A formalism for a general theory of subjective multi-domain indoor-environmental quality perception

Abstract

People can be asked to report their subjective appraisal of specific aspects or domains of indoor-environmental quality (IEQ) including thermal, visual, acoustic, and indoor air conditions in buildings. Specifically, subjective evaluations of these individual IEQ domains as well as the overall IEQ assessment can be obtained via constructs such as “satisfaction” or “comfort”. People can be also asked to provide their overall (or general) appraisal of IEQ. In this context, the present contribution poses the following question: Can people’s assessment of overall IEQ be predicted based on their assessments of individual IEQ aspects? This paper presents a theory and a related formalism to derive people’s overall satisfaction level with IEQ based on the application of weights to their domain-specific IEQ appraisals. Specifically, the theory postulates that domain-specific evaluations of IEQ conditions influence the resultant overall IEQ evaluation in a non-linear fashion, which cannot be fully captured via fixed weight assignments. As such, the weights are suggested not to be constants, but depend on the relative strength of the stimuli in a multi-domain indoor-environmental exposure situation. The paper outlines the concept behind and the elements of this “variable-weights” theory of subjective multi-domain IEQ perception and provides a formalism toward its operationalization. A path to the formalization of the theory is outlined and a preliminary empirical test of its performance is presented.

1 Introduction and background

Good indoor-environmental quality (IEQ) in buildings is important for inhabitants’ health, comfort, satisfaction, and productivity (Torresin et al., 2018; Zhao and Li, 2023). IEQ is typically specified in terms of criteria pertaining to distinct domains. Four such domains pertain to thermal, visual, acoustic, and indoor air quality. More recently, increased attention is being paid to the combined effects of these domains on people’s IEQ perception (Chinazzo et al., 2022). Whereas already the prediction of human responses to individual aspects of indoor-environmental conditions has been shown to be a difficult task, the prediction of the effects of combined multi-domain settings is even a considerably more complex challenge. Given this background, efforts in both fundamental and applied research communities display a rising interest in addressing the combined effects of multi-sensory exposure settings on people’s perception and evaluation of the said settings (Deroy et al., 2016; Guan et al., 2020; Berger and Mahdavi, 2021). These developments have been also tendentially reflected in recent research efforts in the IEQ field, including, but not limited to, an observable interest in the possibility of establishing multi-domain indicators of IEQ (Mahdavi et al., 2020). In this context, the relationship between domain-specific IEQ appraisals on the one hand and the appraisal of IEQ as a whole on the other hand is of central interest. Whereas there are arguably different possibilities to systematically relate perceptual assessment of individual IEQ domains to the genesis of an integrated evaluative response, the present contribution focuses on the exploration of the potential of a specific formalism. The motivation behind the pursuit of this specific formalism can be approached in terms of the following query: Can the overall IEQ appraisal be derived from multiple domain-specific appraisals, and can this be achieved through the use of a weighting-based formalism?

Weights are frequently applied in multiple fields in order to derive general quality or performance indicators based on scores assigned to a number of sub-categories. For instance, weights are routinely applied in assessment and specification procedures of the conjoint indicators of buildings’ quality, used, among other instances, in building rating and certification systems (Mahdavi et al., 2020). The approach thereby is to start with a set of numeric indicators from multiple sub-categories that are assumed to be constitutive of the quality indicator in the global category (Fathi and O’Brien, 2023; Tang et al., 2020). Indicator values in the sub-categories are then modified through assigned weights and subsumed into the total quality indicator’s value. The purpose of a weight assigned to a sub-category is to reflect the relative importance or effect of those sub-categories in relation to other sub-categories (Tran et al., 2023).

Note that weighting schemes used to derive pragmatic conjoint quality indicators in building rating and certifications systems are typically based on opinions of pertinent stakeholders, such as experts (e.g., planners, construction professionals, building scientists) and users (i.e., building occupants). Consequently, such schemes display considerable variations across different sources, categories, building typologies, and contextual circumstances (Rohde et al., 2020; Zalejska-Jonsson and Wilhelmsson, 2013). The scope of this variation is exemplified in Table 1, which entails numeric weighting factors quoted in literature to indicate the assumed relative importance of four IEQ domains (Danza et al., 2020; Fathi and O’Brien, 2023; Mahdavi et al., 2024).

Multiple approaches could be pursued to substantiate the weighting schemes for derivation of subjective multi-domain IEQ appraisals. One possibility would be to seek a deeper empirical understanding of the neurophysiological processes involved in the human perception of inherently complex multi-domain IEQ conditions. This could put the weighting schemes on a more solid ground: Instead of relying on mere opinions or subjective reports, weights would be based on perceptual processes involving non-linear interdependencies and cross-effects between multiple variables in multiple domains. Recent specialized scientific studies of inter-sensory perception in physiology and psychology have achieved considerable progress (Chaudhuri, 2010; Jesse and Massaro, 2010; McGurk and MacDonald, 1976; Thompson et al., 2005; 2010). However, the findings in such studies cannot be necessarily applied directly to practical problems pertaining to people’s subjective multi-domain IEQ appraisal. But there are other approaches and tools in experimental psychology that can be applied to multi-domain IEQ perception phenomena, including experimental studies. For instance, participants in controlled experiments can be subjected to different levels of indoor-environmental exposure in multiple domains. Thereby, their subjective assessments of IEQ can be captured via questionnaires and interviews. Using proper constructs and respective scales, participants can be queried regarding their evaluations of IEQ both in terms of single domains and in terms of their overall effect. The careful analysis of the findings of such multi-domain experimental studies and derivative weighting procedures can provide a more solid foundation for the development of a theory of multi-domain IEQ perception.

The main purpose of the present contribution is to introduce a specific formalism toward the operationalization of a general theory of multi-domain indoor-environmental quality perception. The kind of the formalism that is proposed here is suggested to represent a necessary condition for casting the theory in a format that could yield quantitative results and be thus testable in principle. Whereas a systematic verification of the theory requires a density of empirical data currently unavailable, a preliminary demonstration of the proposed formalism’s utility is illustrated using a limited set of empirical data. This provides thus the iterative refinement, calibration, and ultimately validation of the theory, as ongoing and future studies yield increasing quantities of observational data. Moreover, the proposed theory and the respective formalism can guide the direction and concentration of future empirical investigations pertaining to multi-domain IEQ perception.

2 A variable-weights approach to a theory of multi-domain IEQ appraisal

Let us assume people’s overall appraisal of IEQ can be anticipated based on their appraisal of a number of IEQ-related subcategories. As mentioned before, different paths could be pursued to aggregate domain-specific IEQ indicators into multi-domain indicators of the overall IEQ. One possibility to do this involves the assignment of weights to the domain-specific IEQ appraisals so as to reflect their relative influence. The objective thereby would be to anticipate people’s overall appraisal of a specific indoor-environmental setting based on their appraisals of individual (domain-specific) aspects of the same setting. To illustrate a process–and its underlying theoretical framework–to achieve this, consider the following approach:

Assume the value of a subjective indicator of the overall IEQ in a space (call it Q_T) is to be predicted based on the values of subjective appraisals of IEQ in n distinct domains (call them Q_i, with i from 1 to n) (see Equation 1). Assume the values are obtained for an IEQ appraisal construct using a Likert scale.

Assume further that, to obtain the value of Q_T, there is a function whose solution relies on assigning weights to individual domain indicators (call these w₁ to w_n). Expressed in terms of simple linear functions, and numerically normalizing both votes and weights (from 0 to 1), the general relationship between IEQ’s overall appraisal (Q_T) and its constituent domain-specific counterparts (Q_i) can be formulated as per the following equation (Equation 2):

Suppose a comprehensive empirical study of participants’ appraisal of both overall IEQ and domain-specific IEQ could be conducted for a specific exposure situation. This could yield a specific set of weights that would satisfy Equation 2 for this situation. However, this set of weights cannot be assumed to represent generally applicable values. Rather, it seems plausible to assume that, under a different combination of domain-specific exposure settings, a different set of weights could emerge. Hence, rather than treating weights as generally applicable constants, it would be more prudent to treat them as variables. This observation motivates the pursuit of a variable-weights formalism for a theory of subjective multi-domain IEQ appraisal.

A key requirement for generating such a formalism is to find a plausible relationship between the values of an IEQ sub-domain variable and the weights that should be assigned to it when attempting to derive the value of the overall IEQ construct. To this end, two conceptual propositions may be useful.

The first proposition, which is relevant to the theoretical underpinning of the present contribution, suggests that a negatively rated domain-specific IEQ variable is likely to exert a higher impact on people’s appraisal of the overall IEQ conditions, as compared to more favorably rated ones. In other words, when a specific aspect of the total IEQ leaves a comparatively more negative perceptual mark, it could disproportionately influence people’s overall judgment, acquiring thus a larger weight. There are in fact multiple theoretical and empirical treatments of (and evidence for) this circumstance. Rooting tendentially in the negativity bias, such treatments refer to phenomena such as the revenge and the one vote effects (Chang et al., 2023; Zhao and Li, 2023; Baumeister et al., 2001; Rozin and Royzman, 2001; Pellerin and Candas, 2004; Te Kulve et al., 2018; Tiller et al., 2010; Leaman and Bordass, 1999; Wu et al., 2020; Tang et al., 2022; Huang et al., 2012; Gilovich, 1983; Peeters and Czapinski, 1990; Pratto and John, 1991; Kim et al., 2017; Seyedrezaei et al., 2023; Guan et al., 2020).

The second proposition suggests that the functions relating different domain-specific variables to their respective weights would be different for different domains. It can be hypothesized that different functions would be required to map the relationship of votes (Q_i) and the primary (i.e., pre-normalization) weights for different IEQ domains (w_p,i), as indicated by the generic function in Equation 3.

The exact nature of these functions cannot be determined without sufficient empirical data. However, for illustrative purposes, the aforementioned propositions can be conceptually illustrated via Figure 1, namely, the dependency of the weights on the votes and the domain-dependency of the functions describing the relationship between weights and votes. Consequently, the x-axis of this figure is meant to represent the numeric value of a domain-specific construct, whereby lower values denote a negative appraisal and the positive values denote a positive appraisal. The y-axis of this figure represents the weights associated with the votes in distinct IEQ domains. The functions depict the assumed higher impact of negatively rated domain-specific IEQ variables on people’s appraisal of the overall IEQ conditions, whereby different domain-specific variables come with different correlation functions. The primary weight associated with each specific IEQ domain (Equation 3) is suggested to be a function of the appraisal pertaining to that domain.

FIGURE 1

The effective (normalized) weights (w_i) in Equation 2 can be derived based on primary (pre-normalization) weights (w_p,i) using Equation 4.

Figure 1 and Equations 1–4 exemplify a formalism for the proposed variable-weights approach to a theory of multi-domain IEQ appraisal. To summarize, the theory suggests that people’s overall appraisal of IEQ (as denoted in terms of Q_T) can be predicted based on the weighted aggregates of domain-specific IEQ appraisals (Q_i) (see Equation 2). However, the weights are not conceived as constants, but are assumed to depend on the relative values of the domain-specific appraisals. This means that lower satisfaction votes result in larger weights of the respective IEQ domain. A simplified representation of this dependency in terms of linear functions is entailed in Figure 1.

3 A path to the operationalization of the theory

To operationalize the proposed theoretical framework, consider the following scenario. People are asked to report the degree of their satisfaction with indoor-environmental conditions. This can be done, for instance, using the perceived “satisfaction” construct and a six-point Likert scale (ranging from “highly dissatisfied” to “highly satisfied”) to obtain its values. Suppose we query, in the course of an experimental study, participants’ degree of satisfaction with four key dimensions of indoor-environmental exposure, namely, thermal (Q_TH), visual (O_VI), acoustic (Q_AC), and air quality (Q_AQ) conditions in a specific space and at a specific time. Simultaneously, we record people’s overall (aggregate) level of satisfaction (Q_T) with the same settings. According to the proposed theory, it would be possible to predict participants’ overall satisfaction level based on the weighted aggregation of the domain-specific IEQ assessments. This of course would require knowledge of applicable numeric values of the weights. Experimental studies involving a sample from a properly defined population can yield, in principle, such values at the group level (i.e., for the population that the sample of participants is meant to represent and for the conditions that the experimental study covers). Assuming the availability of these weights, an individual’s expected overall assessment of IEQ can be estimated based on Equation 5. Thereby, w_TH, w_VI, w_AC, and w_AQ denote the weights that would have to be applied to domain-specific satisfaction votes of the individual j in order to obtain that individual’s assessment of the overall IEQ conditions (Q_T,j).

In the course of such studies, participants’ reported votes can be used to assign, to each participant, a respective function. For participant j, the formulation of this function is given in Equation 5.

A possible approach to derive the weights based on the result of empirical studies is to construct a system of equations (see Equation 6), whereby, w₁, w₂, w₃, and w₄ represent weights to be applied to subjective votes in different IEQ domains (expressed as coefficients Q_TH,j, Q_VI,j, Q_AC,j, Q_AQ,j) in order to arrive at the values of the overall (aggregate) evaluation scores (Q_T,j). Each row of this matrix represents one participant’s appraisal of the four IEQ domains as well as the overall IEQ appraisal. By solving the matrix associated with this set of equations, the values of the weights corresponding to domain-specific appraisals could be obtained. Of course, in any experimental study with a reasonable number of participants the number of equations in this system would be much larger than the number of unknowns, thus resulting in a largely overdetermined matrix. As such, proper methods (e.g., the least square method) have to be applied in order to obtain best approximations to satisfy the system of equations (Menke, 2012; Chen, 2018).

Assuming we can repeat the experiments for different combinations of indoor-environmental conditions (i.e., combinations of different intensity levels of domain-specific exposure parameter), the theory suggests that we would obtain different sets of values for the weights from a multitude of matrices each representing a distinct combination of domain-specific exposure settings. Moreover, the theory implies that the more negatively an IEQ dimension is appraised by the participants, the larger would be the weight of that dimension in the formation of participants’ overall judgment of IEQ conditions. Consequently, a set of functions can be established that would relate participants’ votes and the respective weights (see Figure 1 for an illustrative depiction of such functions). Finally, the primary weights (w_p) derived based on these functions (see Equation 3), can be normalized using Equation 4 to predict any individual’s overall appraisal of overall indoor-environmental conditions based on their appraisal of the domain-specific dimensions of IEQ.

Conducting the kinds of experiments required for the operationalization of the proposed theory is of course not a trivial matter. As such, the collection of sufficient and reliable data remains a challenge. However, assuming the availability of some measure of applicable data, one could derive the weights such that, if applied to domain-specific votes, they would yield approximations of the overall IEQ appraisals. Given the aforementioned lack of a sufficiently rich empirical data set, a comprehensive verification test of the proposed theory and the variable-weights formalism cannot be provided at this stage. However, one can attempt a preliminary examination of the potential and limitations of the proposed theory and formalism based on available empirical information on people’s appraisal of both domain-specific and general aspects of indoor-environmental conditions. Such an attempt is described in the following section of the paper. It is important to note that the discussion in this section cannot (and is not meant to) provide evidence for the theory’s validity. Rather, it is intended to offer an initial plausibility test of the theory and inform ongoing and future research efforts in this area.

4 Exploring the potential for empirical examination of the theory

As with any scientific theory, the proposed variable-weights approach to a theory of multi-domain IEQ appraisal requires empirical scrutiny to establish credibility. However, as previously alluded to, a robust empirical examination of the theory would require a rich experimental data set that is currently unavailable. This is due to the relatively small number and limitations of the relevant studies (Chinazzo et al., 2022; Schweiker et al., 2020; Martínez-Muñoz et al., 2025a). Nonetheless, the working of the formalism and a principal path to its future development and calibration can be illustrated on a provisional basis using available data. Moreover, this illustrative empirical treatment of the formalism can also inform efforts toward design and execution of the kinds of experimental strategies that would adjust, refine, and ultimately validate the theory in the long run.

4.1 A demonstrative empirical data set

To illustrate this possibility, consider an experimental data set generated during a recent collaborative project pertaining to potential perceptually relevant cross-domain effects of various IEQ variables. One of the main objectives of this research project was to explore potential cross-effects of visual and acoustic dimensions of the exposure situation in an office space setting. Information about this collaborative project and the specific empirical study have been referred to in other publications (Martínez-Muñoz and Mahdavi, 2025b). Hence, in this paper we provide only a brief description of the study to provide the context for the empirical data set used in the present study.

Individual sessions were conducted in a real office at Graz University of Technology (TU Graz, Austria). The experiments received prior ethical approval from the Ethics Committee of TU Graz (datenschutz.tugraz.at), and participants provided written informed consent prior to participation. During these sessions, participants were exposed to specific indoor-environmental conditions, and were asked to evaluate these conditions while engaging in computer-based tasks. Each participant spent about 90 min at the workstation for the experiments. The total number of participants was 78, of whom 63% were female and 37% male. The age range of participants was between 22 and 30 years old. None of the participants displayed any health issues. Specifically, none reported as having any noteworthy visual or hearing impairments.

The evaluations were obtained for different visual and acoustic exposure combinations. The visual component of exposure included four different intensity levels of a luminaire positioned in the participants’ field of view, resulting in two ranges of glare intensity in the viewing field. The high visual exposure corresponds to treatments with UGR >20, whereas the low visual exposure corresponds to UGR <20. Note that UGR (Unified Glare Rating) is a measure of the presence of glare in the viewing field (Sorensen, 1987; CIE, 1995). The acoustic component of the exposure included two acoustic conditions in terms of sound pressure levels. Whereas one setting involved relatively low intensity exposure (i.e., background sound with an equivalent sound pressure level of 40 dB(A)), the other was of rather high intensity (i.e., office activity noise or vehicular traffic noise, both with an equivalent sound pressure level of 60 dB(A)). The two visual settings and two acoustic settings yielded the aforementioned four combinations (see Table 2). Thermal and air quality conditions were not actively controlled. However, the ranges of the physical variables associated with these two factors (mainly temperature and CO₂ concentration) were continuously monitored.

Occupants’ evaluations of multiple IEQ items were recorded using various Likert scales. For the purpose of the present treatment, the focus is on participants’ reported satisfaction levels, which were obtained using a six-point scale with the semantic descriptors “very dissatisfied”, “dissatisfied”, “slightly dissatisfied”, “slightly satisfied”, “satisfied”, “very satisfied”. This scale was used to report satisfaction levels with the four aforementioned IEQ domains (thermal, visual, acoustic, and air quality) as well as for the aggregate category “overall satisfaction” with the prevailing IEQ conditions.

4.2 Matrix-based derivation of weights

The initial set of reported votes was subjected to a filtering procedure relevant to data quality and adequacy. This resulted in a total number of 189 quintuple votes (four IEQ domain votes plus the overall vote) and, with the exception of the A_LV_H exposure category, in a statistically meaningful number of votes in the exposure sub-categories (see Table 3). The votes were supplied to the previously mentioned system of equations (Equation 6) as coefficients Q_TH,i, Q_VI,i, Q_AC,i, Q_AQ,i, and Q_T,i. Solving the matrix associated with this system resulted in the estimated values of the weights for the four IEQ domains as summarized in Table 3. To this end, weights were derived for the entirety of data, as well as separately for the four subsets specified in Table 3.

The results shown in Table 3 warrant a number of relevant observations regarding the key underlying assumption of the proposed theory. A first obvious observation points to the fact that the relative values of weights in the four IEQ domains vary considerably depending on the relative strengths of the exposure variables. This underlines the assertion that predictions of people’s overall appraisal of IEQ cannot be based on a set of constant weights. Rather, it is likely that such weights are variable and their variability is probably related to how individual IEQ domains are perceived. Pursuing further this line of reasoning, a key question may be posed as follows: Why do the visual and acoustic weights in Table 3 display significantly larger values, as compared to those associated with thermal and air quality aspects? Obviously, the weights in Table 3 for the four IEQ domains display a distinct disparity. This can be further highlighted if we focus on the two data sets that involved either a high-intensity visual exposure (A_LV_H) or a high-intensity acoustic exposure (A_HV_L). As illustrated in Figure 2, the weight for visual domain is significantly higher in the former case, whereas the weight for the acoustic domain is significantly higher in the latter case. An explanation for this circumstance can be provided, if we recall that in the underlying experiments, thermal and air quality conditions were not manipulated and remained largely in ranges that most participants considered satisfactory. The visual and acoustic conditions, however, were subject to controlled manipulations and involved high-intensity, and negatively perceived ranges. This seems to confirm the proposition that when a specific aspect of the IEQ in a specific setting is perceived as distinctly more unsatisfactory than the other aspects, it is more likely to exert a disproportionately larger influence on the appraisal of IEQ as a whole.

FIGURE 2

4.3 Derivation of functions relating weights to votes

These observations in fact advise against the derivation of the value of a perceived total IEQ indicator based on a function of multiple single-domain evaluations to which one would simply assign a set of fixed weights. Rather, it appears to suggest that an effective formalism meant to yield such a total quality prediction should conceive weights themselves as variables, whose values would depend, possibly in a non-linear fashion, on the relative strength of exposure variables from different domains and the corresponding domain-specific subjective evaluations. In fact, Table 3 and Figure 2 clearly demonstrate the variability of weights and their dependence on exposure constellations. To further explore the potential for a formal operationalization of the proposed theory, it would be beneficial to focus on the relationship between subjective appraisals of individual IEQ domains and the corresponding weights. Such a relationship is illustrated in Figure 3, using the data from the above-mentioned experimental study. In this Figure, the y-axis and the x-axis represent the mean values of weights and the participants’ votes respectively, as averaged over the respective categories. Thereby, each point in this Figure represents the participants’ mean satisfaction votes obtained under the same exposure configuration. Thereby, to make the comparisons easier, participants’ original numeric votes are mapped onto a scale ranging from 0 to 1.

FIGURE 3

Broadly speaking, the relationships depicted in Figure 3 suggests that more unfavorable evaluations of conditions in a domain result in larger weights. This is specifically observable in case of the visual and acoustic exposure components, for which the empirical data covered a larger range of the applicable metrics. As such, the tendency captured via these functions is consistent with the previously stated supposition that if a domain-specific variable is perceived as unsatisfactory, it could play a disproportionately larger role in the emergence of people’s view of the total perceived IEQ, which in turn could translate into a larger weight. As far as the thermal and indoor air quality domains are concerned, one can observe a grouping or proximity of votes and weights. The votes are consistently between 0.6 (“slightly satisfied”) and 0.8 (“satisfied”) and the corresponding weights are consistently below 0.2. This circumstance is consistent with the specific circumstances of the experimental setting mentioned at the outset: Thermal and air quality conditions, while not actively controlled, were generally in an acceptable range and did not involve extremes. In contrast, the actively controlled visual and acoustic conditions involved both low-intensity and high-intensity exposure settings. Needless to say, future–more comprehensive–empirical efforts aimed at the examination of the theory’s validity would require a substantially more expansive data base, including a diversity of populations, building typologies, exposure settings, and contextual circumstances.

To further pursue the operationalization of the theory, the general relationship postulated via Equation 3 can be formulated, in concrete terms, using the empirical data depicted in Figure 3. This possibility is depicted in Figure 3 in terms of four exponential functions, which are meant to represent the dependency of weights (w) in each of the four domains on participants’ respective mean votes (v). Note that these functions (see Equations 7–10) are derived as illustrative domain-specific instantiations of Equation 3 under the assumption that they all converge to the maximum weight value of one when the votes converge to the minimum value of zero.

4.4 A preliminary comparison of calculated and reported IEQ evaluations

These functions are derived mainly for illustration of the proposed operationalization formalism and are not suggested to be of general validity, given the insufficient quantity, spread, and representativeness of the data used for their derivation. Nonetheless, a preliminary assessment of their predictive performance can be undertaken using available data from the aforementioned experimental study. To this end, Equations 7–10 were used to calculate the total IEQ evaluations based on votes in the exposure sub-categories. For this purpose, participants’ votes in the four IEQ sub-categories were entered in the matrix (Equation 6) to derive the respective preliminary weights. Subsequent to the normalization of these preliminary weights using Equation 4, the resulting normalized weights were used as independent variables in Equation 7 to calculate participants’ resulting votes. The calculated values were then compared with the actual votes. The calculated and reported values are plotted in Figure 4, which also entails a regression function (with a Pearson correlation coefficient of 0.63).

FIGURE 4

Calculated and reported votes were also contrasted using a confusion matrix (see Table 4), considering the fact that, whereas reported votes are obtained in terms of an ordinal satisfaction scale with six discrete values, the calculated ones yield real numbers. Rounding the latter, they can be also arranged in terms of an ordinal scale, hence facilitating a direct comparison with reported values. According to Table 4, reported and calculated votes display a perfect categorical match in 55% of the cases. In 14% of the cases, the calculated values were one step lower in the six-point satisfaction scale than the reported ones and in 26% of the cases, they were one step higher. In 5% of the cases the calculated values were two steps higher than the reported ones. When evaluating these results, it is important to bear in mind that the exponential functions used for calculations were constructed on the basis of a sparse data set and involved–particularly in the case of thermal and air quality functions–rather speculative extrapolations. Provided the availability of sufficient empirical data, distinct variable-weight function could be derived addressing the variance in populations, building types, and contextual settings. Notwithstanding these constraints, the empirically-based matrix-based derivation of domain-specific weights for specific exposure configurations and the formalism involving exponential functions that establish relationships between participants’ vote and resultant relative weights, appear to constitute a promising approach toward the operationalization, verification, and application of the proposed theory of multi-domain IEQ evaluation.

5 Conclusion

This paper introduced a formalism for the operationalization of a variable-weights theory of multi-domain indoor-environmental quality perception. The proposed theory and associated formalism allow for the investigation of the influence of people’s perception of individual (domain-specific) aspects of indoor-environmental conditions on the formation of their overall appraisal of those conditions. One possibility to effectuate the aggregation of domain-specific evaluations of IEQ into an overall assessment involves the application of weighting procedures. For instance, building certification and rating systems frequently apply weights to different quality categories, as means of deriving a single-number total (or conjoint) quality score. Such procedures have been also applied to IEQ evaluation. However, the manner they approach numeric weights should not be conflated with the kind of weights explored in the present contribution. Specifically, the proposed theory involves two key suppositions: Firstly, the weights are not conceived as constants, but–as the “variable-weights” attribution suggests–as variables whose values depend on the specific configurations of particular indoor-environmental exposure settings. Secondly, leaning on the notion of negativity bias, it is assumed that, if a domain is perceived as less favorable than others, it would exert a larger influence on the people’s overall IEQ evaluation, acquiring thus a larger weight. As such, different configurations of indoor-environmental exposure variables are expected to impact the resulting aggregate perception of IEQ in a functionally non-linear manner, necessitating thus a multiplicity of context-dependent weights.

To demonstrate the potential of the proposed formalism for the operationalization of the variable-weights theory, an available set of experimental data provided a point of entry. This data pertained to participants’ concurrent evaluation of four dimensions of indoor-environmental conditions in an office setting (thermal, visual, acoustic, air quality) as well as the overall IEQ appraisal. The targeted variation of the visual and acoustic dimensions of the environment resulted in four distinct exposure configurations. Using a matrix-based formalism, participants’ votes (obtained using the satisfaction construct and a six-point scale) were mapped onto a set of weights. Moreover, the relationship between the votes and the resultant weights were exploited to generate four exponential functions for each of the four domains. These exploratory functions allow, in principle, to compute, for any vote in a domain, the respective weight. Once weights are derived for each of the four domains, they can be normalized and applied to the respective votes of any individual to predict his/her total IEQ appraisal.

Given the limited data availability, a comprehensive empirical assessment of the proposed theory is not feasible at this stage. Nonetheless, available data was used to demonstrate both the formalism for the operationalization of the theory as well as to conduct a preliminary examination of its general plausibility and application viability. In the course of this preliminary test, participants’ evaluations of the overall IEQ conditions using a six-point overall IEQ satisfaction scale were calculated following the formalism and using the knowledge of their domain-specific votes. Compared to the actual (reported) overall votes, the calculated votes displayed an exact matching degree of 55%. In 40% of the cases, calculations matched the reported data with one scale step deviation. Additional tests using a larger and more comprehensive set of empirical data are needed to arrive at more reliable and representative functions for the derivation of the variable weights required for a systematic verification and practical application of the theory. The limitations notwithstanding, future research efforts can arguably remedy the obstacles to a comprehensive testing of the theory, as its transparent logic and structure of the associated formalism allows for an independent examination by parties in possession of applicable empirical data sets. As such, the performance of the derived exponential functions that map satisfaction votes in a specific domain to the respective weight may be expected to be improved once a richer repository of experimental data becomes available. Independent of the issue of predictive accuracy, the theory and the formalism developed for its operationalization are also of conceptual value and practical relevance, as they have the potential to contribute to the construction of a coherent conceptual model for the understanding of integrative evaluation processes of indoor-environmental conditions in buildings.

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