A New Hybrid MCDM Model for Insulation Material Evaluation for Healthier Environment

Abstract

One of the easiest and most common methods for effectively reducing building energy demand is the selection of adequate thermal insulation materials. Thermal insulation is a substantial contribution and an evident, logical and practical first stage toward improving energy performance, particularly in envelope-load-dominant structures located in difficult climate zones. Today’s insulating materials come in a broad variety of sizes and shapes, each with its a own qualities. It is well acknowledged that material selection is one of the most difficult and time-consuming aspects of a construction project. Therefore, choosing the right insulation material is also a very important topic to increase energy efficiency. However, it is a complex problem with many criteria and alternatives. This study integrates three different multi criteria decision making methods, which are Fuzzy Best-Worst Method, CRiteria Importance Through Inter-criteria Correlation and Mixed Aggregation by COmprehensive Normalization Technique. In this study, the following eight criteria were taken into account in the evaluation: thermal conductivity, periodic thermal transmittance, specific heat, density, decrement factor, surface mass, thermal transmittance, and thermal wave shift. The first method will be used to find the subjective weights, while the second method will be used to find the objective weights. The third method will be used to rank the insulation materials. According to the results of the Fuzzy Best-Worst Method, the most important criterion was determined as thermal conductivity. According to the results of the CRiteria Importance Through Inter-criteria Correlation, the most important criterion was determined as thermal wave shift. According to the results of the Mixed Aggregation by COmprehensive Normalization Technique, the top 10 insulation materials are as follows: polyisocyanurate, polyurethane (1), polyurethane (2), wood fiber (1), kenaf, jute, cellulose (2), wood fiber (1), XPS (1) and XPS (2). According to the results of the proposed method, polyisocyanurate was determined as the best insulation material for healthier environment. This study makes two contributions to the literature: first, a new hybrid method was developed in this study. Secondly, in this study, the newly introduced Mixed Aggregation by COmprehensive Normalization Technique method was used.

1. Introduction

Energy conservation is one of the most important topics for all science divisions in the recent years. In a society with finite energy sources and severe ecological pollution, it is clear that a more maintainable way of life will become increasingly vital. Gradual depletion of fossil fuel sources and environmental factors require the efficient use of energy. As energy prices continue to rise, energy efficiency will become increasingly critical. Buildings play an important role in society and in people’s lives. Buildings account for a significant portion of raw material and energy usage, global carbon emissions, etc. Residential buildings consume two-thirds of the total energy consumed in the construction industry [1]. Residential structures are among the highest energy consumers; as a result, energy-inefficient buildings must be retrofitted. Residential buildings built in recent years have had insufficient thermal insulation in their envelopes. As a result, we now face the challenge of restoring deteriorating structures. Additional insulation should be built into the structures’ external walls to improve energy efficiency [2].

Many steps have been taken around the world under this framework. This framework means that by insulating buildings, energy efficiency is increased, and environmental pollution is reduced. For example, the remodel of the Buildings Directive of Energy Efficiency in 2010 set a number of stricter regulations, like the need for overall novel constructions in Europe to achieve near zero energy consumption throughout the year. These directives’ implementation into public regulations have had an impact on the achievement of energy-saving goals. The following were the principal provisions of this directive [3,4]:

• Overall novel structures must be zero-energy constructions, and overall official structures must be almost zero-energy constructions.
• Cost-effective and energy-saving requirements should be installed based on the regional climate circumstances in each country.
• In comparison to the year 1990, a 20% reduction in greenhouse emissions, and 30% reduction if international agreement is reached.
• It must reduce energy consumption by 20%.

Various studies have shown that well insulated buildings have better performance, which helps to maximize the building’s performance. For example, because an increased vitreous envelope is a costly envelope resolution, stronger construction massing is suggested to decrease thermal losses and gains [5]. Utilizing a thermal mass of building can also improve thermal quality conditions while lowering power usage, depending on the type of use and location [6]. As a result, the qualities of external walls have a considerable impact on energy efficiency and indoor thermal comfort conditions [7]. Integrating a construction envelope utilizing appropriate materials has an effect on the building’s thermal efficiency. Thus, the building envelope’s thermal insulation is an unavoidable aspect in reducing building energy demand [8], which is generated by the temperature difference between the interior and exterior [9]. Insulation that is properly placed might help to increase HVAC efficiency. High electricity costs indicate a faulty heating system or inadequate insulation. Due to condensation, poor insulation can cause a variety of issues such as mold on the external walls and pipes, humid and rotted wood-work, oxidation and other concerns on metal work that are harmful to the structure and fabric of the property and are costly to repair. Thermal insulation contributes about 55 percent in constructions for developing thermal efficiency at total thermal transmission [10,11,12]. If used correctly, insulation materials can help to reduce unwanted noise and reduce fire hazards [13]. Furthermore, the insulating materials’ embodied energy is an important consideration. If the degradation in operational power is greater than the power utilized to produce the building insulation materials, the net energy balance in insulated buildings is positive [14]. When choosing insulation materials for the building, an evaluation should be made by considering different aspects. Whichever purpose is more important for the insulated building, the selection criteria should be determined and evaluated accordingly.

The worldwide insulation market, which was valued at $52.3 bn in 2017, is predicted to reach $101.3 bn through 2025, representing an 8.6% increase between 2018 and 2025. During the forecast period, the Asia–Pacific region is predicted to expand at the quickest rate in the market [15]. This may largely be attributed to rising requisition for insulation goods in both non-residential and residential construction, owing to rising population, rapid industrialization, and rapid economic expansion, especially in obtaining economies like India and China.

Regardless of the purpose, the building design in terms of where the insulation material will be applied is more important, with building insulation materials especially important for reaching energy efficiency goals in structures. One of the simplest and most popular ways for efficiently reducing building energy demand is the selection of adequate thermal insulation materials [16]. The insulating material choice is influenced by more than the building’s thermal efficiency. The materials chosen can also have an impact on elements such as quality of life and environmental impact [17,18]. Today’s insulating materials come in a large variety of sizes and shapes, each with a unique series of qualities. Some types of materials for the thermal insulation of buildings are given in

Table 1. Some types of materials for thermal insulation of buildings.

THERMAL INSULATION MATERIALS
Inorganic Mineral Derived	Organic Fossil Fuel Derived	Organic Plants/Animal Derived	Innovative
Stone wool	EPS	Wood fibre	Aerogels
Glass wool	PUR/PIR	Cork	VIP
Glass foam	XPS	Cellulose	NIM
Perlite		Straw bale	Textile fibers
Vermiculite		Cotton	Recycled PET
Expanded clay		Hemp
		Flax
		Sheep wool
		Reeds

[19].

Some types of insulation materials are more ecologically beneficial than others, while some are more cost-effective, and the remainder provide greater thermal insulation [20,21,22]. The material selection for a certain project and country is influenced by a variety of elements, including pricing, material availability, shipping expenses, climatic circumstances, national structure restrictions, and the type of heating in the building. Inorganic fiber materials, stone wool, and glass wool, for example, account for used more than 0.60 of the thermal insulation materials in Europe, while organic-foam materials, polystyrene, and extruded-expanded polystyrene account for less than 0.30 [23].

It is well acknowledged that material selection is time-consuming and one of the most important problems in construction planning [18]. In the literature, different techniques have been used to handle the material choice problem, and one of the most popular approaches used is the multi-criteria decision-making methodology (MCDM). When faced with several choices with multiple conflicting and non-commensurable decision criteria, MCDM tools are commonly used to arrive at an optimal conclusion. Owing to its connatural capability to appraise many options according to these various selection criteria to determine the optimum option, the strategy is a noted for addressing complex real life cases. Researchers have used AHP, ELECTRE, MAUA, PROMETHEE, TOPSIS, VIKOR, WPM, WSM, and other common MCDM strategies to solve material choice problems in the literature. While selecting building materials, the most significant criteria must be considered [13].

Research concentrating on appropriate material selection for a certain project can be found in the literature on both a practical and scientific level. There has been a lot of work on material selection analysis in the literature, but there has been limited research on assessing the efficacy of diverse methods for investigation. The literature has mostly documented the use of a single methodology alone to solve material choice problems in a variety of fields. In recent years, the use of hybrid methods have increased. Some prominent studies have been given below.

For concrete repair, AHP was used in a study by Do et al. to determine the best patching material [24]. Ugura et al. used the AHP approach to analyze the choice of the best material for external wall structure among materials like pumice concrete, brick, and aerated sand autoclaved concrete [25]. WASPAS, a new system for assessing viable facade choices for public and commercial buildings, was created and used [26]. VIKOR, COPRAS, and TOPSIS methodologies were used to analyze redevelopment options for derelict rural structures [27,28]. For the complete assessment and analysis of retrofit and construction planning, the MAMVA technique was presented [29]. The interval TOPSIS approach was used by Streimikiene et al. to evaluate and rate the sustainability of inorganic and organic construction insulating materials. The researchers used four diverse types (technological, equal balanced, and ecological) with various weights for the specified attributes to conduct the sensitivity analysis. The recycled-glass was found to be the best option in all three types (technological, balanced, and equal), according to the analysis. Sheep wool is the best alternative in the ecological category, according to the evaluation [30]. Rocchi et al. presented a study on the assessment of the long-term sustainability of insulating materials. In central Italy, the sustainability of 12 roof insulation options was assessed using seven criteria in the case study of a farmhouse. Combining thermal comfort and energy optimization with economic and environmental LCC and LLA analyses were among the assessment criteria. The inorganic and organic construction insulating material options are ranked using the ELECTRE TRI-rC technique. Kenaf fibers, polystyrene-foam slabs, cellulose, and hemp fibres were shown to be the most beneficial materials [31]. Ruzgys et al. looked at modernized building design solutions in Lithuania. Using the integrated SWARA-TODIM technique, the authors graded six exterior wall insulating choices for construction modernization (thin plaster and polystyrene foam; fibre cement and mineral wool panels). A vented system with fibrocement panels and mineral wool insulation (130 mm) was proven to be the best option for residential building upgrading [32]. For retrofitting old constructions, Zagorskas et al. used the TOPSIS Grey approach to sort five modern insulation solutions (flax-hemp fibre, eco wool, thermal wool, a vacuum panel, and aerogel). The optimum insulation solution was found to be eco-wool. The outcomes of the other options, on the other hand, are very similar [33]. The VIKOR approach was used to evaluate eight insulating materials by Civic and Vucijak. Seven criteria were chosen by the authors to show environmental and technical perspectives. Both the criteria’ choice and their weighting in this study are dependent on the authors’ choices. The findings suggest that Styrofoam is the most desired material, followed by glass wool in second place, and wood wool in the third place [34]. The natural fiber assessment strategy is implied, which covers a lot of criteria. Comparative assessment of diverse natural fiber types is conducted by using a hierarchical decision-making approach by Balo et al. [35]. The best performing fiber choice is made by comparatively evaluating the materials related to green buildings. For a building restoration, Ginevicius et al. used a variety of MCDM approaches (TOPSIS, SAW, COPRAS, VIKOR) to rank five external wall insulating technologies and choose the most economic option [36]. The study assessed subcontractor proposals. Zavadskas et al. proposed a system for ranking several design choices for the external walls of a building [37]. The method used is COPRAS and includes both qualitative and quantitative criteria. Building thermo-modernization options were investigated by Basinska et al. [38]. To discover the optimal solution in terms of economic, energy-related, and environmental factors, the authors employed the WSM technique. More than 400 alternative solutions were examined. The variant with extra heat insulation of XPS with an extra thickness of 30 cm and timber windows was considered to be the optimum choice. The findings demonstrate that using insulation with a thickness greater than 36 cm has no substantial energy or cost savings. Marques et al. developed new composite materials that include cork and rice husk grains [39]. The materials given are part of a long-term building solution. The AHP approach was used on a variety of formulations with varying material ratios. The experiment’s findings demonstrate that rice husk in a higher percentage in composite compositions can improve acoustic efficiency. The thermal conductivity of expanded cork grains is reduced. Bostancioglu assessed the four forms of the double-exterior wall envelope (multistory, hallway, box window, and shaft-box) [40]. The options were rated using a fuzzy-AHP system. The box-window came in first, the corridor came in second, the multi-story double exterior wall envelope came in the third place, and the box of shaft came in last place in the evaluation. A box window was deemed to be the best option based on three factors (thermal insulation and noise, fire prevention). The findings were compared to those of a prior study that used the AHP approach to analyze double-skin façades [41]. The order of the possibilities remained unaltered. Moghtadernejad et al. established a method for determining design decisions for building facades. The method combined the Choquet integrals and AHP [5]. In the study, the instructions for each of plan phases are described. Because of one of the structure envelope’s components, the examination also involves the evaluation of building insulation materials. The evaluation criteria are chosen in accordance with the project’s aims and are not always focused on the sustainability goals. In the construction industry, Zavadskas et al. proposed a method for evaluating and rating technology [42]. The researchers looked at six options for polystyrene foam and mineral wool for external wall thermal insulation. The evaluation was conducted using the MULTIMOORA, ELECTRE-IV, and hybrid TOPSIS/SWARA, ELECTRE-3/SWARA, and VIKOR/SWARA methods. Sua and Balo investigated the life cycle environmental effect of roof insulation materials and construction materials [43,44]. Balo and Sua used an expert-decision framework for the optimal fiber selection of green building design components [45,46]. They analyzed the selection of ecological, energy efficient and optimal insulation material with AHP [47,48]. Ulutaş et al. [49] selected insulation materials with the PSI-CRITIC based CoCoSo Method.

One of the most significant challenges in reducing thermal losses in buildings is to choose the right insulating material, as there are many different types of building insulation materials to choose from [50]. Single-piece insulation materials are the most utilized materials for the thermal insulation of residential buildings’ external walls. To reduce costs, protection should be encouraged. By measuring power usage per unit, sources can be identified, and yearly operational expenses associated with energy generation reduced. Thus, construction planners may contribute to resolving the power challenge if suitable early planning is undertaken for the integration and selection of structure elements.

In this study, an MCDM model consisting of Fuzzy BWM (Fuzzy Best-Worst Method), CRITIC (CRiteria Importance Through Inter-criteria Correlation) and the MACONT (Mixed Aggregation by COmprehensive Normalization Technique) method is proposed. With the Fuzzy BWM and CRITIC methods, the subjective and objective weights of the criteria will be found. In this study, the objective weights of the criteria will be found with the CRITIC method, and the subjective weights of the criteria will be found with the Fuzzy BWM. Thus, the article will not be weighted unilaterally (only subjective weights or only objective weights), and this will lead to more rigorous results. With the MACONT method, the insulation materials will be sorted. This study makes two contributions to the literature. Unlike the MULTIMOORA, CoCoSo, and WASPAS methods, the MACONT method uses more normalization techniques and more aggregation operators. Therefore, it can achieve more precise and rigorous results compared to the mentioned MCDM methods. This study makes two contributions to the literature. First, a new hybrid MCDM model was developed. To the best of our knowledge, these methods have not been used together in the literature before. Therefore, the proposed MCDM model is new. Secondly, the MACONT method is a newly developed method and the number of studies using this method is limited. Therefore, the second contribution of this study is the use of the MACONT method.

2. Materials and Methods

In this study, Fuzzy BWM, CRITIC, and MACONT methods are used. With Fuzzy BWM, the subjective weights of the criteria will be found. With CRITIC, the objective weights of the criteria will be found. These two types of weights will be combined and then used in the MACONT method. Alternatives will be sorted using the MACONT method.

2.1. Fuzzy BWM

The crisp BWM (Best-Worst Method) uses a 1–9 scale and this scale does not handle vagueness and uncertainty. In some practical problems, BWM comparisons can be carried out by using fuzzy numbers rather than crisp numbers, which may be more in line with real circumstances and can achieve more persuasive ranking results [51]. A triangular fuzzy number may be represented as $A=\left(l, m, u\right)$ and indicates the relative strength of each pair of components in the same hierarchy, where $u\ge m\ge l$ [52]. The parameters $u$, $m$, $l$ indicate the upper value, modal value and the lower value, respectively [52].

In this study, Fuzzy BWM is used to identify the subjective weights of criteria. The steps of the method are summarized as [51,52]:

Step 1: Criteria are determined.

Step 2: Best ($C_B$) and worst ($C_W$) criteria are determined.

Step 3: Pairwise comparisons of the best and worst criteria with other criteria are computed. By comparing the best criterion with the other criteria, the fuzzy Best-to-Others (BO) (${\tilde{A}}_B=({\tilde{a}}_{B1},{\tilde{a}}_{B2},\dots ,{\tilde{a}}_{Bn}$)) vector is obtained. In this vector, ${\tilde{a}}_{Bj}$ indicates the fuzzy preference of $C_B$ over the $j$th criterion and ${\tilde{a}}_{BB}$ equals to (1, 1, 1). By comparing the other criteria with the worst criterion, the fuzzy Others-to-Worst (OW) (${\tilde{A}}_W=({\tilde{a}}_{1W},{\tilde{a}}_{2W},\dots ,{\tilde{a}}_{nW}$)) vector is obtained. In this vector, ${\tilde{a}}_{jW}$ indicates the fuzzy preference of the $j$th criterion over $C_W$ and ${\tilde{a}}_{WW}$ equals to (1, 1, 1). Decision-makers will use the linguistic expressions shown in

Table 2. Linguistic Terms and Fuzzy Numbers [51,52].

Linguistic Terms	Fuzzy Numbers	CI
Absolutely Significant (AS)	(7/2, 4, 9/2)	8.04
Very Significant (VS)	(5/2, 3, 7/2)	6.69
Fairly Significant (FS)	(3/2, 2, 5/2)	5.29
Weakly Significant (WS)	(2/3, 1, 3/2)	3.80
Equally Significant (ES)	(1, 1, 1)	3.00

when making specified pairwise comparisons. The $CI$ values shown in Table 2 are calculated based on the ${\tilde{a}}_{BW}$ values. For detailed information, please see [51].

Step 4: Fuzzy weight of each criterion is obtained.

$$min \vartheta { }^{*}$$

$$s.t.\left\{\begin{array}{c}\left|\frac{l_B^w,m_B^w,u_B^w}{l_j^w,m_j^w,u_j^w}-l_{Bj},m_{Bj},u_{Bj}\right|\le \left(k^{*},k^{*},k^{*}\right)\hfill \\ \left|\frac{l_j^w,m_j^w,u_j^w}{l_W^w,m_W^w,u_W^w}-l_{jW},m_{jW},u_{jW}\right|\le \left(k^{*},k^{*},k^{*}\right)\hfill \\ {\displaystyle \sum }_{j=1}^n\frac{l_j^w+4m_j^w+u_j^w}{6}=1\hfill \\ l_j^w\le m_j^w\le u_j^w\hfill \\ l_j^w\ge 0\hfill \end{array}\right.$$

(1)

In Equation (1), ${\tilde{w}}_j=\left(l_j^w,m_j^w,u_j^w\right)$, ${\tilde{w}}_B=\left(l_B^w,m_B^w,u_B^w\right)$, ${\tilde{w}}_W=\left(l_W^w,m_W^w,u_W^w\right)$ and ${\vartheta }^{*}=\left(k^{*},k^{*},k^{*}\right)$represent the fuzzy weight of the $j$th criterion, the fuzzy weight of the best criterion, the fuzzy weight of the worst criterion and the ${\vartheta }^{*}$ coefficient. The consistency ratio ($CR)$ is computed utilizing equation $CR={\vartheta }^{*}/CI$ and the $CR<0.1$ is admissible [53]. In this equation, $CI$ indicates the consistency index and this value is shown in Table 2.

Step 4: The fuzzy weights of criteria are converted into crisp weights ($w_{jBWM}$) of criteria by using following equation [51].

$$w_{jBWM}=\frac{l_j^w+4m_j^w+u_j^w}{6}$$

(2)

After these values are found for each decision-maker, the values of the decision-makers are combined with the geometric mean [54]. The geometric mean is computed by Equation (3).

$$w_{jBWM}^{*}={\left({{\displaystyle \prod }}_{p=1}^P{w}_{jBWM}^p\right)}^{1/P}$$

(3)

2.2. CRITIC Method

The CRITIC method is utilized to determine the objective weights of criteria [55]. The steps of the method are described below [56].

Step 1: Decision matrix ($B$) is constructed.

$$B={\left[b_{ij}\right]}_{m\times n}$$

(4)

Step 2: This matrix is normalized by Equations (5) and (6).

$$d_{ij}=\frac{b_{ij}-\min \left(b_{ij}\right)}{\max \left(b_{ij}\right)-\min \left(b_{ij}\right)}\hspace{1em}\hspace{1em}{b}_{ij}\in BNF$$

(5)

$$d_{ij}=\frac{\max \left(b_{ij}\right)-b_{ij}}{\max \left(b_{ij}\right)-\min \left(b_{ij}\right)}\hspace{1em}\hspace{1em}{b}_{ij}\in NBNF$$

(6)

In Equations (5) and (6), $BNF$ and $NBNF$ show the set of beneficial and non-beneficial criteria, respectively.

Step 3: The weights of criteria ($w_{jCTC}$) for CRITIC method are computed.

$$w_{jCTC}=\frac{f_j}{{{\displaystyle \sum }}_{e=1}^n{f}_e}$$

(7)

In the above equation, $f_j$ represents the amount of information stored in the $j$th criterion. This value is calculated as [57].

$$f_j={\sigma }_j{{\displaystyle \sum }}_{e=1}^n(1-g_{ej})$$

(8)

In Equation (8), ${\sigma }_j$ represents the $j$th criterion’s standard deviation and $g_{ej}$ indicates the correlation coefficient between the $j$th criterion and $e$th criterion. The subjective weights from the Fuzzy Best-Worst Method and the objective weights from the CRITIC method are combined with the help of Equation (9) [58,59].

$$w_{jCMB}=\nabla w_{jBWM}+\left(1-\nabla \right)w_{jCTC}$$

(9)

In Equation (9), $w_{jCMB}$ indicates the criteria combined weights. Additionally, $\nabla$ will be taken as 0.5 in this study.

2.3. MACONT Method

The MACONT method will be used in this study to rank insulation materials. The steps of the method are summarized below [60].

Step 1: The decision matrix is constructed. This matrix is shown in Equation (4).

Step 2: Normalization Procedure 1 (Equation (10)), Normalization Procedure 2 (Equation (11)) and Normalization Procedure 3 (Equation (12)) are applied to the decision matrix. Then, normalized values are aggregated by using Equation (13).

$${\widehat{b}}_{ij}^1=\left\{\begin{array}{c}{b}_{ij}/{\displaystyle \sum }_{i=1}^m{b}_{ij}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{b}_{ij}\in BNF\hfill \\ {\frac{1}{b}}_{ij}/{\displaystyle \sum }_{i=1}^m{\frac{1}{b}}_{ij}\hspace{1em}\hspace{1em}\hspace{1em}{b}_{ij}\in NBNF\hfill \end{array}\right.$$

(10)

$${\widehat{b}}_{ij}^2=\left\{\begin{array}{c}{b}_{ij}/ma{x}_i{b}_{ij}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{b}_{ij}\in BNF\hfill \\ mi{n}_i{b}_{ij}/b_{ij}\hspace{1em}\hspace{1em}\hspace{1em}{b}_{ij}\in NBNF\hfill \end{array}\right.$$

(11)

$${\widehat{b}}_{ij}^3=\left\{\begin{array}{c}(b_{ij}-mi{n}_i{b}_{ij})/(ma{x}_i{b}_{ij}-mi{n}_i{b}_{ij})\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{b}_{ij}\in BNF\hfill \\ (b_{ij}-ma{x}_i{b}_{ij})/(mi{n}_i{b}_{ij}-ma{x}_i{b}_{ij})\hspace{1em}\hspace{1em}\hspace{1em}{b}_{ij}\in NBNF\hfill \end{array}\right.$$

(12)

$${\widehat{b}}_{ij}=\theta {\widehat{b}}_{ij}^1+\mu {\widehat{b}}_{ij}^2+\left(1-\theta -\mu \right){\widehat{b}}_{ij}^3$$

(13)

In this study, $\theta$ and $\mu$ values will be taken as 0.33.

Step 3: Two mixed aggregation operators ($U_1$ and $U_2$) are computed as:

$$U_{1i}=\delta \frac{{\pi }_i}{\sqrt{{{\displaystyle \sum }}_{i=1}^m{\left({\pi }_i\right)}^2}}+\left(1-\delta \right)\frac{Q_i}{\sqrt{{{\displaystyle \sum }}_{i=1}^m{\left(Q_i\right)}^2}}$$

(14)

$$U_{2i}=\beta ma{x}_j\left(w_{jCMB}\left({\widehat{b}}_{ij}-{\overline{b}}_j\right)\right)+\left(1-\beta \right)mi{n}_j\left(w_{jCMB}\left({\widehat{b}}_{ij}-{\overline{b}}_j\right)\right)$$

(15)

where ${\pi }_i={\displaystyle \sum }_{j=1}^n{w}_{jCMB}\left({\widehat{b}}_{ij}-{\overline{b}}_j\right)$ and $Q_i={\displaystyle \prod }_{\gamma =1}^n{\left({\overline{b}}_j-{\widehat{b}}_{ij}\right)}^{w_{jCMB}}/{\displaystyle \prod }_{\omega =1}^n{\left({\widehat{b}}_{ij}-{\overline{b}}_j\right)}^{w_{jCMB}}$ and $\gamma$ indicates the part of criteria that satisfy ${\widehat{b}}_{ij}<{\overline{b}}_j$ and $\omega$ indicates the part of criteria that satisfy ${\widehat{b}}_{ij}\ge {\overline{b}}_j$. In addition, the sum of the weights of the criteria must be equal to “1”. In this study, $\delta$ and $\beta$ values will be taken as 0.5.

Step 4: The final comprehensive score ($U_i$) is determined as:

$$U_i=\frac{1}{2}\left(U_{1i}+\frac{U_{2i}}{\sqrt{{{\displaystyle \sum }}_{i=1}^m{\left(U_{2i}\right)}^2}}\right)$$

(16)

The alternative with the highest $U_i$ is determined as the best one.

3. Results

In this study, the best insulation material was selected by using the Fuzzy BWM, CRITIC, and MACONT methods. Questionnaires were sent to 10 experts who are highly interested in insulation materials. Only four of these experts gave feedback. An expert team was formed from these four experts. Of these experts, Expert 1 is a 20-year Civil Engineer and sells insulation materials. Expert 2 is a 15-year Chemical Engineer who is working at a factory that produces insulation materials. Expert 3 is the manager of a factory that produces insulation materials, and Expert 4 is an academic who has been working on insulation materials for 25 years. The criteria found in the literature were shown to the experts. Experts selected eight of these criteria for evaluation. The criteria used in the study are shown below.

• Thermal Conductivity (TC)
• Periodic Thermal Transmittance (PTT)
• Specific Heat (SH)
• Density (D)
• Decrement Factor (DF)
• Surface Mass (SM)
• Thermal Transmittance (TT)
• Thermal Wave Shift (TWS)

Thermal insulation refers to a material’s or a system’s ability to resist thermal passage from the framework to the environment or vice versa.

When a temperature gradient exits perpendicular to the area, thermal conductivity (TC) is defined as the rate at which heat is transported by conduction through a unit cross-section area of a material. The heat loss from the area where the insulation is placed diminishes as the TC value lowers.

Parameters like the modulus of decrement factor and periodic thermal-transmittance impact the dynamic responsiveness of building components, all of which are established in standard procedures like ISO 13786 [61]. As they are closely connected to thermal performance, the first two criteria are the most critical.

Thermal inertia is another name for periodic thermal-transmittance (PTT). The thermal-flux generated through a temperature change in the component’s opposite side is described by periodic thermal transmittance, the assumption that the environmental temperature on the external wall’s same side remains constant.

The decrement-factor (DF) controls the amount through which a construction element moderates circumstances. This would be the amount by which the maximum temperature on the exterior superficies of a structure on a hot summer day is decreased by the time it reaches the interior surface.

Density (D) is a substance’s mass per unit volume, measured in kg/m³. An object with a high density maximizes its weight and has a ‘high’ thermal mass and a ‘low’ thermal diffusivity.

The required heat to raise the temperature 1000 g of a substance through 10 K is referred to as its specific heat (SH). As it takes time to adsorb enough heat to begin to transmit the heat, a well isolated object has a bigger specific heat.

Surface mass (SM) should be minimized to avoid putting undue strain on the structure.

The multi-layered insulating material’s U value is linked to thermal-transmittance (TT). The heat flow by an anisotropic and non-homogeneous insulating material per unit area owing to a 1 °K temperature increase is known as thermal transmittance.

The capacity of materials that make up the housing envelope to slow down heat exchanges, especially summer solar radiation, is known as thermal wave shift (TWS) in building thermals. In the summer, this thermal phase shift is very effective for preventing solar radiation energy penetration during the day and rejecting it at night.

The subjective weights of the criteria shown above will be found first with Fuzzy BWM. For this, data were obtained from the expert team through a questionnaire. The pairwise comparisons, BO vector, and OW vector of experts are shown in

Table 3. The pairwise comparisons, BO vector, and OW vector of experts.

BO Vector
	Best	TC	PTT	SH	D	DF	SM	TT	TWS
Expert 1	TT	WS	VS	VS	FS	VS	AS	ES	WS
Expert 2	TC	ES	ES	VS	VS	ES	VS	VS	FS
Expert 3	TC	ES	FS	AS	VS	ES	ES	VS	VS
Expert 4	TC	ES	FS	VS	VS	ES	WS	VS	FS
OW Vector
	Worst	TC	PTT	SH	D	DF	SM	TT	TWS
Expert 1	SM	VS	WS	ES	FS	WS	ES	AS	VS
Expert 2	SH	VS	VS	ES	WS	VS	ES	ES	FS
Expert 3	SH	AS	FS	ES	WS	VS	VS	WS	WS
Expert 4	SH	VS	FS	ES	ES	VS	FS	ES	VS

.

The linguistic values shown in Table 3 are converted into fuzzy numbers with the help of Table 2, then Equation (1) is written with these fuzzy numbers. The model in Equation (1) is solved with Lindo 18 software. Then, the fuzzy weights of the criteria found with Fuzzy BWM are converted to crisp weights (subjective) with Equation (2). The criteria weights of the experts were combined with the geometric mean (GM) (Equation (3)), then these values were normalized with Equation (7). These normalized values found will be taken as $w_{jBWM}$.

Table 4. The results of Fuzzy BWM.

	Criteria	TC	PTT	SH	D
Experts
Expert 1		(0.176, 0.182, 0.214)	(0.063, 0.072, 0.094)	(0.072, 0.072, 0.074)	(0.102, 0.108, 0.153)
Expert 2		(0.199, 0.199, 0.229)	(0.199, 0.199, 0.218)	(0.062, 0.062, 0.078)	(0.068, 0.071, 0.087)
Expert 3		(0.232, 0.232, 0.232)	(0.091, 0.106, 0.135)	(0.051, 0.059, 0.071)	(0.062, 0.072, 0.085)
Expert 4		(0.174, 0.190, 0.217)	(0.111, 0.131, 0.163)	(0.053, 0.053, 0.057)	(0.073, 0.078, 0.083)
GM		0.203	0.121	0.062	0.083
Normalized GM		0.215	0.128	0.066	0.088
	Criteria	DF	SM	TT	TWS
Experts
Expert 1		(0.063, 0.072, 0.074)	(0.057, 0.064, 0.065)	(0.208, 0.237, 0.239)	(0.182, 0.182, 0.214)
Expert 2		(0.199, 0.199, 0.205)	(0.070, 0.071, 0.073)	(0.070, 0.071, 0.075)	(0.100, 0.111, 0.143)
Expert 3		(0.191, 0.191, 0.191)	(0.191, 0.191, 0.191)	(0.062, 0.072, 0.085)	(0.062, 0.072, 0.085)
Expert 4		(0.174, 0.190, 0.217)	(0.117, 0.136, 0.163)	(0.073, 0.078, 0.083)	(0.111, 0.131, 0.183)
GM		0.151	0.104	0.099	0.121
Normalized GM		0.160	0.110	0.105	0.128

shows the results of Fuzzy BWM.

The judgments of four experts are consistent according to Fuzzy BWM. Expert 1’s consistency ratio is 0.038, Expert 2’s consistency ratio is 0.031, Expert 3’s consistency ratio is 0.027, and Expert 4’s consistency ratio is 0.082. As can be seen, all the consistency ratios found are less than 0.1, so the results are consistent. According to the results of the Fuzzy BWM, the criteria are listed as follows: TC, DF, PTT, TWS, SM, TT, D, and SH. According to these results, the most important criterion was determined as TC. After the subjective weights of the criteria are found, the decision matrix was created for the CRITIC and MACONT methods. The decision matrix used in this study was taken from the literature [13]. The decision matrix is presented in

Table 5. Decision Matrix [13].

	Criteria	TC	PTT	SH	D	DF	SM	TT	TWS
Materials
Polyurethane (1)		0.023	0.076	1.40	36.00	0.406	70.00	0.187	7.70
Polyurethane (2)		0.025	0.081	1.50	44.00	0.404	70.00	0.200	7.80
Recycled textile (1)		0.042	0.135	1.60	10.00	0.456	67.00	0.295	6.50
Recycled textile (2)		0.040	0.125	1.20	50.00	0.437	71.00	0.285	7.20
Wood fiber (1)		0.038	0.095	2.10	110.00	0.345	77.00	0.275	9.60
Wood fiber (2)		0.049	0.078	2.10	270.00	0.237	93.00	0.328	11.90
Stone wool (1)		0.033	0.104	1.00	70.00	0.418	73.00	0.248	7.60
Stone wool (2)		0.040	0.109	1.00	165.00	0.383	83.00	0.285	8.70
Cellulose (1)		0.037	0.119	1.30	30.00	0.440	69.00	0.270	7.00
Cellulose (2)		0.039	0.111	2.00	70.00	0.396	73.00	0.280	8.40
Vermiculite (1)		0.057	0.165	0.90	90.00	0.456	75.00	0.362	7.10
Vermiculite (2)		0.062	0.178	0.90	80.00	0.466	74.00	0.382	6.90
Recycled glass fiber(commercial)		0.055	0.148	1.00	165.00	0.417	83.00	0.354	8.10
Recycled glass fiber		0.031	0.058	0.80	450.00	0.245	111.00	0.236	11.90
XPS (1)		0.032	0.103	1.70	32.00	0.424	69.00	0.242	7.40
XPS (2)		0.034	0.107	1.70	40.00	0.422	70.00	0.253	7.50
Straw bale		0.067	0.194	0.60	60.00	0.485	72.00	0.400	6.50
Cork		0.04	0.094	2.10	130.00	0.329	79.00	0.285	10.00
Perlite		0.052	0.152	0.80	100.00	0.446	76.00	0.340	7.30
Kenaf		0.03	0.082	1.70	100.00	0.357	76.00	0.230	9.30
Hemp		0.04	0.112	1.70	90.00	0.392	75.00	0.285	8.50
Flax		0.04	0.126	1.60	30.00	0.442	69.00	0.285	7.00
Recycled PET(commercial)		0.034	0.106	1.20	60.00	0.420	72.00	0.253	7.60
Cotton (recycled)		0.039	0.124	1.60	25.00	0.443	69.00	0.280	6.90
Mineralized wood fiber		0.065	0.071	1.80	533.00	0.180	119.00	0.393	13.10
EPS		0.035	0.114	1.30	22.00	0.440	68.00	0.259	6.90
Sheep wool		0.038	0.122	1.80	20.00	0.443	68.00	0.275	6.90
Coir		0.043	0.12	1.50	105.00	0.399	77.00	0.300	8.40
Jute		0.038	0.116	2.40	35.00	0.423	70.00	0.275	7.60
Polyisocyanurate		0.022	0.074	1.40	30.00	0.409	69.00	0.180	7.50
Glass wool		0.035	0.115	1.00	21.00	0.443	68.00	0.259	6.70
Reeds		0.056	0.14	1.20	190.00	0.390	85.00	0.358	8.70

.

Except for the two criteria (SH and TWS) in the decision matrix, the others are non-beneficial criteria. The objective weights of the criteria are obtained by applying the steps of the CRITIC method to the decision matrix. The objective weights and subjective weights of the criteria are combined with Equation (9). The criteria weights according to the Fuzzy Best-Worst Method ($w_{jBWM}$), the criteria weights according to the CRITIC ($w_{jCTC}$) method, and the combined weights ($w_{jCMB}$) of the criteria are shown in

Table 6. The criteria weights.

	Criteria	TC	PTT	SH	D	DF	SM	TT	TWS
Weights
$w_{jCTC}$		0.102	0.093	0.117	0.147	0.135	0.148	0.102	0.156
$w_{jBWM}$		0.215	0.128	0.066	0.088	0.16	0.11	0.105	0.128
$w_{jCMB}$		0.159	0.111	0.092	0.118	0.148	0.129	0.104	0.142

.

According to the results of the CRITIC method, the criteria are listed as follows: TWS, SM, D, DF, SH, TC, TT, and PTT. If the criteria are ordered by their combined weights, they are listed as follows: TC, DF, TWS, SM, D, PTT, TT and SH. After the combined weights of the criteria are found, the MACONT method is used. With Equation (10), Normalization Procedure 1 is performed. Normalization Procedure 2 is performed with Equation (11). With Equation (12), Normalization Procedure 3 is performed. The results of Normalization Procedure 1, Normalization Procedure 2, and Normalization Procedure 3 are presented in

Table 7. The results of Normalization Procedure 1.

	Criteria	TC	PTT	SH	D	DF	SM	TT	TWS
Materials
Polyurethane (1)		0.052	0.044	0.031	0.039	0.029	0.033	0.046	0.030
Polyurethane (2)		0.048	0.041	0.033	0.032	0.030	0.033	0.043	0.030
Recycled textile (1)		0.028	0.025	0.035	0.142	0.026	0.035	0.029	0.025
Recycled textile (2)		0.030	0.027	0.026	0.028	0.027	0.033	0.030	0.028
Wood fiber (1)		0.031	0.035	0.046	0.013	0.035	0.030	0.031	0.037
Wood fiber (2)		0.024	0.043	0.046	0.005	0.050	0.025	0.026	0.046
Stone wool (1)		0.036	0.032	0.022	0.020	0.029	0.032	0.035	0.029
Stone wool (2)		0.03	0.03	0.022	0.009	0.031	0.028	0.030	0.033
Cellulose (1)		0.032	0.028	0.028	0.047	0.027	0.034	0.032	0.027
Cellulose (2)		0.03	0.03	0.044	0.020	0.030	0.032	0.031	0.032
Vermiculite (1)		0.021	0.02	0.020	0.016	0.026	0.031	0.024	0.027
Vermiculite (2)		0.019	0.019	0.020	0.018	0.026	0.032	0.023	0.027
Recycled glass fiber(commercial)		0.022	0.022	0.022	0.009	0.029	0.028	0.024	0.031
Recycled glass fiber		0.038	0.057	0.017	0.003	0.049	0.021	0.036	0.046
XPS (1)		0.037	0.032	0.037	0.044	0.028	0.034	0.036	0.028
XPS (2)		0.035	0.031	0.037	0.035	0.028	0.033	0.034	0.029
Straw bale		0.018	0.017	0.013	0.024	0.025	0.033	0.021	0.025
Cork		0.03	0.035	0.046	0.011	0.036	0.030	0.030	0.038
Perlite		0.023	0.022	0.017	0.014	0.027	0.031	0.025	0.028
Kenaf		0.04	0.04	0.037	0.014	0.033	0.031	0.037	0.036
Hemp		0.03	0.03	0.037	0.016	0.030	0.031	0.030	0.033
Flax		0.03	0.026	0.035	0.047	0.027	0.034	0.030	0.027
Recycled PET(commercial)		0.035	0.031	0.026	0.024	0.028	0.033	0.034	0.029
Cotton (recycled)		0.03	0.027	0.035	0.057	0.027	0.034	0.031	0.027
Mineralized wood fiber		0.018	0.047	0.039	0.003	0.066	0.020	0.022	0.050
EPS		0.034	0.029	0.028	0.064	0.027	0.034	0.033	0.027
Sheep wool		0.031	0.027	0.039	0.071	0.027	0.034	0.031	0.027
Coir		0.028	0.028	0.033	0.013	0.030	0.030	0.029	0.032
Jute		0.031	0.029	0.052	0.040	0.028	0.033	0.031	0.029
Polyisocyanurate		0.054	0.045	0.031	0.047	0.029	0.034	0.048	0.029
Glass wool		0.034	0.029	0.022	0.067	0.027	0.034	0.033	0.026
Reeds		0.021	0.024	0.026	0.007	0.031	0.028	0.024	0.033

,

Table 8. The results of Normalization Procedure 2.

	Criteria	TC	PTT	SH	D	DF	SM	TT	TWS
Materials
Polyurethane (1)		0.957	0.763	0.583	0.278	0.443	0.957	0.963	0.588
Polyurethane (2)		0.88	0.716	0.625	0.227	0.446	0.957	0.9	0.595
Recycled textile (1)		0.524	0.43	0.667	1	0.395	1	0.61	0.496
Recycled textile (2)		0.55	0.464	0.5	0.2	0.412	0.944	0.632	0.550
Wood fiber (1)		0.579	0.611	0.875	0.091	0.522	0.87	0.655	0.733
Wood fiber (2)		0.449	0.744	0.875	0.037	0.759	0.72	0.549	0.908
Stone wool (1)		0.667	0.558	0.417	0.143	0.431	0.918	0.726	0.580
Stone wool (2)		0.55	0.532	0.417	0.061	0.47	0.807	0.632	0.664
Cellulose (1)		0.595	0.487	0.542	0.333	0.409	0.971	0.667	0.534
Cellulose (2)		0.564	0.523	0.833	0.143	0.455	0.918	0.643	0.641
Vermiculite (1)		0.386	0.352	0.375	0.111	0.395	0.893	0.497	0.542
Vermiculite (2)		0.355	0.326	0.375	0.125	0.386	0.905	0.471	0.527
Recycled glass fiber(commercial)		0.4	0.392	0.417	0.061	0.432	0.807	0.508	0.618
Recycled glass fiber		0.71	1	0.333	0.022	0.735	0.604	0.763	0.908
XPS (1)		0.688	0.563	0.708	0.313	0.425	0.971	0.744	0.565
XPS (2)		0.647	0.542	0.708	0.25	0.427	0.957	0.711	0.573
Straw bale		0.328	0.299	0.25	0.167	0.371	0.931	0.45	0.496
Cork		0.55	0.617	0.875	0.077	0.547	0.848	0.632	0.763
Perlite		0.423	0.382	0.333	0.1	0.404	0.882	0.529	0.557
Kenaf		0.733	0.707	0.708	0.1	0.504	0.882	0.783	0.710
Hemp		0.55	0.518	0.708	0.111	0.459	0.893	0.632	0.649
Flax		0.55	0.46	0.667	0.333	0.407	0.971	0.632	0.534
Recycled PET(commercial)		0.647	0.547	0.5	0.167	0.429	0.931	0.711	0.580
Cotton (recycled)		0.564	0.468	0.667	0.4	0.406	0.971	0.643	0.527
Mineralized wood fiber		0.338	0.817	0.75	0.019	1	0.563	0.458	1.000
EPS		0.629	0.509	0.542	0.455	0.409	0.985	0.695	0.527
Sheep wool		0.579	0.475	0.75	0.5	0.406	0.985	0.655	0.527
Coir		0.512	0.483	0.625	0.095	0.451	0.87	0.6	0.641
Jute		0.579	0.5	1	0.286	0.426	0.957	0.655	0.580
Polyisocyanurate		1	0.784	0.583	0.333	0.44	0.971	1	0.573
Glass wool		0.629	0.504	0.417	0.476	0.406	0.985	0.695	0.511
Reeds		0.393	0.414	0.5	0.053	0.462	0.788	0.503	0.664

and

Table 9. The results of Normalization Procedure 3.

	Criteria	TC	PTT	SH	D	DF	SM	TT	TWS
Materials
Polyurethane (1)		0.978	0.868	0.444	0.95	0.259	0.942	0.968	0.182
Polyurethane (2)		0.933	0.831	0.5	0.935	0.266	0.942	0.909	0.197
Recycled textile (1)		0.556	0.434	0.556	1	0.095	1	0.477	0
Recycled textile (2)		0.6	0.507	0.333	0.924	0.157	0.923	0.523	0.106
Wood fiber (1)		0.644	0.728	0.833	0.809	0.459	0.808	0.568	0.47
Wood fiber (2)		0.4	0.853	0.833	0.503	0.813	0.5	0.327	0.818
Stone wool (1)		0.756	0.662	0.222	0.885	0.22	0.885	0.691	0.167
Stone wool (2)		0.6	0.625	0.222	0.704	0.334	0.692	0.523	0.333
Cellulose (1)		0.667	0.551	0.389	0.962	0.148	0.962	0.591	0.076
Cellulose (2)		0.622	0.61	0.778	0.885	0.292	0.885	0.545	0.288
Vermiculite (1)		0.222	0.213	0.167	0.847	0.095	0.846	0.173	0.091
Vermiculite (2)		0.111	0.118	0.167	0.866	0.062	0.865	0.082	0.061
Recycled glass fiber(commercial)		0.267	0.338	0.222	0.704	0.223	0.692	0.209	0.242
Recycled glass fiber		0.8	1	0.111	0.159	0.787	0.154	0.745	0.818
XPS (1)		0.778	0.669	0.611	0.958	0.2	0.962	0.718	0.136
XPS (2)		0.733	0.64	0.611	0.943	0.207	0.942	0.668	0.152
Straw bale		0	0	0	0.904	0	0.904	0	0
Cork		0.6	0.735	0.833	0.771	0.511	0.769	0.523	0.53
Perlite		0.333	0.309	0.111	0.828	0.128	0.827	0.273	0.121
Kenaf		0.822	0.824	0.611	0.828	0.42	0.827	0.773	0.424
Hemp		0.6	0.603	0.611	0.847	0.305	0.846	0.523	0.303
Flax		0.6	0.5	0.556	0.962	0.141	0.962	0.523	0.076
Recycled PET(commercial)		0.733	0.647	0.333	0.904	0.213	0.904	0.668	0.167
Cotton (recycled)		0.622	0.515	0.556	0.971	0.138	0.962	0.545	0.061
Mineralized wood fiber		0.044	0.904	0.667	0	1	0	0.032	1
EPS		0.711	0.588	0.389	0.977	0.148	0.981	0.641	0.061
Sheep wool		0.644	0.529	0.667	0.981	0.138	0.981	0.568	0.061
Coir		0.533	0.544	0.5	0.818	0.282	0.808	0.455	0.288
Jute		0.644	0.574	1	0.952	0.203	0.942	0.568	0.167
Polyisocyanurate		1	0.882	0.444	0.962	0.249	0.962	1	0.152
Glass wool		0.711	0.581	0.222	0.979	0.138	0.981	0.641	0.03
Reeds		0.244	0.397	0.333	0.656	0.311	0.654	0.191	0.333

, respectively.

The three normalized values found by the normalization procedures are combined with Equation (13).

Table 10. The combined normalized values.

	Criteria	TC	PTT	SH	D	DF	SM	TT	TWS
Materials
Polyurethane (1)		0.665	0.561	0.354	0.428	0.244	0.647	0.662	0.266
Polyurethane (2)		0.623	0.532	0.387	0.403	0.248	0.647	0.62	0.273
Recycled textile (1)		0.371	0.298	0.421	0.717	0.171	0.682	0.373	0.172
Recycled textile (2)		0.395	0.334	0.287	0.389	0.198	0.636	0.396	0.227
Wood fiber (1)		0.42	0.461	0.587	0.309	0.34	0.572	0.42	0.414
Wood fiber (2)		0.292	0.55	0.587	0.185	0.543	0.416	0.301	0.593
Stone wool (1)		0.489	0.42	0.22	0.355	0.227	0.614	0.486	0.258
Stone wool (2)		0.395	0.398	0.22	0.262	0.279	0.511	0.396	0.343
Cellulose (1)		0.434	0.357	0.32	0.452	0.194	0.659	0.432	0.211
Cellulose (2)		0.408	0.39	0.554	0.355	0.259	0.614	0.408	0.32
Vermiculite (1)		0.21	0.195	0.187	0.33	0.171	0.593	0.231	0.219
Vermiculite (2)		0.161	0.154	0.187	0.342	0.157	0.603	0.191	0.204
Recycled glass fiber(commercial)		0.23	0.252	0.22	0.262	0.228	0.511	0.247	0.296
Recycled glass fiber		0.519	0.689	0.153	0.062	0.526	0.259	0.517	0.593
XPS (1)		0.504	0.424	0.454	0.444	0.217	0.659	0.502	0.242
XPS (2)		0.474	0.407	0.454	0.415	0.221	0.647	0.473	0.25
Straw bale		0.114	0.104	0.087	0.37	0.131	0.625	0.155	0.172
Cork		0.395	0.465	0.587	0.291	0.366	0.551	0.396	0.445
Perlite		0.26	0.238	0.153	0.319	0.186	0.582	0.276	0.234
Kenaf		0.535	0.527	0.454	0.319	0.32	0.582	0.533	0.39
Hemp		0.395	0.386	0.454	0.33	0.265	0.593	0.396	0.328
Flax		0.395	0.33	0.421	0.452	0.191	0.659	0.396	0.211
Recycled PET(commercial)		0.474	0.411	0.287	0.37	0.223	0.625	0.473	0.258
Cotton (recycled)		0.408	0.338	0.421	0.481	0.19	0.659	0.408	0.204
Mineralized wood fiber		0.132	0.592	0.487	0.007	0.692	0.192	0.169	0.687
EPS		0.461	0.377	0.32	0.503	0.194	0.67	0.458	0.204
Sheep wool		0.42	0.346	0.487	0.522	0.19	0.67	0.42	0.204
Coir		0.359	0.354	0.387	0.314	0.255	0.572	0.362	0.32
Jute		0.42	0.37	0.687	0.431	0.219	0.647	0.42	0.258
Polyisocyanurate		0.688	0.573	0.354	0.452	0.239	0.659	0.686	0.25
Glass wool		0.461	0.373	0.22	0.512	0.19	0.67	0.458	0.187
Reeds		0.22	0.28	0.287	0.243	0.268	0.492	0.239	0.343

shows the combined normalized values.

Using Equations (14)–(16), the final comprehensive scores of insulation materials are obtained.

Table 11. The results of MACONT.

	Results	${\mathit{\pi }}_{\mathit{i}}$	${\mathit{Q}}_{\mathit{i}}$	${\mathit{U}}_{1\mathit{i}}$	${\mathit{U}}_{2\mathit{i}}$	${\mathit{U}}_{\mathit{i}}$	Rankings
Materials
Polyurethane (1)		0.096	0.76	0.175638	0.018884	0.25853573	2
Polyurethane (2)		0.083	1.718	0.212675	0.016042	0.25136079	3
Recycled textile (1)		0.01	0.312	0.031644	0.011869	0.1231237	11
Recycled textile (2)		−0.024	0.14	−0.02499	−0.001823	−0.02897192	25
Wood fiber (1)		0.054	3.458	0.272531	0.007026	0.19978396	4
Wood fiber (2)		0.051	0.723	0.11161	0.009974	0.14597057	8
Stone wool (1)		0.005	0.806	0.053085	0.000564	0.03164605	21
Stone wool (2)		−0.026	0.522	−0.00584	−0.003546	−0.03497922	26
Cellulose (1)		−0.001	1.115	0.062546	−0.000997	0.02225939	22
Cellulose (2)		0.025	2.592	0.182988	0.008222	0.1658253	7
Vermiculite (1)		−0.113	0.277	−0.13958	−0.01443	−0.20024253	30
Vermiculite (2)		−0.131	0.268	−0.16485	−0.017681	−0.24226814	31
Recycled glass fiber(commercial)		−0.098	0.06	−0.13138	−0.013569	−0.18836093	29
Recycled glass fiber		0.048	1.891	0.174443	−0.000153	0.08583807	16
XPS (1)		0.044	2.608	0.210044	0.00438	0.14461956	9
XPS (2)		0.031	3.203	0.22627	0.002563	0.13630603	10
Straw bale		−0.16	0.822	−0.17299	−0.019998	−0.26728741	32
Cork		0.051	0.316	0.088277	0.006118	0.09944851	13
Perlite		−0.097	0.063	−0.12983	−0.011165	−0.16584916	28
Kenaf		0.075	1.845	0.20895	0.008296	0.17947046	5
Hemp		0.008	0.748	0.053887	0.002147	0.04635371	19
Flax		−0.006	0.201	0.003269	−0.000997	−0.00737902	23
Recycled PET(commercial)		0.009	2.569	0.159658	0.002454	0.10201461	12
Cotton (recycled)		0.001	2.952	0.170609	0.000217	0.08726653	15
Mineralized wood fiber		−0.007	1.026	0.049189	0.006545	0.08376922	17
EPS		0.014	0.81	0.065696	0.001515	0.04654443	18
Sheep wool		0.017	1.987	0.137299	0.002636	0.09248025	14
Coir		−0.018	0.137	−0.01691	−0.00161	−0.02300514	24
Jute		0.037	1.574	0.141137	0.011704	0.17637846	6
Polyisocyanurate		0.105	0.763	0.188192	0.019576	0.27107299	1
Glass wool		0.003	0.953	0.058761	0.000839	0.0369656	20
Reeds		−0.084	0.726	−0.07394	−0.011027	−0.13665954	27

shows the results of the MACONT method.

According to the results of the proposed model, the top 10 insulation materials are as follows: polyisocyanurate, polyurethane (1), polyurethane (2), wood fiber (1), kenaf, jute, cellulose (2), wood fiber (1), XPS (1) and XPS (2). Furthermore, the best insulation material for healthier environment is determined as polyisocyanurate.

4. Discussion

MARCOS, WASPAS, and ARAS methods are applied to the decision matrix to determine whether the MACONT method obtained accurate results or not. The results of these methods and the results of the MACONT method are shown in

Table 12. The results of MCDM methods.

	Materials	MARCOS	WASPAS	ARAS	MACONT
Materials
Polyurethane (1)		2	2	3	2
Polyurethane (2)		3	3	4	3
Recycled textile (1)		6	4	1	11
Recycled textile (2)		25	24	24	25
Wood fiber (1)		10	11	16	4
Wood fiber (2)		7	16	13	8
Stone wool (1)		23	21	22	21
Stone wool (2)		26	26	26	26
Cellulose (1)		20	17	18	22
Cellulose (2)		16	18	20	7
Vermiculite (1)		30	30	30	30
Vermiculite (2)		31	31	31	31
Recycled glass fiber(commercial)		28	29	29	29
Recycled glass fiber		4	15	6	16
XPS (1)		9	5	7	9
XPS (2)		14	10	15	10
Straw bale		32	32	32	32
Cork		12	14	17	13
Perlite		29	28	28	28
Kenaf		5	6	10	5
Hemp		22	22	23	19
Flax		21	19	19	23
Recycled PET(commercial)		19	20	21	12
Cotton (recycled)		18	13	14	15
Mineralized wood fiber		8	23	9	17
EPS		15	9	8	18
Sheep wool		13	7	5	14
Coir		24	25	25	24
Jute		11	8	12	6
Polyisocyanurate		1	1	2	1
Glass wool		17	12	11	20
Reeds		27	27	27	27

.

MARCOS, WASPAS, and MACONT methods found the best three insulation materials as the same insulation materials. The ARAS method, on the other hand, found the best insulation material to be recycled textile (1). However, the Pearson correlation coefficient between the MACONT method and the ARAS method was found to be 0.797. This value shows that there is a high correlation between the results of the ARAS method and the results of the MACONT method. The Pearson correlation coefficient between the results of the MACONT method and the results of the MARCOS method was found to be 0.907. The Pearson correlation coefficient between the results of the MACONT method and the results of the WASPAS method was found to be 0.880. Both results show that there is a very high correlation between the results of the MACONT method and the results of the MARCOS and WASPAS methods. As a result, it can be said that the MACONT method has achieved accurate results.

When the weights of the evaluation criteria were changed, we tested whether there was a change in the order of the insulation materials. For this, five different scenarios consisting of different criteria weights were created. These scenarios are shown in

Table 13. The scenarios.

	Scenarios	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
Criteria
TC		0.120	0.050	0.050	0.100	0.100
PTT		0.120	0.150	0.100	0.250	0.200
SH		0.220	0.200	0.050	0.150	0.050
D		0.120	0.100	0.250	0.250	0.050
DF		0.120	0.100	0.100	0.050	0.250
SM		0.100	0.050	0.100	0.100	0.150
TT		0.100	0.150	0.200	0.050	0.150
TWS		0.100	0.200	0.150	0.050	0.050

.

Results of the scenarios are shown in Figure 1.

According to the results of scenario 1, the first 10 materials are as follows, respectively: jute, wood fiber (1), cellulose (2), polyurethane (2), XPS (2), cork, XPS (1), polyisocyanurate, polyurethane (1), and wood fiber (2). According to the results of scenario 2, the first 10 materials are as follows, respectively: wood fiber (1), jute, cellulose (2), wood fiber (2), mineralized wood fiber, kenaf, cork, polyurethane (2), polyisocyanurate, and polyurethane (1). According to the results of scenario 3, the first 10 materials are as follows, respectively: recycled textile (1), polyisocyanurate, polyurethane (1), polyurethane (2), sheep wool, recycled PET (commercial), XPS (1), cotton (recycled), XPS (2), and EPS. According to the results of scenario 4, the first 10 materials are as follows, respectively: polyurethane (2), recycled textile (1), polyisocyanurate, XPS (2), polyurethane (1), XPS (1), jute, sheep wool, kenaf, and recycled PET (commercial). According to the results of scenario 5, the first 10 materials are as follows, respectively: wood fiber (2), mineralized wood fiber, polyisocyanurate, wood fiber (1), polyurethane (1), kenaf, polyurethane (2), recycled glass fiber, cork, and XPS (1). The insulation material with the best performance varied in all scenarios. This means that the MACONT method adapts to the changes in the criteria weights. In other words, this method is sensitive to changes in the criteria weights. In addition, according to all scenarios, there are three insulation materials in the top 10: polyisocyanurate, polyurethane (1), and polyurethane (2).

5. Conclusions

Building insulation is one of the most efficient methods of energy conservation both in heating and cooling. Building insulation is an efficient method of energy saving, so it has become compulsory for new constructions in Turkey. This subject closely interests all engineering fields, such as: structural, material science, chemical, manufacturing, and industry engineering. All of these fields can make a contribution to the development or application of insulation materials. In recent history, many types of insulation materials have been manufactured and each of them has different values in material properties.

Multi-criteria assessment has recently become increasingly important for solving a variety of complex decision-making problems [62,63,64]. In the last decade, a multi-criteria assessment has occurred using one of the most essential techniques in energy improvement research, allowing for the comparison of many options [50]. The approach chosen and its logical rationale play a critical part in this review. A proper selection of the assessment methodology and criteria on which the assessment will depend can help to resolve difficult issues connected to the alternatives being considered.

In this study, a new MCDM model consisting of Fuzzy BWM, CRITIC and MACONT methods is proposed. The subjective weights of the criteria were found by taking the opinions of four experts with Fuzzy BWM. According to the results of the Fuzzy BWM, the criteria are listed as follows: TC, DF, PTT, TWS, SM, TT, D, and SH. According to these results, the most important criterion was determined as TC. The objective weights of the criteria were found with the CRITIC method. According to the results of the CRITIC method, the criteria are listed as follows: TWS, SM, D, DF, SH, TC, TT, and PTT. If the criteria are ordered by their combined weights, they are listed as follows: TC, DF, TWS, SM, D, PTT, TT and SH. With the MACONT method, the order of the insulation materials was obtained. According to the results of the MACONT method, the top 10 insulation materials are as follows: polyisocyanurate, polyurethane (1), polyurethane (2), wood fiber (1), kenaf, jute, cellulose (2), wood fiber (1), XPS (1) and XPS (2). According to the results, the best insulation material for healthier environment is determined as polyisocyanurate.

This study has some limitations. The most important one is that opinions were received from only four experts. Obtaining the opinion of four experts may be insufficient to find subjective weights. Future studies can do a more comprehensive study by getting more expert opinions. In addition, only one subjective weighting and one objective weighting method were used in this study. Future studies may refine the work by using more subjective weighting methods (Fuzzy FUCOM and Fuzzy AHP) and more objective weighting methods (CCSD and MEREC). Finally, BIM (building information modeling) was not used in this study. It has not been determined whether the results of the proposed MCDM methods are valid in practice. Therefore, future studies can test the validity of these methods in the practical field by combining the proposed MCDM methods with BIM.