Multiple Criteria Assessment of Insulating Materials with a Group Decision Framework Incorporating Outranking Preference Model and Characteristic Class Profiles

This paper presents a group decision framework for evaluating sustainability of the insulating materials to retrofit traditional rural buildings. The importance of this research derives from the previous studies on both retrofitting solutions tailored to traditional rural buildings as well as judging an overall desirability of coating materials (see, e.g., Krarti 2015; Fabbri et al. 2012; Ma et al. 2012; Yung and Chan 2012; Martínez-Molina et al. 2016). These studies prove that energy efficiency and thermal comfort are crucial for the maintenance of historic buildings.

The context of the study is that of a typical farmhouse in central Italy. The incorporated building model derives from the analysis of over 800 farmhouses surveyed by the census of the scattered rural buildings of the municipality of Perugia (Umbria region). The high landscape values of traditional buildings and the legislation about their preservation prevent external alterations (Mazzarella 2015). Therefore, the most viable solutions are to intervene on the roof of these structures, increasing their thermal inertia with coating materials (Verbeeck and Hens 2005; Kumar and Suman 2013; Taylor et al. 2000).

We comprehensively evaluate the materials for the roof insulation by considering economic, social, and environmental viewpoints. For this purpose, we incorporate a life cycle costing (LCC) approach, a life cycle assessment (LCA), and a dynamic thermal simulation for the evaluation of energy savings and thermal comfort. As such, we aim at identifying the materials that guarantee the indoor thermal comfort, at the same time reducing the consumption of resources in their entire life cycle as well as maintaining cultural and historic significance of the buildings. In this perspective, we differentiate from the vast majority of previous studies concerning coating materials which incorporate a mono-disciplinary approach (Copiello 2017).

To provide an overall sustainability assessment of coating materials, we incorporate Multiple Criteria Decision Analysis (MCDA). MCDA offers a diversity of approaches designed for providing the decision makers (DMs) with a recommendation concerning a set of alternatives evaluated in terms of multiple conflicting points of view. Few applications of MCDA methods for the evaluation of building materials, which are reported in the literature (Ginevicius et al. 2008) deal mainly with the environmental sustainability of materials (Papadopoulos and Giama 2007; Khoshnava et al. 2016). Some combinations of LCA and MCDA were considered by Santos et al. (2017) and Piombo et al. (2016). Applications which included both LCC and LCA for the definition of criteria to be used in MCDA are still rare (Piombo et al. 2016). Decision analysis methods used in the above-mentioned studies involved different variants of AHP (Motuziene et al. 2016; Khoshnava et al. 2016), PROMETHEE II (Kumar et al. 2017), Weighted Sum, TOPSIS (Čuláková et al. 2013), VIKOR, and COPRAS (Ginevicius et al. 2008).

From the viewpoint of MCDA, our study differs from the aforementioned ones in terms of the following major aspects:The remainder of the paper is organized in the following way. In the next section, we review the existing group decision making methods for multiple criteria sorting. Section 3 describes a three-stage decision aiding method that has been used to evaluate the insulating materials while taking into account preferences of a group of stakeholders. Section 4 exhibits comprehensive results of multiple criteria assessment of the insulating materials. The last section concludes.

The objective of the case study presented in this paper is to give an easily interpretable comprehensive assessment of the insulating materials’ sustainability. This is achieved by assigning them to a set of pre-defined and ordered decision classes based on their performances on multiple criteria (Kadziński et al. 2015b). While computing the sorting recommendation, we account for the preferences of a group of experts and stakeholders. This requires implementation of a group decision making framework.

As real-world situations often involve multiple stakeholders, some methods have been proposed to support groups in making collective sorting decisions (Daher and Almeida 2010). These approaches can be distinguished at different levels. In particular, they differ in terms of a preference model employed to represent preferences of the DMs. Furthermore, an underlying classification rule may involve analysis of a single preference model instance or all sets of parameters compatible with the DMs’ preference information. Moreover, sorting methods can be divided with respect to the level on which individual viewpoints are aggregated (Dias and Climaco 2000). Finally, some approaches account for the importance degrees of the involved DMs, while other methods assume that all DMs play the same role in the committee.

Among multiple criteria sorting group decision methods, outranking-based approaches are prevailing. Most decision support systems in this stream incorporate Electre TRI-B (Yu 1992; Roy 1996). For example, Dias and Climaco (2000) proposed an approach that admits each DM to specify imprecise constraints on the parameters of an outranking model, then exploits a set of compatible parameters using robust assignment rule, and finally aggregates individual perspectives in a disjunctive or conjunctive manner (thus, not accounting for the DMs’ powers). The former accepts an assignment if it is justified by at least one DM, whereas the latter confirms some classification only if it is consistent with the preferences of all DMs. In this way, a group may agree on some result even if its members do not share the same model parameters. This idea was extended by Damart et al. (2007) to an interactive preference disaggregation approach that accepts assignment examples provided by different DMs. The method incorporates robustness analysis by deriving for each DM the possible class assignments (confirmed by at least one compatible preference model instance) and guides the group on sorting exemplary alternatives by exhibiting the levels of consensus between the DMs. Analogously, Shen et al. (2016) developed an adaptive approach under intuitionistic fuzzy environment that allows to reach a classification with an acceptable individual and group consensus levels. Moreover, de Morais Bezerra et al. (2017) enriched Electre TRI-B with the tools for visualizing the comparison of individual results and procedures for guiding the changes of model parameters for deriving a better consensus.

Furthermore, Jabeur and Martel (2007) proposed a framework, which derives a collective sorting decision at the output level from the individual non-robust classifications by additionally accounting for the relative importance of group members. Then, Morais et al. (2014) used a stochastic variant of Electre TRI-B, called SMAA-TRI, to consider uncertainty in criteria weights and to derive for each DM the shares of the relevant parameter vectors that assign a given alternative to a certain category. An overview of thus obtained individual results leads to a collective recommendation. Conversely, Cailloux et al. (2012) employed assignment examples provided by multiple DMs for reaching an agreement at the input level. In particular, they proposed some linear programming models for deriving a joint set of boundary class profiles and veto thresholds.

As far as outranking-based sorting approaches incorporating a model typical for PROMETHEE are concerned, Nemery (2008) extended the FlowSort method to group decision making. His proposal derives an assignment for each alternative from its relative comparison (strength and weakness) against the boundary or central class profiles specified by each individual DM. A similar idea was implemented by Lolli et al. (2015) in FlowSort-GDSS. The underlying procedure derives class assignments by comparing comprehensive (global) net flows of alternatives and reference profiles. The proposed sorting rules distinguish between scenarios in which analysis of the individual assignments leads to either univocal or non-unanimous recommendation. Although the viewpoints of different DMs are aggregated at the output level, the method defines some consistency conditions on the preference information (in particular, reference profiles) provided by the individual DMs.

The majority of existing value-based approaches derive a sorting recommendation incorporating robustness analysis and not differentiating between the roles played by the DMs. In particular, the \(\hbox {UTADIS}^\mathrm{GMS}\)-GROUP method (Greco et al. 2012) accounts for the assignment examples provided by each DM and derives collective results that concern two levels of certainty. The first level refers to the necessary and possible consequences of individual preference information, which is typical for Robust Ordinal Regression (ROR) (Greco et al. 2010; Kadziński et al. 2015b). The other level is related to the necessity or possibility of a support that a particular assignment is given in the set of DMs. This method was further adapted by Liu et al. (2015) to account for the uncertain evaluations represented with the evidential reasoning approach, to provide some measures on the agreement between the DMs, and to derive a collective univocal assignment.

Conversely, Kadziński et al. (2013) aimed at a joint representation of assignment examples provided by all DMs by a set of additive value functions and investigating the necessary and possible consequences of applying the latter on the set of alternatives. When there is no value function compatible with preferences of all DMs, some linear programming techniques can be used to remove a minimal subset of inconsistent assignment examples. A similar approach was proposed by Cai et al. (2012), though additionally accounting for the DMs’ priorities. The latter ones intervene in the selection of a representative value function and in resolving inconsistency in the provided assignment examples. These priorities are updated with the progressive preference elicitation process to reflect the preciseness, quantity and consistency of the example decisions supplied by each DM.

Finally, when it comes to using “if ...then ...” decision rules for representing preferences of the DMs, one proposed various extensions of the Dominance-based Rough Set Approach (DRSA) (Greco et al. 2001). These accept preference information in form of individual assignment examples. First, Greco et al. (2006) introduced some concepts (e.g., multi-union and mega-union) related to dominance with respect to minimal profiles of evaluations provided by different DMs. Then, Chen et al. (2012) proposed to aggregate the recommendations suggested by individual linguistic decision rules into an overall assignment be means of a Dempster–Shafer Theory. The crucial concepts incorporated in the DRSA sorting method proposed by Sun and Ma (2015) are a dominance relation on the set of multiple sorting decisions (each provided by an individual DM) and a multi-agent conflict analysis framework. Furthermore, Chakhar and Saad (2012) and Chakhar et al. (2016) illustrated how to combine individual approximations of class unions and derive collective decision rules that permit classification of all alternatives in a way consistent with the judgments of all DMs. These approaches measure the contribution of each expert to the collective assignment in terms of the individual quality of classification. Finally, Kadziński et al. (2016) adapted the principle of ROR to a group decision framework with DRSA, thus considering all sets of rules compatible with the individual assignment examples and combining their indications only at the output level.

In this paper, we propose an outranking-based group decision approach that incorporates Electre TRI-rC. Thus, it derives the assignments by comparing alternatives with the characteristic class profiles rather than with the boundary profiles as in Electre TRI-B. The basic procedure we use takes into account a single preference model instance (incorporating criteria weights derived from the SRF procedure) for each DM and aggregates the individual viewpoints at the output level. While still aggregating the preferences at the output level, we extend the basic framework to offer results of robustness analysis with multiple sets of parameters compatible with the DMs’ value systems. Additionally, we propose a new algorithm for constructing a group compromise ranking of criteria, hence offering aggregation of the individual viewpoints also at the input level. At all stages, we assume that the involved stakeholders have the same importance degrees. Moreover, instead of providing precise assignments, our framework offers acceptability indices indicating the support that is given to the assignment of each alternative to various classes by different DMs and/or preference model instances compatible with their preferences.

This section describes a three-stage multiple criteria decision analysis method that has been used to evaluate the insulating materials while taking into account preferences of a group of stakeholders. Firstly, we discuss the Electre TRI-rC method (Kadziński et al. 2015b) that has been employed to assign the materials to a set of pre-defined and ordered classes. It incorporates the SRF procedure to compute the criteria weights (Figueira and Roy 2002). The method has been extended to a group decision setting to derive for each material some group class acceptability indices, which indicate the proportion of stakeholders that accept an assignment of the material to a given class. Secondly, we have adapted Stochastic Multi-criteria Acceptability Analysis (SMAA; Lahdelma and Salminen 2001; Tervonen and Figueira 2008; Tervonen et al. 2007) to the context of Electre TRI-rC and SRF procedure. It has been used to conduct robustness analysis (Roy 2010) for the results obtained in the first part, i.e., to validate their certainty while avoiding the arbitrary choice of criteria weights, which is conducted by the SRF procedure. Thirdly, we have proposed an algorithm for constructing a group compromise ranking of criteria based on the orders provided by the individual DMs. This ranking of criteria has been used as an input for SMAA to offer yet another view on the stability of computed results.

Let us use the following notation (Kadziński et al. 2015a):

The study aims at evaluating overall sustainability of coating materials used in buildings retrofitting. We consider 13 materials listed in Table 2 (they are denoted by \(A=\left\{ {a_1 ,a_2 ,\ldots ,a_{13} } \right\} )\). All materials having a thickness of 15cm were placed internally on the roof of a model building typical for central Italy, and evaluated from the socio-economic and environmental viewpoints. The six relevant criteria which have been used to assess the materials are: hour of discomfort (\(g_1 \); DH),\(\hbox {CO}_{2}\) avoidance (\(g_2\)); Net Present Value (\(g_3\); NPV), human health (\(g_4\)); ecosystem quality (\(g_5\)), and consumed resources (\(g_6\)). In what follows, we explain their meaning.

Discomfort degree Hour (\(g_1 \); the less, the better) evaluates a thermal performance of a building on an annual basis (CEN 2007) in accordance with the EN 15251 standard. Thus defined, it serves as a measure of comfort. The performance on \(g_1 \) is quantified as an overall time during which the temperature falls outside the second comfort category that was considered in the study (Carlucci and Pagliano 2012), and then weighing it by how much the limit has been exceeded. For this purpose, we have used the following equation:where \(CC_2 \) is the lower or upper limit of the assumed comfort category, \(OT_i \) is the operative temperature at hour ì, and the multiplier \(\frac{10}{60}\) refers to an employed time step of 10 minutes.

\(\hbox {CO}_{2}\) avoidance (\(g_2 \); the more, the better) measures the energy saved during the building life by using a particular insulating material when compared to the case of no insulation in the following way:where ES is the estimated Energy Saved in GJ at time t with a time horizon of 25 years, 277.78 is a conversion factor to GJ in kWH, while 406.31 is the conversion factor for Italy from kWH to kg of \(\hbox {CO}_{2}\) per year (EIA, 2015). Therefore, the \(\hbox {CO}_{2}\) avoided refers only to the use phase, which is not considered in the LCA study.

Net present value (\(g_3\); the more, the better) is the difference between the present values of cash outflows and inflows. On one hand, the outflows involve Primary Energy Input (PEI) cost, installation cost I at time t = 0, and the dismissing cost \(EL_T \) after the lifespan T of the investment (25 years). On the other hand, the inflows refer to the Cost of Energy Saved \(ES_t \) in different time periods t. Overall, we have computed NPV as follows:where i is the discount rate. For a detailed justification of this measure, see Menconi and Grohmann (2014). Thus defined, NPV can be seen as an outcome of Life Cycle Costing, which is an economic methodology for assessing the profitability of using different alternatives by taking into account the costs they incur at different stages of a life cycle (e.g., construction, operations, and maintenance).

For the assessment of environmental impacts, we have used the Eco-indicator 99 method (Goedkoop and Spriensma 2001) implemented in the SimaPro software (Product Ecology Consultants 1990). The method aggregates the results of Life Cycle Assessment into a set of parameters that can be interpreted as damage categories. In general, LCA is useful for identifying the environmental implications of a given alternative through the quantification of consumed resources (e.g., energy, raw materials, water) and related emissions (e.g., emissions into the air, water and soil, waste and co-products) (Paolotti et al. 2017). We used the following three environmental Eco-indicators expressed on a dedicated point scale:The LCA focused on the production phase, starting from the production of a raw material to the obtaining of its complete version. We omitted the use and disposal phases, hence implementing an LCA “from cradle to gate” (Paolotti et al. 2016). All the impacts were calculated considering a functional unit of 1 m\(^{3}\) of insulating material.

The performances of 13 insulating materials with respect to 6 criteria are provided in Table 2. For all materials but hemp fibres, Ecoinvent Database (Ecoinvent 2010) was used as a source of foreground and background data related to both production and assembly processes as well as to the transport, electricity and fuel consumption. Instead, for the hemp processes the underlying data was derived from Zampori et al. (2013).

The objective of the case study is to give an easily interpretable comprehensive assessment of the materials’ sustainability. This is achieved by assigning them to a set of three pre-defined and ordered classes: \(C_1\) (low sustainability), \(C_2\) (medium sustainability), and \(C_3\) (high sustainability).

The study involved elicitation of preferences from the two groups of stakeholders. On one hand, a characteristic profile \(b_h\) for each class \(C_h\), \(h=1,2,3\), has been collectively specified by the experts from the university-based engineering team specialized in the materials and retrofitting of rural buildings. On the other hand, the preferences on the importance of individual criteria have been elicited individually from multiple stakeholders who were owners of rural buildings interested in a renovation of their houses for improving the energetic performance. Thus, they can be perceived as potential consumers of the insulating materials.

When it comes to the characteristic profiles, the experts decided to define them by indicating one of the performances observed in the set of materials. The consensus between the experts on the most typical performance levels for each class has been reached during an interactive focus group. These levels are summarized in Table 3.

We considered a multiple criteria problem of sustainability assessment of insulating materials. We combined Life Cycle Costing, Life Cycle Assessment, and adaptive comfort evaluation to derive performances of these materials on six socio-economic and environmental criteria. The comprehensive assessment of the materials involved their assignment to three preference-ordered sustainability classes. The classification was performed with a group decision counterpart of the Electre TRI-rC method that compares alternatives with the characteristic class profiles defined by the experts.

To derive a recommendation that would reflect viewpoints of a wide spectrum of potential customers, we accounted for the preference information of a few tens of rural buildings’ owners being interested in the roof’s insulation. The initial recommendation was derived by computing the proportion of stakeholders who accepted an assignment of a particular material to a given class. These results were subsequently validated against the outcomes of a two-fold robustness analysis realized with the Monte Carlo simulation. The latter exploited the space of all criteria weights compatible with either each stakeholder’s preference information provided in the SRF procedure or collective ranking of criteria that was derived with an original algorithm proposed in this paper.

The three-stage analysis revealed that the most sustainable materials were glass wool, hemp fibres, kenaf fibres, polystyrene foam, polyurethane, and rock wool. This was mainly due to their favorable performances quantified with the Net Present Value and Eco-indicators. On the contrary, gypsum fibreboard, mineralized wood and plywood were assessed as the least sustainable materials. This can be justified in terms of their poor performances on thermal comfort, human health, and ecosystem quality. Overall, the proposed method provided greater clarity for decision making and guaranteed credibility in the eyes of the traditional rural houses’ owners. Moreover, all research results—concerning both materials’ performances on the individual criteria and comprehensive sorting recommendation—were well perceived by the experts on insulating materials in Italy.

The proposed framework can be applied to other decision contexts than that of a typical farmhouse in central Italy. This would require, however, accounting for a comfort model as well as warm and cold periods suitable to a particular geographical context, specification of a relevant lifespan for the investment, and adapting life cycle assessment to the reality of a particular study.

From the methodological viewpoint, we envisage the following future developments. Firstly, we plan to extend the SRF procedure to a group decision context so that it tolerates intensities of preference for different pairs of criteria and accepts information on different roles (weights) of the decision makers. Secondly, we aim at extending the proposed group decision framework to methods dealing with choice and ranking problems. This would require elaboration of the algorithms for deriving a compromise recommendation that would appropriately combine results of robustness analysis computed individually for each stakeholder.