 Materials and methods

2.1 Ordered weighted average

Definition 1. An ordered weighed average (OWA) operator (Yager, 1988) of dimension n is a mapping of FOWA:RnR that has an associated weighting vector W = [ω1, ω2, …, ωn], such that ωi ∈ [0, 1] and i=1nωi=1 defined as:

FOWA(a1,a2,...,an)=j=1nωjbj    (1)

where bj is the jth largest of the ai.

The OWA operator is a non-linear function of elements, since it implies an ordering process. It presents the properties of commutativity, monotonicity, and boundedness:

• Commutativity: The initial ordering of the arguments does not matter.

• Monotonicity: FOWA(a1,a2,...,an)FOWA(a1*,a2*,...,an*) if aiai* for all i.

• Boundedness: Min(a1, ..., an) ≤ FOWA(a1, ..., an) ≤ Max(a1, ..., an).

An immediate application of boundness is idempotency: if aj = a for all j, then F(ai, ..., an) = a.

Definition 2. A Probabilistic OWA operator (POWA) of dimension n (Merigó, 2008, 2009) is a mapping of FPOWA:RnR with two associated weighting vectors W and V of dimension n, such that ωj and vi ∈ [0, 1] and j=1nωj=1 and i=1nvi=1 :

FPOWA(a1,...,an)=j=1nυ^jbj    (2)

where bj is the jth largest of the ai, each argument ai has an associated weight (probability) vi, ν^j=δωj+(1-δ)νj with δ ∈ [0, 1], and νj is the weight (probability), with νi ordered according to bj, that is, according to the jth largest of the ai. If δ = 0 or ωj = 1/n for all the bj, a probabilistic mean is obtained; on the contrary, if δ = 1 o vj = 1/n for all the bj, the OWA operator is obtained.

The induced ordered weighted average operator (IOWA) introduced by Yager and Filev (1999) uses a second variable, the induced variable, to perform the ordering as a prior step to its aggregation.

Definition 3. An IOWA operator of dimension n is a mapping of FIOWA:Rn×RnR; it has an associated weighting vector W of dimension n , such that ωi ∈ [0, 1] and i=1nωi=1 :

FIOWA(u1,a1,u2,a2,...,un,an)=j=1nωjbj    (3)

Where bj is the ai value of the IOWA pair 〈ui, ai〉 having the jth largest ui, ui is the order inducing variable, and ai is the argument variable.

The induced probabilistic ordered weighted average (IPOWA) is an aggregation operator that uses probability and the OWA operator. Thus, the reordering of the values is performed according to the induced variable that represents a complex process of reordering of the individual distances formed by comparing two sets (Merigó and Casanovas, 2010). This contribution is interesting, as it combines the possibility of occurrence of certain results and the attitudinal character of decision-makers, who assess using inductive variables in order to represent their attitude completely. For this, it considers aspects such as the degree of optimism, psychological aspects, or the pressure of time.

Definition 4. An IPOWA operator (Merigó, 2014) of dimension n is a mapping of FIPOWA:Rn×RnR that has the associated weighting vectors W and of dimension n, such that ωj and υi ∈ [0, 1] and j=1nωj=1 and i=1nυi=1:

FIPOWA(a1,u1,...,an,un)=j=1nυ^jbj    (4)

Where bj is the ai value of the IOWA pair 〈ui, ai〉 having the jth largest ui, ui is the order inducing variable, each argument ai is the argument variable with an associated weight (probability) vi, v^j=δωj+(1-δ)vj with δ ∈ [0, 1], and vj is the weight (probability), with vi ordered according to bj, that is, according to the jth largest of the ui.

2.2 Variance, covariance, and correlation coefficient

In this section, some previous concepts, such as the OWA-variance and the OWA-covariance, are analyzed and the Pearson-OWA operator is proposed. These elements will allow for the development of a new methodology named OWA-CRITIC, which allows the ordering of different alternatives, based on a multicriteria system, and the introduction of the possibility that Pearson's correlation coefficient is obtained based on a reordering of the elements to which weights are assigned, not the element itself, but to the position they occupy in the set.

Definition 5. Pearson's correlation coefficient measures the linear relationship between two variables A = {a1, …, an} and B = {b1, …, bn} whose means are μa and μb, respectively. Each argument (ai − μa)(bi − μb) has an associated weight vi with i=1nvi=1 and vi ∈ [0, 1], each argument (ai-μa)2 has an associated weight νia with i=1nνia=1 and νia[0,1], each argument (bi-μb)2 has an associated weight vib with i=1nvib=1 and vib[0,1], and can be defined as FPearson(a1,b1,,an,bn)=i=1nvi(ai-μa)(bi-μb)i=1nvia(ai-μa)2i=1nvib(bi-μb)2. For the case in which vi=via=vib=1/n for all the i, we obtain

FPearson(a1,b1,...,an,bn)=i=1n(ai-μa)(bi-μb)i=1n(ai-μa)2i=1n(bi-μb)2    (5)

Definition 6. The variance OWA operator (Yager, 1996b) of dimension n is a mapping of FVar-OWA:RnR that has an associated weighting vector W = [ω1, ω2, ..., ωn], such that ωi ∈ [0, 1] and defined as

FVar-OWA(a1,a2,...,an)=j=1nωjDj    (6)

where Dj is the jth largest of the (ai-μ)2, ai is the argument variable, and μ is the average (in this case, the OWA operator).

The Var-OWA accomplishes properties similar to other OWA operators, including commutativity, monotonicity, and boundedness. When considering, it becomes the classical variance.

Definition 7. The covariance OWA operator (Merigó, 2011) of dimension n is a mapping of FCovar-OWA:Rn×RnR that has an associated weighting vector, such that and defined as

FCovar-OWA(a1,b1,...,an,bn)=j=1nωjKj    (7)

where Kj is the jth largest of the (ai − μa)(bi − μb), ai is the argument variable of the first set of elements A = {a1, …, an}, bi is the argument variable of the second set of elements B = {b1, …, bn}, and μa and μb are the mean of the sets A and B, respectively.

The Covar-OWA accomplishes properties similar to other OWA operators, including commutativity, monotonicity, and boundedness. When considering ωi = 1/n, it becomes the classical covariance.

The OWA operator can also be implemented into Pearson's correlation coefficient. The use of Pearson-OWA is proposed next, which allows modifying the process of aggregation of the squares of the differences with respect to the mean, and the products of the differences with respect to the means of the two variables to be compared, assigning a higher or lower importance as a function of the degree of optimism or pessimism of the decision-maker.

Definition 8. Pearson-OWA of dimension n is a mapping of FPearson-OWA:Rn×RnR that has an associated weighting vector W = [ω1, ω2, ..., ωn], such that and i=1nωi=1 defined as:

FPearson-OWA(a1,b1,...,an,bn)=j=1nωj(aj-μa)(bj-μb)j=1nωj(aj-μa)2j=1nωj(bj-μa)2    (8)

Where aj and bj are the jth largest arguments in the sets of elements A = {a1, ..., an} and B = {b1, ..., bn}, and μa and μb are the mean of the sets A and B, respectively. When considering ωi = 1/n, it becomes the classical covariance.

The Pearson-OWA accomplishes the properties of the OWA operators: symmetry and boundedness, but not monotonicity.

Some special cases are as follows: if ωj = 0, ∀j ≠ k y ωk = 1, we obtain the maximum as an absolute value, that is, the maximum or the minimum, and if ωj = 1/n, ∀j we have the traditional Pearson's coefficient.

The coefficient FPearsonOWA can be calculated in different ways depending on whether the OWA operator is considered (Table 1). For the study of the OWA variance and the OWA covariance, please see Yager (1996b, 2006). The study can be completed using different types of OWA, such as the maximum [ω = (1, 0, ..., 0)], the minimum [ω = (0, ..., 0, 1)], or the arithmetic mean [ω = (1/n, ..., 1/n)] where n is the number of elements of each variable, as well as weights that only depend on the values of the variables, or additive neat OWA ω = (ω1, …, ωn), where ω1=f(xi)/i=1nf(xi).

Table 1
www.frontiersin.org

Table 1. Pearson-OWA analysis.

On some occasions, aside from the attitudinal character of the decision-maker, which is introduced through the use of the OWA, objective information is available about the possibility of the occurrence of certain results, or the probability of application of the results, so that they will have to be used. Pearson-POWA is proposed, as it allows combining both types of information.

Definition 9. The Pearson-POWA of dimension n is a mapping of FPearson-POWA:Rn×RnR that has an associated weighting vector W of dimension n, such that ωi and i=1nωi=1:

FPearson-POWA(a1,b1,...,an,bn)=i=1nυ^i(aj-μa)(bj-μb)i=1nυ^i(aj-μa)2i=1nυ^i(bj-μa)2    (9)

Where aj and bj are the jth largest arguments in the sets of elements A = {a1, …, an} and B = {b1, …, bn}, and μa and μb are the mean of the sets A and B, respectively. The arguments (aj-μa)(bj-μb),(aj-μa)2, and (bj-μa)2 have an associated weight (probability) vi ordered according to (aj-μa)(bj-μb),(aj-μa)2, and (bj-μa)2, respectively, ν^j=δωj+(1-δ)vj with δ ∈ [0, 1]. If δ = 0 or ωj = 1/n for all the (aj-μa)(bj-μb),(aj-μa)2 and (bj-μa)2, the Pearson probability is obtained, in which the weight of each sum is given by the assigned probabilities, while if δ = 1 or vj = 1/n for all the (aj-μa)(bj-μb),(aj-μa)2, and (bj-μa)2, the FPearson-OWA operator is obtained.

Pearson-IPOWA combines the concept of the probability of occurrence or applicability of specific events with the ordering of elements according to the attitudinal character of the decision maker, but in this case, this ordering is performed based on inducting variables of order, which can represent a broad range of aspects, such as the degree of optimism or pessimism, or psychological or time pressure aspects.

Definition 10. The Pearson-IPOWA of dimension n is a mapping of FPearson-IPOWA:Rn×Rn×RnR that has an associated weighting vector W of dimension n, such that ωi ∈ [0, 1] and i=1nωi=1, defined as:

FPearson-IPOWA([a1,b1,u1],...,[an,bn,un])=j=1nυ^jDjj=1nυ^jKjj=1nυ^iHj    (10)

Where Dj, Kj, Hj are the values of (aj-μa)(bj-μb),(aj-μa)2, and (bj-μa)2- respectively, having the jth largest ui, ui is the order inducing variable. Each argument, Di, Ki, and Hi, has an associated weight (probability) vi ordered according to the largest of the ui,v^j=δωj+(1-δ)vj with δ ∈ [0, 1], and vj is the weight (probability); vi is ordered according to Dj, that is, according to the j th largest of the ui. If δ = 0 o ωj = 1/n for all the Dj, Kj, Hj, the Pearson probability FPearson-POWA is obtained, on the other hand, if δ = 1 or vj = 1/n for all the Dj, Kj, Hj the induced Pearson-OWA, FPearson-IOWA is obtained.

2.3 IPOWA-CRITIC and its extensions

The following section proposes diverse extensions of the CRITIC methodology, using the operator proposed in the previous section, to obtain the correlation between the values of the different criteria and the use of OWA to obtain the multicriteria score.

The CRITIC methodology uses the multicriteria system to order a set of alternatives. This study is an extension of the proposal by Diakoulaki et al. (1995). The objective is to order a set of alternatives A = {1, ..., |I|}, with cardinality |I|, and according to a set of criteria C = {1, ..., |J|} with cardinality |J|. The following steps are proposed (Figure 1):

Figure 1
Flowchart illustrating the IPOWA-CRITIC method and its extensions. It consists of seven steps: (1) generic criteria-alternatives matrix, (2) relative score with profit and cost equations, (3) OWA standard deviation of criterion j, (4) conflict of dimensions matrix, (5) quantity of information, (6) weight of criterion 1, and (7) multicriteria score and final order. The final decision options include IPOWA-CRITIC, IPOWA-OWA-S-CRITIC, IPOWA-OWA-W-CRITIC, and IPOWA-OWA-S-W-CRITIC. Mathematical expressions are included for each step.

Figure 1. IPOWA-CRITIC and its extensions process.

Step 1. The generic criteria-alternatives matrix shows the mij values of alternative i for criteria j (Table 2).

Table 2
www.frontiersin.org

Table 2. Values of criteria used (C1, …, Cj) to rank the treatments applied (A1,…, Ai).

Step 2. Transformation of the generic criteria-alternatives matrix into the relative score or closeness matrix to the ideal values [xij]. For each j criterion, the minimum is obtained, mini(mij), as well as the maximum maxi(mij) of all the alternatives, in a similar manner to the crisp case. When the ideal value is the maximum value (benefits), the closeness to the ideal value is obtained as:

xij=mij-mini(mij)maxi(mij)-mini(mij)    (11)

and the ideal value is the minimum value (cost):

xij=maxi(mij)-mijmaxi(mij)-mini(mij)    (12)

Step 3. Obtaining the OWA standard deviation of criterion j, for each vector xj = (x1j, x2j, ..., x|I|j) of the transformed matrix, from Equation 6

FSD-OWA(x1j,x2j,...,xnj)=(h=1nωhXhj)1/2    (13)

Where Xhj is the hth largest value of (xij-μj)2,ωi[0,1], and i=1nωi=1.

Step 4. Construction of the conflict of dimensions matrix |J| × |J|, whose generic term FPearson-IPOWA j, k represents the correlation between elements xj and xk. Therefore, the weaker the relationship between the criteria j and k, the smallest the value of FPearson-IPOWAj, k will be.

FPearsonIPOWAj,k([x1j,y1k,u1],...,[xnj,ynk,un])=h=1nυ^hZh,kh=1nυ^hVh,jh=1nυ^hWh,k    (14)

where Zh, k, Vh, j, and Wh, k are the values of (xij-μxj)(yik-μyk),(xij-μxj)2, and (xik-μxk)2, respectively, having the hth largest ui, with ui being the order inducing variable, and with μxj being the mean of the first set of values for criterion j, Xj = {x1j, …, xnj}, and μy, k the mean of the second set, Xk = {x1k, …, xnk}. Each Zi, k, Vi, j, and Wi, k has an associated weight (probability) vi with i=1nvi and vi[0,1],v^h=δωh+(1-δ)vh with δ ∈ [0, 1] and vh is the weight (probability), with vi ordered according to the hth largest ui, with ui=j=1|J|xij, that is, the sum of all the relative scores of the alternative Ai. This probability represents the probability of occurrence, or in this particular case, the probability of commercially implementing this treatment. This coefficient will be obtained from the opinions of the experts related with the present project.

Step 5. Quantity of information COWAj is emitted by the jth criterion, which represents the quantity of information transmitted by said criterion, so that the more information transmitted, the greater the value of COWAj:

C-OWAj=FSD-OWAj(x1j,x2j,...,xnj)·k=1|J|(1-FPearson-IPOWAj,k)    (15)

Step 6. The weight of criterion j is obtained by normalizing the values of COWAj.

ωj=C-OWAjj=1|J|C-OWAj    (16)

Step 7. Obtaining the multicriteria score for alternative i: For this step, four alternatives are proposed depending on how the OWA is used for the relative scores, the weights, for both, or none of them.

7.1. Multicriteria score with IPOWA-CRITIC to order the different alternatives. The Multicriteria score with IPOWA-CRITIC (Di) is obtained as the product of the weights obtained in Equation 16 by the relative scores obtained in Equations 11, 12.

Di=j=1|J|ωjxij    (17)

7.2. Multicriteria score with the IPOWA-OWA-S-CRITIC to order the different alternatives. The IPOWA-OWA-S-CRITIC multicriteria score for alternative i is a mapping of FIPOWA-OWA-S-CRIIC:RnR that has the weighted vector obtained in Equation 16 associated: W = [ω1, ω2, …, ω1|J|] where ωi ∈ [0, 1] and i=1nωi=1 is defined as:

FIPOWA-OWA-S-CRITIC(xi1,xi2,...,xi|J|)=h=1|J|ωhzih    (18)

where zih is the hth largest of the xij (alternative Ai), and ωh is the weight obtained in Equation 16.

7.3. Multicriteria score with IPOWA-OWA-W-CRITIC to order the different alternatives. The IPOWA-OWA-S-CRITIC multicriteria score for alternative i is a mapping of FIPOWA-OWA-W-CRITIC:RnR that has the weighted vector obtained in Equation 16 associated: W = [ω1, ω2, ..., ω|J|], where and i=1nωi=1 is defined as:

FIPOWA-OWA-W-CRITIC(xi1,xi2,...,xi|J|)=h=1|J|ψhxih    (19)

where ψh is the hth largest of the ωj, and xih is the relative score obtained in Equations 11, 12.

7.4. Multicriteria score with IPOWA-OWA-S-W-CRITIC to order the different alternatives. The IPOWA-OWA-S-CRITIC multicriteria score for alternative i is a mapping of FIPOWA-OWA-S-W-CRITIC:RnR that has the weighted vector obtained in Equation 16 associated: W = [ω1, ω2, ..., ω|J|], where ωi ∈ [0, 1] and i=1nωi=1 is defined as:

FIPOWA-OWA-S-W-CRITIC(xi1,xi2,...,xi|J|)=h=1|J|ψhzih    (20)

where ψh is the hth largest of the ωj and zih is the hth largest of the (alternative Ai) obtained in Equations 11, 12.

2.4 Empirical application

Muchamiel tomatoes were grown in a multi-span mesh greenhouse (windbreak greenhouse) that was 26 m wide, 36 m long, and 4 m high until the gutter and 5 m to the ridge, located at the CIAGRO-UMH (Orihuela, Alicante, Spain, Latitude: 38° 05' 05” North; Longitude: 0° 56' 38” West). A short spring-summer cycle was used for 2 consecutive years. The first with a transplantation on 6th March 2023 and harvesting of plants on 28th June 2023. The second is between 4th March and 28th June 2024. Inside the greenhouse, three plots with different shading systems were set up: (i) without shade (W), (ii) with a fixed and conventional shade nets with 50% of reflection of the solar radiation (F), and (iii) a mobile mesh with photovoltaic shading (P). In each of the plots and on the exterior of the greenhouse, the mean values of the main climate variables were recorded at 10-min intervals, such as ambient temperature and humidity, as well as the intensity of the solar radiation. The mean values of the energy variables were also determined, related to the photovoltaic mesh, at 10-min intervals. In each plot, grafted plants (G) and non-grafted plants (N) were used, with two watering events, according to the needs of the crop, through Allen et al. (2006) method (complete irrigation, C), and with deficit irrigation at 60% of said value (D). The total number of plants used in each treatment was 36 plants. Agroecological strategies and techniques were followed during the management of the crop, such as the application of biostimulants and integrated pest management. Table 3 shows the treatments applied during the assay.

Table 3
www.frontiersin.org

Table 3. Treatments (W, without shading; C, conventional shading; SF, photovoltaic shading; G, grafted plants; N, non-grafted plants; C, complete irrigation; and D, deficit irrigation).

To establish the sustainability of the production strategies used, criteria related to the agronomical, physiological, and biochemical responses of the plant were used, such as production (kg ha−1) and quality, determined starting with the maturity index (°Brix/Acidity) and nutritional composition (%). The profit obtained (€ ha−1) with respect to the economic sustainability of the treatments was also considered. The water consumption (m3 ha−1) and CO2 fixation (t ha−1) allowed us to consider the environmental sustainability of the treatments. In addition, the social effect was determined starting from the labor used in each treatment. Table 4 shows the criteria used.

Table 4
www.frontiersin.org

Table 4. Criteria taken into account to grade the treatments.

Five experts on the subject were consulted to establish confidence in the results obtained in each of the criteria for each of the treatments utilized, and to support the making of decisions on its possible application at a commercial exploitation scale.

To improve the analysis of the sustainability of the agronomic strategies utilized, a sustainability index calculated from the IPOWA CRITIC assignment is proposed. The value of this index varies between 0 and 1. A value of 0 corresponds to the treatment with the worst results according to the criteria used (Table 4), and a value of 1 indicates the best treatment.

2.5 Statistical analysis

The results were statistically evaluated using an analysis of variance, ANOVA, with a 95% confidence interval. The differences between the means of the treatments were analyzed using the least significant difference test of Fisher (LSD) at a probability level of 95%. Significance levels were expressed as: * p < 0.05; ** p < 0.01; *** p < 0.001; NS not significant. The results of all treatments were analyzed in each of the 2 years of cultivation, and no significant differences were found between them. The results for the 1st year of cultivation are presented here.

3 Results and discussion

The values of the IPOWA-CRITIC and its extensions were obtained according to the procedure described above.

Step 1. Identify the results matrix for each criterion and alternative (Table 5). The results obtained in each of the criteria by the treatments applied are shown in Table 5. As shown, treatment A1 (WGC) showed a production of 72,870 kg ha−1, higher than the rest. With respect to the water consumption, the treatments were mainly distributed into two groups, the ones that were irrigated at 100% of their needs (C), with a consumption of approximately 3,300 m3 ha−1, and those that were irrigated at 60% (D), with a consumption of approximately 2,000 m3 ha−1. As for CO2 fixation, this was higher in the treatments with photovoltaic shades due to the elimination of CO2 during the generation of the electrical energy consumed. The use of labor is related to production, being higher in the treatments with a higher production, such as WGC. The plants without shading had a higher maturity index value, followed by plants with fixed and conventional shading (F) and plants with photovoltaic shading. On its part, the nutritional composition of the tomatoes in the plot without shading was similar to that from the plot with photovoltaic shading (P), and both were inferior to that determined in the plot with F treatments.

Table 5
www.frontiersin.org

Table 5. Values of the criteria used (from BI1 to BI7) to rank the treatments applied (from A1 to A12).

Step 2. To be able to compare all the criteria, they are standardized. The normalized values are shown in Table 6. Except for the consumption of water, all the criteria show profits, as it is better if the values are higher. In the case of water consumption, BI3, the value represents a cost, so it is better if this value is lower. Therefore, expression (11) was used for all, except for BI3, in which case, expression (12) was used. As can be observed, treatment A1 (WGC) has higher values in most of the criteria, except for water consumption and CO2 fixation, which show a null value, and nutritional composition (% nutrients), with a value of 0.605. Table 6 also shows the sum of the distances relative to the ideal values of each treatment, which will be used as an induced value in the case of using the IOWA. Moreover, the OWA standard deviation is shown, in agreement with the expression (Equation 13).

Table 6
www.frontiersin.org

Table 6. Normalized values of the criteria used (from BI1 to BI7) to rank the treatments performed (from A1 to A12), sum of the relative distances to the ideal values, and values of the OWA standard deviation.

Step 3. Since the weights of each criterion in OWA-CRITIC depend on its dispersion, the OWA standard deviation of each criterion is obtained. As a prior step before obtaining the standard deviation of each criterion, Table 7 (column 2) shows the confidence of the results of the treatment for their subsequent passage to commercial exploitation, where 0 represents no confidence, and 1 represents maximum confidence. For this, five experts were consulted, and mean values were calculated. The third column in Table 7 shows the probability of each treatment, dividing the confidence of each treatment by the total sum of the treatments. The fifth column provides the weight ωi assigned in expression (Equation 14) corresponding to , so that a higher weight is assigned to the totals that correspond to a treatment closer to ideal values. FPearsonIPAOWA uses the same weights but assigns a greater weight to the treatment with lower values in Table 6 (column 9). OWA standard deviation values of criterion j are presented in Table 8 (row 9).

Table 7
www.frontiersin.org

Table 7. Level of confidence in the treatments and probability, and weight coefficients of for each position.

Table 8
www.frontiersin.org

Table 8. Pearson-IPOWA matrix and aggregation of values.

Step 4. To analyze the conflict between criteria, Table 8 shows the Pearson-IPOWA considering δ = 0.6, that is, considering the weighting of its differences and quadratic differences with 60% of the OWA element and 40% of the probability element.

Step 5. Determination of the quantity of information emitted by the jth criterion (Table 9, row 4) was obtained as the product of the standard deviation (Table 9, row 2) by the aggregates k=1|J|(1-FPearson-IPOWAj,k) (Table 9, row 3).

Table 9
www.frontiersin.org

Table 9. Standard deviation, aggregation of the Pearson-IPOWA, quantity of information emitted by the jth criterion, and final weight of the criterion j.

Step 6. Obtaining the weight of the jth criterion. The quotient of the amount of information emitted by criterion j divided by the sum of the amount of information emitted by all the criteria allows us to obtain the weight of criterion j (Table 9, row 5).

Step 7. Calculation of the multicriteria score.

7.1. Multicriteria score with IPOWA-CRITIC of alternative i (Table 10, column 2) is obtained by multiplying the weighting vectors from Table 9 (row 5) by the relative scores of Table 6 (row Ai).

Table 10
www.frontiersin.org

Table 10. Multicriteria score for the IPOWA CRITIC and its extensions.

7.2. Multicriteria score with IPOWA-S-CRITIC. The multicriteria score of the alternative i (Table 10, column 3) is obtained by multiplying the weighting vectors from Table 9 (row 5) by the relative scores zih, h = 1, ...7, where zih is the highest hth of the (Table 6) of the row corresponding to the alternative Ai, i = 1, ..., 12.

Step 7.3. Multicriteria score with IPOWA-W-CRITIC. The multicriteria score of the alternative i (Table 10, column 4) is obtained by multiplying the weighting vector ψh, h = 1, ..., 7, where ψh is the highest hth of the ωj from Table 9 (row 5) by the relative scores of Table 6 (row Ai).

Step 7.4. Multicriteria score with IPOWA-S-W-CRITIC. The multicriteria score of the alternative i (Table 10, column 5) is obtained by multiplying the weighting vectors ψh, h = 1, ..., 7, where ψh is the highest hth of the from Table 9 (row 5) by the relative score zih, h = 1, ...7, where zih is the highest hth of the (Table 6, row Ai) of the row corresponding to the alternative Ai, i = 1, ..., 12.

3.1 Comparative analysis

In order to validate the proposed model, we proceeded to compare the results obtained by applying IPOWA-CRITIC, aside from IPOWA-S-CRITIC, IPOWA-W-CRITIC, and IPOWA-S-W-CRITIC, with other methodologies such as CRITIC, and other selected due to their simplicity, rationality, comprehensibility, good computational efficiency and ability to measure the relative performance for each alternative in a simple mathematical form, such as the scoring methods: Simple additive weighting, SAW (Podvezko, 2011), and Complex Proportional Assessment, COPRAS, based on the evaluation of different alternative through basic arithmetic operations, adding each normalized value of each criterion by its corresponding weight; and distance-based methods: Multicriteria optimization and compromise solution, VIKOR (Opricovic and Tzeng, 2004), and Technique for order of preference by similarity to ideal solution (TOPSIS), based on the calculation of each distance between each alternative and specific point.

Table 11 shows the rank of different alternatives. For CRITIC, TOPSIS, VIKOR, and SAW, the following was used as the weighting vector: ω = {0.20, 0.18, 0.17, 0.15, 0.13, 0.10, 0.07}, using a coefficient of 0.90 for the Manhattan distance and 0.10 for infinite one in the VIKOR method. As shown, the proposed extensions (IPOWA-S-CRITIC, IPOWA-W-CRITIC, IPOWA-S-W-CRITIC) show a very high correlation, obtained from Spearman's correlation coefficient (rs), with respect to the IPOWA CRITIC method, being higher than 0.64 in all cases, and also of the IPOWA CRITIC with respect to other methodologies such as CRITIC, TOPSIS, VIKOR and SAW, being higher than 0.76 in all of these cases.

The analysis of the sustainability of the agroecological strategies used in Muchamiel tomato cultivation, obtained from the IPOWA-CRITIC ranking, offers very consistent results. To improve the interpretation of the results, Figure 2 shows the average allocation values obtained for each of the main factors used. The sustainability of the agronomic strategies is inversely proportional to the values obtained.

Figure 2
Bar chart illustrating the sustainability index for three treatments: shading, grafting, and irrigation. Shading (red) includes W and F, with W scoring higher. Grafting (green) includes P, G, and N, with P having the highest value. Irrigation (blue) includes C and D, with D scoring highest. “a,” “b,” “ns,” and asterisks indicate statistical significance.

Figure 2. Mean values and standard deviation of the sustainability index for the main factors used (shading, grafting, and irrigation). In each shading type, n = 4, W: no shading; F: conventional fixed shading; P: photovoltaic shading. In grafting, n = 6, G: grafted plants; N: non-grafted plants. In irrigation, n = 6, C: full irrigation; D: deficit irrigation. The differences were analyzed with Fisher's least significant difference test (LSD; p = 0.05); different letters in each column indicate significant differences between treatments at p < 0.05. In the ANOVA, the significance level is represented by p < 0.01 and 0.001 (** and ***, respectively) and “NS” indicates no significant differences.

The Muchamiel tomato is a crop that is well adapted to Mediterranean edaphoclimatic conditions (Garcia-Martínez, 2016). Thus, the values of commercial production in the treatments without shading are adequate. The plants with fixed and conventional shading had lower production values, perhaps due to reduced photoassimilates. However, their nutritional composition was the best in all the treatments applied. This effect coincides with what was described by Milenkovic et al. (2020); in our experimental conditions, the shading nets were not beneficial for Muchamiel tomatoes. Despite the tomato plants using diffused light more efficiently than direct radiation (Hemming et al., 2008), in our experimental conditions, photoassimilation was limited, negatively affecting production and the index of maturity. It is possible that the reduction in solar radiation caused by the shading nets used was excessive. Milenkovic et al. (2020) used shading nets of different colors, with a reduction in solar radiation similar to that recorded in our study, with tomatoes Optima' F1 and “Big beef” F1, finding an improvement in production and quality. These results can be explained, considering the influence of the genetic material on the response of these plants to these types of treatments. In addition, the color nets have an influence not only on the quantity of solar radiation that reaches the plants but also on their quality (Timmermans et al., 2020).

The shading treatments showed significant differences considering the sustainability criteria used. Thus, the sustainability of the Muchamiel tomato crop without shading and with mobile photovoltaic shading was similar between them, and was higher than the plants with conventional fixed shading (Figure 2). This is because the 50% fixed shade used in the assay limited the photosynthetic activity of the plants, reducing production. Among the no-shade treatments, only the non-grafted plants with full irrigation obtained an unfavorable score (treatment A3 occupies 10th place, Table 11). Independent of the shading used, this result can be generalized, that is, the non-grafted plants and those with full irrigation had the worst behavior (treatments A3, A7, and A11 occupied the 10th, 12th, and 6th positions, respectively, Table 11). The results can be explained if we take into account the effect of the graft on production. Non-grafted plants had a lower production, perhaps due to the presence of fungi and nematodes in the soil, which reduce the absorption of water and nutrients (Phani et al., 2024). Intensive production to maximize performance and satisfy demand makes attacks by plagues and diseases critical threats for producers, in both field conditions and greenhouses (Capinera, 2020; Phani et al., 2021). Despite the heavy losses due to the action of nematodes, the management options of this disease are limited, highlighting grafting among them (Martínez-Ballesta et al., 2010). Therefore, the full irrigation of non-grafted plants implies higher operational costs, although the production is lower than that of the treatments that used grafted plants, so the use of non-grafted plants is particularly unfavorable in our experimental conditions.

Table 11
www.frontiersin.org

Table 11. Ranking alternatives.

The use of grafts tends to improve the sustainability of the production, considering the criteria utilized (Figure 2). Thus, the evaluation of the grafted plants was better than that of non-grafted ones, in every case, with the exception of the plants under photovoltaic shading and deficit irrigation treatment (treatments A10 and A12, Table 11). This exception is particularly notable, as treatment A12 (PND) was found in first place (Table 11). This result can be explained by considering the multicriteria analysis performed. In this way, the use of deficit irrigation, along with the mobile photovoltaic mesh, mitigates the reduction of production, which implies the use of non-grafted plants in the experimental conditions utilized. On the one hand, the appropriate deficit irrigation of tomatoes can save a significant amount of water and improve quality, without negatively affecting production or the economic results (Khapte et al., 2019). On the other hand, the shade produced by the photovoltaic installation can avoid the reduction in tomato production (Ureña-Sánchez et al., 2012). This could be true, especially in our case, due to the use of the mobile mesh, which only produces shade in the middle of the day. In this way, the photoinhibition of tomato could be avoided, which is produced by excessive radiation, and can lead to a reduction in photosynthetic activity and production (Shi et al., 2022; Wang et al., 2018).

Tomato crops demand a large amount of water (Peet, 2005), especially during the flowering phase (Khapte et al., 2019). Deficit irrigation in the experimental conditions utilized improved the sustainability of the Muchamiel tomato. Thus, the top four treatments used deficit irrigation, and in general, all the even-numbered treatments (deficit irrigation) were better evaluated, that is, their allocation is lower than the odd-numbered treatments just before (identical treatment with full irrigation) (Table 11). Irrigation is a determining factor in the sustainability of production. In areas with warm and/or Mediterranean climates, with a scarcity of water, the maximization of the productivity of water of crops can be more beneficial for the farmer than the maximization of crop performance (Pereira et al., 2002).

Currently, the Overall Life Cycle Sustainability Assessment (OLCSA) is the most utilized method to estimate the sustainability of products, goods, or services. The application to agri-food systems has specific limitations related to the definition of the system, the interval of assessment, or the spatiotemporal resolution of the databases utilized, among others. In addition, there is a potentially high variability between independent agricultural businesses due to the differences on cultivation practices, agroclimatic conditions, seasonality, and distances between the places where activities considered in the lifecycle of the product are carried out (Notarnicola et al., 2017). To avoid these inconveniences, the application of multicriteria methods has been recently developed, such as the one proposed in the present study, which seeks to organize the different strategies as a function of the environmental, economic, social, cultural, etc., criteria. Thus, studies have been conducted on the valorization of agricultural waste (Escalante et al., 2016), joint management of agro-livestock farms and agricultural farms (Reyna-Ramírez et al., 2025), tomato ketchup packaging design (Wohnera et al., 2020), irrigation management in conditions of water deficit (Montazar and Snyder, 2012), fertigation management in tomato cultivation (Heiba et al., 2023), strategies for improving field-grown cereal yield (Di Bene et al., 2022), and evaluation of the sustainability of tomato cultivation (Sadiq et al., 2025). Overall, this is a very interesting approach and is considered a suitable complement to OLCSA methods for decision-making in the agri-food value chain. The continued performance of this type of analysis is needed to make advances on the sustainability of the agricultural sector, improve its resilience, and respond to societal demands.

4 Conclusion

The prioritization of agricultural production processes is an extremely complex process, which on many occasions requires subjectivity from the agents involved in the selection process. The CRITIC methodology is based on the objective information from the results of different treatments. However, the opinion of the decision-makers must be considered, so that the introduction of the OWA allows us to weigh the different attributes so that they can be overestimated or underestimated according to the attitudinal character of the decision-maker.

The present study has proposed an extension of Pearson's correlation coefficient, named Pearson-IPOWA, which allows for the calculation of the correlation, considering the attitudinal character of the decision-maker, weighing to a greater or lesser extent, and the elements that have a sum higher than their relative scores.

The introduction of the IPOWA correlation coefficient, together with the use of the OWA-variance, has allowed us to propose an IPOWA-CRITIC that adequately introduces the attitudinal character of the decision-maker, as well as its extensions IPOWA-S-CRITIC, IPOWA-W-CRITIC, and IPOWA-S-W-CRITIC. Finally, the comparison with the traditional CRITIC method with the diverse alternatives proposed allows us to see how the attitudinal character of the decision-makers affects the final ranking of the treatments.

The results of the classifications conducted indicate that the use of mobile photovoltaic mesh is a sustainable production strategy, due to its effect on production and quality of the crop, CO2 fixation, and irrigation water savings.

The proposed methodology for calculating the correlation coefficient and its application in the CRITIC is a generalization of the traditional method. It is evident that the use of different induced variables can lead to differences in the final results, so the result shown can be considered a particular case of all the possibilities offered by the proposed methodology. Therefore, it is essential that in each case, the decision-maker selects the one most appropriate to their objectives and needs. In this case, the selected variable shows a very high degree of correlation with the other methodologies with which it has been compared. It is necessary to continue with this type of analysis to facilitate the making of decision of farmers and to make advances on the sustainability of the processes of agricultural production and the agri-food sector.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

JB-M: Formal analysis, Visualization, Writing – original draft, Data curation, Resources, Project administration, Validation, Software, Methodology, Supervision, Investigation, Conceptualization, Funding acquisition, Writing – review & editing. JC-Z: Validation, Investigation, Data curation, Software, Methodology, Supervision, Writing – review & editing, Visualization, Resources, Funding acquisition, Formal analysis, Conceptualization, Writing – original draft, Project administration.

Funding

The author(s) declare that financial support was received for the research and/or publication of this article. This research was funded by the AGCOOP_A/2022/004 project financed by the Valencian Agency for Agricultural Promotion and Guarantee, with funds from the European Union, the Ministry of Agriculture, Fisheries and Food and the Generalitat Valenciana.

Conflict of interest

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.

Generative AI statement

The author(s) declare that no Gen AI was used in the creation of this manuscript.

Publisher's note

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.

References

Allen, R. G., Pereira, L. S., Raes, D., and Smith, M. (2006). Crop Evapotranspiration. Guidelines for Determining Crop Water Requirements. Rome: FAO Irrigation and Drainage Study 56.

PubMed Abstract | Google Scholar

Anwar, M. (2021). Potential vs prevalent vs popular vs proven biodiesel feedstocks: a critical 4P selection process. Fuel 298:120712. doi: 10.1016/j.fuel.2021.120712

Crossref Full Text | Google Scholar

Briassoulis, D., Mistriotis, A., and Eleftherakis, D. (2007). Mechanical behaviour andproperties of agricultural nets — Part I: testing methods for agricultural nets. J. Polym. Test. 26, 822–832. doi: 10.1016/j.polymertesting.2007.05.007

Crossref Full Text | Google Scholar

Brotons-Martínez, J. M., Nares-Lara, B., and Chávez-Rivera, R. (2024). “Assessment of biohazard waste by generating center in Morelia using critics and OWA,” in International Congress on Innovation and Sustainable, Mazatlán, México, May 29-31. Conference Proceedings, 83–387.

Google Scholar

Cámara-Zapata, J. M., Brotons-Martínez, J. M., Simón, S., Martínez-Nicolás, J. J., and Garcia-Sánchez, F. (2019). Cost-benefit analysis of tomato in soilless culture systems with saline water under greenhouse conditions. J. Sci. Food Agr. 99, 5842–5851. doi: 10.1002/jsfa.9857

PubMed Abstract | Crossref Full Text | Google Scholar

Capinera, J. (2020). Handbook of Vegetable Pests. London: Academic Press.

Google Scholar

Cossu, M., Cossu, A., Deligios, P. A., Ledda, L., Li, Z., Fatnassi, H., et al. (2018). Assessment and comparison of the solar radiation distribution inside the main commercial photovoltaic greenhouse types in Europe. Renew. Sustain. Energy Rev. 94, 822–834. doi: 10.1016/j.rser.2018.06.001

Crossref Full Text | Google Scholar

Di Bene, C., Gómez-López, M. D., Francaviglia, R., Farina, R., Blasi, E., Martínez-Granados, D., et al. (2022). Barriers and opportunities for sustainable farming practices and crop diversification strategies in mediterranean cereal- based systems. Front. Environ. Sci. 10:861225. doi: 10.3389/fenvs.2022.861225

Crossref Full Text | Google Scholar

Diakoulaki, D., Mavrotas, G., and Papayannakis, L. (1995). Determining objective weights in multiple criteria problems: the critic method. Comput. Ops. Res. 22, 763–770. doi: 10.1016/0305-0548(94)00059-H

Crossref Full Text | Google Scholar

Escalante, H., Castro, L., Gauthier-Maradei, P., and Rodríguez De La Vega, R. (2016). Spatial decision support system to evaluate crop residue energy potential by anaerobic digestion. Bioresour. Technol. 219, 80–90. doi: 10.1016/j.biortech.2016.06.136

PubMed Abstract | Crossref Full Text | Google Scholar

FAOSTAT (2025). Available online at: https://www.fao.org/faostat/en/#home (accessed March 4, 2025).

Google Scholar

Feng, Y. K., Lang, K., Zhang, Y. J., and Xing, S. W. (2021). “Optimal selection model for life emergency rescue ship based on game theory and VIKOR method,” in Sixth International Conference on Electromechanical Control Technology and Transportation (ICECTT 2021), Chongqing, China, May 14-16. Proceedings of SPIE, 120813R. doi: 10.1117/12.2623978

Crossref Full Text | Google Scholar

Flores-Sosa, M., Avilés-Ochoa, E., and Merigó, J. M. (2020). Induced OWA operators in linear regression. J. Intell. Fuzzy Syst. 38, 5509–5520. doi: 10.3233/JIFS-179642

PubMed Abstract | Crossref Full Text | Google Scholar

Garcia-Martínez, S. (2016). Genetic Improvement of Traditional Tomato Varieties from Southeastern Spain (In Spanish). PhD Thesis. Miguel Hernández University, Spain.

Google Scholar

Ghoulem, M., El Moueddeb, K., Nehdi, E., Boukhanouf, R., and Calautit, J. K. (2019). Greenhouse design and cooling technologies for sustainable food cultivation in hot climates: Review of current practice and future status. Biosyst. Eng. 183, 121–150. doi: 10.1016/j.biosystemseng.2019.04.016

Crossref Full Text | Google Scholar

Giordano, M., Petropoulos, S. A., and Rouphael, Y. (2021). Response and defence mechanisms of vegetable crops against drought, heat and salinity stress. Agriculture 11:463. doi: 10.3390/agriculture11050463

PubMed Abstract | Crossref Full Text | Google Scholar

Heiba, Y., Ibrahim, M. G., Mohamed, A. E., Fujii, M., and Nasr, M. (2023). Developing smart sustainable irrigation matrix (SIM)-based model for selection of best irrigation techniques: a framework to achieve SDGs. J. Cleaner Prod. 420:138404. doi: 10.1016/j.jclepro.2023.138404

Crossref Full Text | Google Scholar

Hemming, S., Dueck, T., Janse, J., and Van Noort, F. (2008). The effect of diffuse lighton crops. Acta Hortic. 801, 1293–1300. doi: 10.17660/ActaHortic.2008.801.158

Crossref Full Text | Google Scholar

Hezam, I. M., Ali, A. M., Sallam, K., and Abdel-Basset, M. (2024). An efficient decision-making model for evaluating irrigation systems under uncertainty: toward integrated approaches to sustainability. Agr. Water Manage. 303:109034. doi: 10.1016/j.agwat.2024.109034

Crossref Full Text | Google Scholar

Islam, S., Abdullah, R. A. B., Tirth, V., Shahid, S., Algarni, S., and Hirol, H. (2020). Evaluation of mass transfer evapotranspiration models under semiarid conditions using MCDM approach. Appl. Ecol. Env. Res. 8, 6355–6375. doi: 10.15666/aeer/1805_63556375

Crossref Full Text | Google Scholar

Khapte, P. S., Kumar, P., Burman, U., and Kumar, P. (2019). Deficit irrigation in tomato: agronomical and physio-biochemical implications. Sci. Hortic-Amsterdam. 248, 256–264. doi: 10.1016/j.scienta.2019.01.006

Crossref Full Text | Google Scholar

Kumar, M., Haillot, D., and Gibout, S. (2022). Survey and evaluation of solar technologies for agricultural greenhouse application. Sol. Energy. 232, 18–34. doi: 10.1016/j.solener.2021.12.033

Crossref Full Text | Google Scholar

Kumar, P., Rouphael, Y., Cardarelli, M., and Colla, G. (2017). Vegetable grafting as a tool to improve drought resistance and water use efficiency. Front. Plant Sci. 8:1130. doi: 10.3389/fpls.2017.01130

PubMed Abstract | Crossref Full Text | Google Scholar

Liu, P. D., Pan, Q., Xu, H., and Zhu, B. (2022). An extended QUALIFLEX method with comprehensive weight for green supplier selection in normal q-rung orthopair fuzzy environment. Int. J. Fuzzy Syst. 24, 2174–2202. doi: 10.1007/s40815-021-01234-3

Crossref Full Text | Google Scholar

Liu, W., Liu, A., Qin, H., Yan, Y., Fu, D., and Sing, R. P. (2024). Application of hybrid multi-criteria decision-making approach to analyze wastewater microalgae culture systems for bioenergy production. Environ. Res. 256:119234. doi: 10.1016/j.envres.2024.119234

PubMed Abstract | Crossref Full Text | Google Scholar

Louws, F. J. (2012). IPM diversification: Advancing the science and practice of grafting tomatoes to manage soilborne pathogens. Proc. Amer. Phytopathol. Soc. 102:153.

Google Scholar

Luo, X., Kang, K., Lu, L., Yu, C., Li, C., Li, B., et al. (2024). Resilience evaluation of low-carbon supply chain based on improved matter-element extension model. PLoS ONE 19:e0301390. doi: 10.1371/journal.pone.0301390

PubMed Abstract | Crossref Full Text | Google Scholar

Magadley, E., Teitel, M., Peretz, M. F., Kacira, M., and Yehia, I. (2020). Outdoor behaviour of organic photovoltaics on a greenhouse roof. Sustain. Energy Technol. Assessm. 37:100641. doi: 10.1016/j.seta.2020.100641

Crossref Full Text | Google Scholar

Martínez-Ballesta, M. C., Alcaraz-López, C., Muries, B., Mota-Cadenas, C., and Carvajal, M. (2010). Physiological aspects of rootstock–scion interactions. Sci. Hortic. 127, 112–118. doi: 10.1016/j.scienta.2010.08.002

Crossref Full Text | Google Scholar

Merigó, J. M. (2008). New extensions to the OWA operators and its application in decision making (In Spanish). PhD Thesis, Department of Business Administration, University of Barcelona.

Google Scholar

Merigó, J. M. (2009). “Probabilistic decision making with the OWA operator and its application in investment management,” in IFSA-EUSFLAT Conference, Lisbon, Portugal, July 20-24. Conference Proceedings, 1364–1369.

Google Scholar

Merigó, J. M. (2011). A unified model between the weighted average and the induced OWA operator. Expert Syst. Appl. 38, 11560–11572. doi: 10.1016/j.eswa.2011.03.034

PubMed Abstract | Crossref Full Text | Google Scholar

Merigó, J. M. (2014). Decision-making under risk and uncertainty and its application in strategic management. J. Bus. Econ. Manag. 16, 93–116. doi: 10.3846/16111699.2012.661758

Crossref Full Text | Google Scholar

Merigó, J. M., and Casanovas, M. (2010). “The induced probabilistic OWA distance and its application in decision making,” in SpringSim '10: 2010 Spring Simulation Multiconference, San Diego, EEUU, April, 11-15. Conference Proceedings, 1–6. doi: 10.1145/1878537.1878609

Crossref Full Text | Google Scholar

Merigó, J. M., and Casanovas, M. (2011). Decision-making with distance measures and induced aggregation operators. Comput. Ind. Eng. 60, 66–76. doi: 10.1016/j.cie.2010.09.017

Crossref Full Text | Google Scholar

Milenkovic, L., Mastilovic, J., Kevrešan, Z., Bajic, A., Gledic, A., Stanojevic, L., et al. (2020). Effect of shading and grafting on yield and quality of tomato. J. Sci. Food Agric. 100, 623–633. doi: 10.1002/jsfa.10057

PubMed Abstract | Crossref Full Text | Google Scholar

Mishra, P. S., and Muhuri, S. (2021). Value assessment of existing architectural heritage for future generation using criteria importance through inter-criteria correlation and grey relational analysis method: a case of Odisha temple architecture in India. Curr. Sci. India. 21, 823–833. doi: 10.18520/cs/v121/i6/823-833

Crossref Full Text | Google Scholar

Montazar, A., and Snyder, R. L. (2012). A multi-attribute preference model for optimal irrigated crop planning under water scarcity conditions. Spanish J. Agric. Res. 10, 826–837. doi: 10.5424/sjar/2012103-484-11

Crossref Full Text | Google Scholar

Moreno, A., Chemisana, D., and Fernández, E. F. (2025). Energy performance and crop yield production of a semitransparent photovoltaic greenhouse. Appl. Energ. 382:125285. doi: 10.1016/j.apenergy.2025.125285

PubMed Abstract | Crossref Full Text | Google Scholar

Mutale-Joan, C., Redouane, B., Najib, E., Yassine, K., Lyamlouli, K., Laila, S., et al. (2020). Screening of microalgae liquid extracts for their bio stimulant properties on plant growth, nutrient uptake and metabolite profile of Solanum lycopersicum L. Sci. Rep. 10:1. doi: 10.1038/s41598-020-59840-4

PubMed Abstract | Crossref Full Text | Google Scholar

Narayanamoorthy, S., Annapoorani, V., Kang, D., and Ramya, L. (2019). Sustainable assessment for selecting the best alternative of reclaimed water use under hesitant fuzzy multi-criteria decision making. IEEE Access 7, 37217–137231. doi: 10.1109/ACCESS.2019.2942207

Crossref Full Text | Google Scholar

Notarnicola, B., Sala, S., Anton, A., McLaren, S. J., Saouter, E., and Sonesson, U. (2017). The role of life cycle assessment in supporting sustainable agri-food systems: a review of the challenges. J. Cleaner Prod. 140:399e409. doi: 10.1016/j.jclepro.2016.06.071

PubMed Abstract | Crossref Full Text | Google Scholar

Opricovic, S., and Tzeng, G. H. (2004). Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156, 445–455. doi: 10.1016/S0377-2217(03)00020-1

Crossref Full Text | Google Scholar

Peet, M. M. (2005). “Irrigation and fertilization” in Tomatoes, Crop Production Science in Horticulture, ed. E. Heuvelink (Wallingford: CABI Publishing), 178–198.

Google Scholar

Peng, X., and Huang, H. (2020). Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation. Technol. Econ. Dev. Eco. 26, 695–724. doi: 10.3846/tede.2020.11920

Crossref Full Text | Google Scholar

Pereira, L. S., Oweis, T., and Zairi, A. (2002). Irrigation management under water scarcity. Agric. Water Manage. 57, 175–206. doi: 10.1016/S0378-3774(02)00075-6

Crossref Full Text | Google Scholar

Phani, V., Gowda, M. T., and Dutta, T. K. (2024). Grafting vegetable crops to manage plant-parasitic nematodes: a review. J. Pest Sci. 97, 539–560. doi: 10.1007/s10340-023-01658-w

Crossref Full Text | Google Scholar

Phani, V., Khan, M. R., and Dutta, T. K. (2021). Plant-parasitic nematodes as a potential threat to protected agriculture: current status and management options. Crop Prot. 144:105573. doi: 10.1016/j.cropro.2021.105573

Crossref Full Text | Google Scholar

Podvezko, V. (2011). The comparative analysis of MCDA methods SAW and COPRAS. Eng. Econ. 22, 134–146. doi: 10.5755/j01.ee.22.2.310

Crossref Full Text | Google Scholar

Reyna-Ramírez, C. A., Fuentes-Ponce, M., Rossing, W. A. H., Groot, J. C. J., and López-Ridaura, S. (2025). Experimentation and model-based re-design for sustainable intensification of mixed crop-livestock smallholder farms in the Mixteca-Oaxaqueña region, Mexico. Agric. Syst. 224:104220. doi: 10.1016/j.agsy.2024.104220

Crossref Full Text | Google Scholar

Sadiq, F. K., Yaqub, M. T., Maniyunda, L. M., Alalwany, A. A. M., Abubakar, F., and Anyebe, O. (2025). Soil classification and land suitability evaluation for tomato cultivation using analytic hierarchy process under different land uses. Heliyon 11:e41681. doi: 10.1016/j.heliyon.2025.e41681

PubMed Abstract | Crossref Full Text | Google Scholar

Shi, Q., Sun, H., Timm, S., Zhang, S., and Huang, W. (2022). Photorespiration alleviates photoinhibition of photosystem i under fluctuating light in Tomato. Plants. 11:195. doi: 10.3390/plants11020195

PubMed Abstract | Crossref Full Text | Google Scholar

Sun, H., Wei, G. W., Chen, X. D., and Mo, Z. W. (2022). Extended EDAS method for multiple attribute decision making in mixture z-number environment based on CRITIC method. J. Intell. Fuzzy Syst. 43, 2777–2788. doi: 10.3233/JIFS-212954

Crossref Full Text | Google Scholar

Timmermans, G. H., Hemming, S., Baeza, E., van Thoor, E. A. J., Schenning, A. P. H. J., and Debije, M. G. (2020). Advanced optical materials for sunlight control in greenhouses. Adv. Optical Mater. 8:2000738. doi: 10.1002/adom.202000738

Crossref Full Text | Google Scholar

Turhan, A., Ozmen, N., Serbeci, M. S., and Seniz, V. (2011). Effects of grafting on different rootstocks on tomato fruit yield and quality. Hortic. Sci. 38, 142–149. doi: 10.17221/51/2011-HORTSCI

Crossref Full Text | Google Scholar

Ureña-Sánchez, R., Callejón-Ferre, Á. J., Pérez-Alonso, J., and Carreño-Ortega, Á. (2012). Greenhouse tomato production with electricity generation by roof-mounted flexible solar panels. Sci. Agric. 69, 233–239. doi: 10.1590/S0103-90162012000400001

Crossref Full Text | Google Scholar

Wang, F., Wu, N., Zhang, L., Ahammed, G. J., Chen, X., Xiang, X., et al. (2018). Light signaling-dependent regulation of photoinhibition and photoprotection in Tomato. Plant Physiol. 176, 1311–1326. doi: 10.1104/pp.17.01143

PubMed Abstract | Crossref Full Text | Google Scholar

Wohnera, B., Gabriela, V. H., Krenna, B., Krautera, V., and Tacker, M. (2020). Environmental and economic assessment of food-packaging systems with a focus on food waste. Case study on tomato ketchup. Sci. Total Environ. 738:139846. doi: 10.1016/j.scitotenv.2020.139846

PubMed Abstract | Crossref Full Text | Google Scholar

Xiao, L., Zhang, S. Q., Wei, G. W., Wu, J., Wei, C., Guo, Y. F., et al. (2020). Green supplier selection in steel industry with intuitionistic fuzzy Taxonomy method. J. Intell. Fuzzy Syst. 39, 7247–7258. doi: 10.3233/JIFS-200709

Crossref Full Text | Google Scholar

Xing, C., Yao, L., Wang, Y., and Hu, Z. (2022). Suitability evaluation of the lining form based on combination weighting–set pair analysis. Appl. Sci. 12:4896. doi: 10.3390/app12104896

Crossref Full Text | Google Scholar

Xu, T. Y., Liu, X. J., and Zhang, Z. L. (2020). Simplified likelihood estimation of ship total loss using GRA and CRITIC methods. Transport. Plan. Techn. 43, 223–236. doi: 10.1080/03081060.2020.1717147

Crossref Full Text | Google Scholar

Yager, R. (2006). Generalizing variance to allow the inclusion of decision attitude in decision making under uncertainty. Int. J. Approx. Reason. 42, 137–158. doi: 10.1016/j.ijar.2005.09.001

Crossref Full Text | Google Scholar

Yager, R., and Beliakov, G. (2010). OWA operators in regression problems, IEEE T. Fuzzy Syst. 18, 106–113. doi: 10.1109/TFUZZ.2009.2036908

Crossref Full Text | Google Scholar

Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE T. Syst. Man Cyb. 18, 183–190. doi: 10.1109/21.87068

Crossref Full Text | Google Scholar

Yager, R. R. (1996a). Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 11, 49–73. doi: 10.1002/(SICI)1098-111X(199601)11:1<49::AID-INT3>3.3.CO;2-L

Crossref Full Text | Google Scholar

Yager, R. R. (1996b). On the inclusion of variance in decision making under uncertainty. Int. J. Uncertain. Fuzz. 4, 401–419. doi: 10.1142/S0218488596000238

Crossref Full Text | Google Scholar

Yager, R. R., and Filev, D. (1999). Induced ordered weighted averaging operators. IEEE T. Syst. Man Cyb. 29, 141–150. doi: 10.1109/3477.752789

PubMed Abstract | Crossref Full Text | Google Scholar

Yazdani, M., Ariza-Montes, A., Arjona-Fuentes, J. M., and Radic, A. (2024). Cruise hotel sustainable supplier management using a grey-based decision support framework. J. Travel Tour. Mark. 41, 538–558. doi: 10.1080/10548408.2023.2285927

Crossref Full Text | Google Scholar

Yuan, H. T., Ma, X. J., Cheng, Z. N., and Kari, T. (2024). Dynamic comprehensive evaluation of a 660 MW ultra-supercritical coal-fired unit based on improved criteria importance through inter-criteria correlation and entropy weight method. Energies 17:1765. doi: 10.3390/en17071765

Crossref Full Text | Google Scholar

Zhao, Y. S., Li, P. F., Wang, T., Kang, Y., and Zhao, Y. B. (2022). “Equipment health assessment based on AHP-CRITIC dynamic weight,” in 41ST Chinese Control Conference (CCC). Hefei, China, Jul, 25-27 (Proceedings), 5841–5846. doi: 10.23919/CCC55666.2022.9902488

Crossref Full Text | Google Scholar

Keywords: economic criteria, social criteria, environmental criteria, pearson coefficient, agrovoltaic, photovoltaic energy, deficit irrigation

Citation: Brotons-Martínez JM and Cámara-Zapata JM (2025) The evaluation of performance for agroecological greenhouse tomato strategies by the CRITIC-OWA model. Front. Artif. Intell. 8:1599334. doi: 10.3389/frai.2025.1599334

Received: 24 March 2025; Accepted: 19 May 2025;
Published: 18 June 2025.

Edited by:

Ernesto Leon-Castro, Universidad Catolica de la Santisima Concepcion, Chile

Reviewed by:

Cristhian Uzeta, Autonomous University of the West, Mexico
Tanya Samantha Garcia Gastelum, Autonomous University of Sinaloa, Mexico

Copyright © 2025 Brotons-Martínez and Cámara-Zapata. 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.

*Correspondence: José Manuel Brotons-Martínez, am0uYnJvdG9uc0B1bWguZXM=

Disclaimer: 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.