# Sustainable High-Tech Brick Production with Energy-Oriented Consumption: An Integrated Possibilistic Approach Based on Criteria Interdependencies

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## Abstract

**:**

## 1. Introduction

#### 1.1. Environmental Competencies in Brick Industry

_{2}emissions from clamp kilns, a widely used type of brick kilns in India, and compared it with other prevalent kinds of brick kilns, and Chen et al. [12], who calculated the emission factor of some main air pollutants for current brick kilns in China. In other efforts, Yuan et al. [13] analyzed the environmental impacts, energy consumption, and economic aspects of brick production processes using a cradle-to-grave approach, David et al. [14] assessed both detrimental effects on the environment and workers’ health due to brick operations, and Sherris et al. [15] investigated the health effects of dust and air pollutants on children, which are emitted by brick kilns. Finally, Nasir et al. [16] assessed both detrimental environmental effects and human health problems due to brick production in Pakistan.

#### 1.2. Energy Efficiency Improvement in Brick Industry

#### 1.3. Sustainable and Clean Brick Production

#### 1.4. Background of Technology Assessment with High-Tech Approach

_{2}emission, operation costs, payback period, fuel consumption, social aspect, and so forth.

#### 1.5. Motivation of the Current Research

- ⚬
- Presenting a new hybrid hierarchical FMCDM method for technology evaluation process in the brick industry;
- ⚬
- Proposing an integrated approach of MTFPC and fuzzy DEMATEL methods to measure the criteria weights;
- ⚬
- Proposing a new technique to measure the weight of each expert;
- ⚬
- Developing a ranking method based on the last aggregation of the experts’ judgments to decrease the loss of data;
- ⚬
- Applying the proposed methodology to a case study to indicate its practicability.

## 2. Proposed a Novel Hybrid Fuzzy MCGDM (HFMCGDM) Approach

**Phase 1. Identifying the problem:**Considering the literature review, field study and interview with experts, the problem was identified. Then, the Delphi method was utilized to determine the assessment criteria and high-tech brick manufacturing candidates. After identifying the viable criteria and alternatives, we sent them back to the experts for approval. Finally, the hierarchical structure is built.

**Phase 2. Modified triangular fuzzy pair-wise comparison technique (MTFPC):**The analytic hierarchy process (AHP) method is an effective tool for solving MCDM problems; however, conventional AHP does not consider the vagueness and uncertainty of human judgments to model a real situation [48,49]. To overcome this problem, a fuzzy AHP method can be a more precise approach. Because Chang’s technique [50] is relatively easier and less time-consuming compared to other FAHP methods [51], this paper utilizes Chang’s technique to develop a modified triangular fuzzy pair-wise comparison (MTFPC) technique respecting the last aggregation attitude. The procedures of the proposed MTFPC technique are given as follows:

**Step 2.1.**Construct pair-wise fuzzy comparison matrices based on experts’ opinions (${\tilde{G}}^{k}={\left[{\tilde{g}}^{k}{}_{i{i}^{\prime}}\right]}_{n\times n}$) by using the following Equation:

**Step 2.2.**Compute the fuzzy synthetic extent (${\tilde{F}}_{i}^{k}$) for the i-th criterion as follows:

**Step 2.3**

**.**The possibility degree of ${\tilde{P}}^{\prime}=\left({{l}^{\prime}}_{1},{{m}^{\prime}}_{1},{{u}^{\prime}}_{1}\right)\ge \tilde{P}=\left({l}_{1},{m}_{1},{u}_{1}\right)$ is defined by:

**Step 2.4.**Considering the k-th expert, the following Equation is applied for a fuzzy number (${\tilde{P}}_{c}^{k}$).

**Step 2.5.**Calculate the normalized weight vector (${W}_{k}$) as:

**Phase 3. Proposed fuzzy DEMATEL technique:**The DEMATEL method is considered one of the MCDM techniques to analyze interdependent relationships among all criteria [52]. However, in real situations, owing to the ambiguity of DMs’ preferences, the crisp data cannot reflect human judgments [53]. Therefore, fuzzy DEMATEL and MTFPC methods can be integrated to precisely calculate the weights of the criteria. In the ensuing lines, the procedures of FDEMATEL are described:

**Step 3.1.**Develop the direct-relation fuzzy matrix $\left({\tilde{E}}^{k}\right)$ and then compute the average matrix. To obtain the influences and connection between criteria $\left({C}_{i},i=1,2,\dots ,n\right)$, a team of the DMs $\left(D{M}_{k},k=1,2,\dots ,K\right)$ are requested to drawn pair-wise comparisons. In this technique, the cause-effect relationships between criteria are expressed according to linguistic words adopted from [54]. Subsequently, they translated into fuzzy numbers.

**Step 3.2.**Normalize the direct-relation fuzzy matrix $\left({\tilde{X}}^{k}\right)$ by applying Equation (8).

**Step 3.3.**Calculate the fuzzy total-relation matrix $\left({\tilde{T}}^{k}\right)$ through Equation (9).

**Step 3.4.**Each fuzzy element of the total-relation matrix ${\tilde{e}}_{ij}{}^{k}=({l}_{ij}^{k},{m}_{ij}^{k},{u}_{ij}^{k})$ is transformed into crisp numbers (${e}_{ij}^{k}$) by:

**Phase 4. Proposed integrated approach of FDEMATEL and MTFPC methods:**In this approach, at first, FDEMATEL is used to identify interrelationship among all criteria, and then MTFPC is proposed to measure local weight (${W}_{i}^{k}$) of the criteria. Consequently, the combination of FDEMATEL and MTFPC methods is proposed to calculate the global weight of criteria as follows:

**Phase 5. Triangular fuzzy preference assessment Index method (TFPAI):**By considering all experts’ opinions, we can have a more viable assessment. Consequently, a new methodology is developed to measure the weight of each DM by utilizing the mathematical logic of the TOPSIS technique [55]. The descriptions of the proposed methodology are given as follows:

**Step 5.1.**Construct the fuzzy decision matrix to evaluate alternative performances based on each expert’s opinion. Thereby, m alternatives (A

_{m}), n criteria (C

_{n}), and a group of experts (K

_{k}) have been considered.

**Step 5.2.**Make the normalized fuzzy judgment matrix $\left({\tilde{N}}^{k}\right)$ by utilizing the Equations (13)–(15).

**Step 5.3.**Form the weighted normalized fuzzy judgment matrix ($\tilde{R}$) by:

**Step 5.4.**Specify the positive (${\delta}^{\ast}$) and negative (${\delta}^{-}$) optimum solutions as follows:

**Step 5.5.**Measure the distance of the experts’ preferences from optimum solutions (${\mathsf{\Psi}}_{k}^{*},{\mathsf{\Psi}}_{k}^{-}$) by:

**Step 5.6.**Measure the experts’ weights $\left({\varpi}_{k}\right)$ by utilizing the ensuing relations:

**Phase 6. Extended fuzzy TOPSIS collective index method (EFTOPSIS-CI):**TOPSIS is a multi-criteria methodology to recognize the most appropriate solution among several alternatives [56]. The uncertainty and ambiguity associated with human preferences make it difficult for the DMs to assign an accurate performance rating to alternatives [57]. To overcome this difficulty and also avoiding the loss of data, we develop a new Fuzzy TOPSIS method for prioritizing the options according to the last aggregation of the experts’ opinions. The steps of the proposed method are as below:

**Step 6.1.**Consider the criteria weights obtained from the integration of MTFPC and FDEMATEL as the inputs for TFPAI and EFTOPSIS-CI computations.

**Step 6.2.**Compute the weighted normalized fuzzy judgment matrix through Equations (13)–(16).

**Step 6.3.**Obtain the positive (${\gamma}_{i}^{\ast k}$) and negative (${\gamma}_{i}^{-k}$) optimum solutions by using Equations (23) and (24).

**Step 6.4.**Determine the distance of alternatives from optimum solutions (${\theta}_{j}^{*k}$,${\theta}_{j}^{-k}$) through the following Equations:

**Step 6.5.**Obtain the local priority for all alternatives (${S}_{j}^{k}$) with respect to the similarity to the best solution by:

**Step 6.6.**According to the last aggregation attitude, the global priority of all alternatives (${S}_{j}^{F}$) is calculated by:

## 3. Case Study

#### 3.1. Problem Description

#### 3.2. Application of the Proposed Approach

## 4. Discussion

#### 4.1. Environmental and Energy Analysis

_{2}), Particulate Matter (PM2.5), and Suspended Particulate Matter (SPM). After that, zig-zag and tunnel kilns take the second and third place, respectively. The zig-zag kiln has the minimum amount of carbon monoxide (CO), followed by VSBK and TK. The TK has the highest concentration of carbon dioxide (CO

_{2}), followed by VSBK and ZZK. By comparing the SEC of mentioned kilns, VSBK has the minimum amount, then zig-zag and tunnel kilns have the lowest values, respectively, meaning that VSBK has the best performance in energy consumption. Looking at the Figure 5, it can be concluded that there is a direct relationship between energy consumption and carbon dioxide production. In other words, the more SEC is, the more CO

_{2}will be produced.

#### 4.2. Comparative Analysis

#### 4.3. Sensitivity Analysis

#### 4.4. Managerial Insights

## 5. Conclusions and Future Directions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Relative high-tech brick kilns: (

**a**) zig-zag kiln; (

**b**) Vertical shaft brick kiln; and (

**c**) Tunnel kiln.

Authors | Characteristics of Methods | ||||||
---|---|---|---|---|---|---|---|

Hierarchy Structure | Sustainability Approach | High-Tech Oriented | Computing the Experts’ Weights | Determining the Criteria’s Weights | Uncertainty Modeling | Considering the Last Aggregation | |

Khatri and Srivastava [38] | ✓ | ✓ | ✓ | ✓ | |||

Dinmohammadi and Shafiee [39] | ✓ | ✓ | ✓ | ✓ | |||

Ligus and Peternek [40] | ✓ | ✓ | ✓ | ✓ | |||

Ijadi Maghsoodi et al. [41] | ✓ | ✓ | ✓ | ✓ | |||

Aloini et al. [42] | ✓ | ✓ | ✓ | ✓ | |||

Karat et al. [43] | ✓ | ✓ | ✓ | ✓ | ✓ | ||

Kheybari et al. [44] | ✓ | ✓ | ✓ | ✓ | |||

Rani et al. [45] | ✓ | ✓ | ✓ | ✓ | |||

Mishra et al. [46] | ✓ | ✓ | ✓ | ✓ | |||

Dogan [47] | ✓ | ✓ | ✓ | ||||

This study | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Linguistic Terms | Triangular Fuzzy Numbers |
---|---|

Absolutely strong (AS) | (2, 5/2, 3) |

Very strong (VS) | (3/2, 2, 5/2) |

Fairly strong (FS) | (1, 3/2, 2) |

Slightly strong (SS) | (1, 1, 3/2) |

Equal (E) | (1, 1, 1) |

Slightly weak (SW) | (2/3, 1, 1) |

Fairly weak (FW) | (1/2, 2/3, 1) |

Very weak (VW) | (2/5, 1/2, 2/3) |

Absolutely weak (AW) | (1/3, 2/5, 1/2) |

Criteria | Results | ||
---|---|---|---|

${\mathrm{DM}}_{1}$ | ${\mathrm{DM}}_{2}$ | ${\mathrm{DM}}_{3}$ | |

${C}_{1}\mathrm{vs}.{C}_{2}$ | FW | FW | FW |

${C}_{1}\mathrm{vs}.{C}_{3}$ | FS | VS | FS |

${C}_{1}\mathrm{vs}.{C}_{4}$ | FS | FS | FS |

${C}_{1}\mathrm{vs}.{C}_{5}$ | FW | FW | FW |

${C}_{2}\mathrm{vs}.{C}_{3}$ | FS | FS | FS |

${C}_{2}\mathrm{vs}.{C}_{4}$ | FS | VS | FS |

${C}_{2}\mathrm{vs}.{C}_{5}$ | FS | FS | SS |

${C}_{3}\mathrm{vs}.{C}_{4}$ | SS | FS | SS |

${C}_{3}\mathrm{vs}.{C}_{5}$ | FW | FW | SW |

${C}_{4}\mathrm{vs}.{C}_{5}$ | FW | FW | SW |

Criteria | $\sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{l}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}$ | $\sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{m}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}$ | $\sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{u}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}$ |
---|---|---|---|

C_{1} | 4.000 | 5.333 | 7.000 |

C_{2} | 5.000 | 7.000 | 9.000 |

C_{3} | 3.500 | 4.000 | 5.500 |

C_{4} | 3.167 | 4.000 | 5.000 |

C_{5} | 4.500 | 6.167 | 8.000 |

$\left({\displaystyle \sum _{{i}^{\prime}=1}^{n}{l}_{{i}^{\prime}}^{k},}{\displaystyle \sum _{{i}^{\prime}=1}^{n}{m}_{{i}^{\prime}}^{k},}{\displaystyle \sum _{{i}^{\prime}=1}^{n}{u}_{{i}^{\prime}}^{k}}\right)$ | 20.167 | 26.500 | 34.500 |

${\left({\displaystyle \sum _{{i}^{\prime}=1}^{n}{l}_{{i}^{\prime}}^{k},}{\displaystyle \sum _{{i}^{\prime}=1}^{n}{m}_{{i}^{\prime}}^{k},}{\displaystyle \sum _{{i}^{\prime}=1}^{n}{u}_{{i}^{\prime}}^{k}}\right)}^{-1}$ | 0.0290 | 0.0377 | 0.0496 |

Criteria | $\sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{l}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}}/{\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\displaystyle \sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{u}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}}$ | $\sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{m}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}}/{\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\displaystyle \sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{m}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}}$ | $\sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{u}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}}/{\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\displaystyle \sum _{{\mathit{i}}^{\prime}=1}^{\mathit{n}}{\mathit{l}}_{{\mathit{i}}^{\prime}}^{\mathit{k}}}$ |
---|---|---|---|

C_{1} | 0.116 | 0.201 | 0.347 |

C_{2} | 0.145 | 0.264 | 0.446 |

C_{3} | 0.101 | 0.151 | 0.273 |

C_{4} | 0.092 | 0.151 | 0.248 |

C_{5} | 0.130 | 0.233 | 0.397 |

Criteria | Decision-Makers | ||
---|---|---|---|

${\mathrm{DM}}_{1}$ | ${\mathrm{DM}}_{2}$ | ${\mathrm{DM}}_{3}$ | |

C_{1} | 0.2085 | 0.2256 | 0.2159 |

C_{2} | 0.2733 | 0.2927 | 0.2677 |

C_{3} | 0.1449 | 0.1469 | 0.1550 |

C_{4} | 0.1302 | 0.0935 | 0.1393 |

C_{5} | 0.2430 | 0.2413 | 0.2221 |

**Table 7.**The fuzzy scale to indicate the relationship among criteria [59].

Linguistic Terms | Triangular Fuzzy Numbers |
---|---|

Very high influence (VH) | (0.7, 0.9, 1) |

High influence (H) | (0.5, 0.7, 0.9) |

Low influence (L) | (0.3, 0.5, 0.7) |

Very low influence (VL) | (0.1, 0.3, 0.5) |

No influence (No) | (0, 0.1, 0.3) |

Decision-Makers | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathrm{DM}}_{1}$ | ${\mathrm{DM}}_{2}$ | ${\mathrm{DM}}_{3}$ | |||||||||||||

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | |

C_{1} | No | H | L | L | L | No | H | L | L | L | No | VH | L | H | L |

C_{2} | L | No | L | L | L | H | No | L | L | L | VH | No | H | H | H |

C_{3} | L | L | No | H | H | H | L | No | H | H | H | L | No | H | H |

C_{4} | L | L | L | No | L | L | L | L | No | L | L | L | L | No | L |

C_{5} | H | VH | H | H | No | H | VH | VH | H | No | VH | VH | VH | H | No |

Criteria | Decision-Makers | ||
---|---|---|---|

${\mathrm{DM}}_{1}$ | ${\mathrm{DM}}_{2}$ | ${\mathrm{DM}}_{3}$ | |

C_{1} | 0.1942 | 0.2149 | 0.2105 |

C_{2} | 0.2097 | 0.2052 | 0.1964 |

C_{3} | 0.1951 | 0.1934 | 0.1935 |

C_{4} | 0.2081 | 0.2015 | 0.2145 |

C_{5} | 0.1929 | 0.1850 | 0.1581 |

Sub-Criteria | Experts | ||
---|---|---|---|

${\mathrm{DM}}_{1}$ | ${\mathrm{DM}}_{2}$ | ${\mathrm{DM}}_{3}$ | |

$S{C}_{11}\mathrm{vs}.S{C}_{12}$ | SS | FW | FW |

$S{C}_{11}\mathrm{vs}.S{C}_{13}$ | FW | FW | SW |

$S{C}_{11}\mathrm{vs}.S{C}_{14}$ | FS | SS | SS |

$S{C}_{12}\mathrm{vs}.S{C}_{13}$ | FW | FW | FW |

$S{C}_{12}\mathrm{vs}.S{C}_{14}$ | SS | SS | SS |

$S{C}_{13}\mathrm{vs}.S{C}_{14}$ | FS | FS | FS |

$S{C}_{21}\mathrm{vs}.S{C}_{22}$ | FS | FS | SS |

$S{C}_{21}\mathrm{vs}.S{C}_{23}$ | FS | FS | SS |

$S{C}_{21}\mathrm{vs}.S{C}_{24}$ | VS | VS | VS |

$S{C}_{22}\mathrm{vs}.S{C}_{23}$ | FW | SW | SW |

$S{C}_{22}\mathrm{vs}.S{C}_{24}$ | FW | FW | FW |

$S{C}_{23}\mathrm{vs}.S{C}_{24}$ | FS | FS | SS |

$S{C}_{31}\mathrm{vs}.S{C}_{32}$ | SS | FS | FS |

$S{C}_{31}\mathrm{vs}.S{C}_{33}$ | FS | FS | FS |

$S{C}_{32}\mathrm{vs}.S{C}_{33}$ | SS | SS | FS |

$S{C}_{41}\mathrm{vs}.S{C}_{42}$ | SS | SW | SW |

$S{C}_{41}\mathrm{vs}.S{C}_{43}$ | FS | FS | SW |

$S{C}_{42}\mathrm{vs}.S{C}_{43}$ | SS | SS | SS |

$S{C}_{51}\mathrm{vs}.S{C}_{52}$ | FW | FW | FW |

$S{C}_{51}\mathrm{vs}.S{C}_{53}$ | SW | FW | SS |

$S{C}_{51}\mathrm{vs}.S{C}_{54}$ | SW | SW | SW |

$S{C}_{52}\mathrm{vs}.S{C}_{53}$ | FS | FS | FS |

$S{C}_{52}\mathrm{vs}.S{C}_{54}$ | FS | FS | FS |

$S{C}_{53}\mathrm{vs}.S{C}_{54}$ | SS | SS | FS |

Criteria | Global Weights | Sub- Criteria | Local Weights | Global Weights | ||||||
---|---|---|---|---|---|---|---|---|---|---|

DM_{1} | DM_{2} | DM_{3} | DM_{1} | DM_{2} | DM_{3} | DM_{1} | DM_{2} | DM_{3} | ||

C_{1} | 0.1942 | 0.2149 | 0.2105 | SC_{11} | 0.2659 | 0.1920 | 0.1973 | 0.0516 | 0.0412 | 0.0415 |

SC_{12} | 0.2069 | 0.2659 | 0.2554 | 0.0402 | 0.0571 | 0.0537 | ||||

SC_{13} | 0.3617 | 0.3617 | 0.3501 | 0.0702 | 0.0777 | 0.0737 | ||||

SC_{14} | 0.1654 | 0.1805 | 0.1973 | 0.0321 | 0.0388 | 0.0415 | ||||

C_{2} | 0.2097 | 0.2052 | 0.1964 | SC_{21} | 0.3794 | 0.3985 | 0.3616 | 0.0796 | 0.0818 | 0.0710 |

SC_{22} | 0.1349 | 0.1432 | 0.1567 | 0.0283 | 0.0294 | 0.0308 | ||||

SC_{23} | 0.2887 | 0.2587 | 0.2488 | 0.0605 | 0.0531 | 0.0489 | ||||

SC_{24} | 0.1969 | 0.1995 | 0.2329 | 0.0413 | 0.0409 | 0.0457 | ||||

C_{3} | 0.1951 | 0.1934 | 0.1935 | SC_{31} | 0.4330 | 0.4866 | 0.4495 | 0.0845 | 0.0941 | 0.0870 |

SC_{32} | 0.3297 | 0.2812 | 0.3433 | 0.0643 | 0.0544 | 0.0664 | ||||

SC_{33} | 0.2373 | 0.2322 | 0.2072 | 0.0463 | 0.0449 | 0.0401 | ||||

C_{4} | 0.2081 | 0.2015 | 0.2145 | SC_{41} | 0.4330 | 0.4101 | 0.2876 | 0.0901 | 0.0826 | 0.0617 |

SC_{42} | 0.3297 | 0.3408 | 0.4299 | 0.0686 | 0.0687 | 0.0922 | ||||

SC_{43} | 0.2373 | 0.2490 | 0.2824 | 0.0494 | 0.0502 | 0.0606 | ||||

C_{5} | 0.1929 | 0.1850 | 0.1581 | SC_{51} | 0.1803 | 0.1654 | 0.2043 | 0.0348 | 0.0306 | 0.0378 |

SC_{52} | 0.3784 | 0.3617 | 0.3571 | 0.0730 | 0.0669 | 0.0661 | ||||

SC_{53} | 0.2316 | 0.2659 | 0.2491 | 0.0477 | 0.0492 | 0.0461 | ||||

SC_{54} | 0.2097 | 0.2069 | 0.1895 | 0.0405 | 0.0383 | 0.0351 |

Sub-Criteria | Alternatives | ||||||||
---|---|---|---|---|---|---|---|---|---|

A_{1} | A_{2} | A_{3} | |||||||

DM_{1} | DM_{2} | DM_{3} | DM_{1} | DM_{2} | DM_{3} | DM_{1} | DM_{2} | DM_{3} | |

SC_{11} | MG | MG | G | F | F | MP | G | VG | VG |

SC_{12} | MG | F | MG | P | P | P | VG | G | VG |

SC_{13} | G | MG | MG | F | F | MG | VG | VG | VG |

SC_{14} | MG | G | G | P | MP | F | VG | G | VG |

SC_{21} | VG | VG | G | MG | MG | G | P | P | P |

SC_{22} | G | G | VG | MG | G | MG | P | F | P |

SC_{23} | G | G | G | G | MG | MG | P | P | F |

SC_{24} | MG | G | G | MG | F | F | F | F | P |

SC_{31} | G | MG | MG | G | G | VG | P | F | F |

SC_{32} | G | MG | MG | F | MG | F | G | G | G |

SC_{33} | F | MG | MG | G | G | G | MG | G | MG |

SC_{41} | MG | F | F | G | G | MG | F | MG | MG |

SC_{42} | P | P | P | F | F | F | MG | G | G |

SC_{43} | F | F | F | MP | F | MP | G | G | G |

SC_{51} | F | MG | F | G | G | MG | P | P | P |

SC_{52} | MG | G | G | VG | VG | G | F | P | MP |

SC_{53} | F | F | F | P | P | F | G | MG | G |

SC_{54} | F | F | MP | P | P | MP | VG | G | G |

Options | Experts | |||||
---|---|---|---|---|---|---|

DM_{1} | DM_{2} | DM_{3} | ||||

${\mathit{\psi}}_{\mathit{k}}^{*}$ | ${\mathit{\psi}}_{\mathit{k}}^{-}$ | ${\mathit{\psi}}_{\mathit{k}}^{*}$ | ${\mathit{\psi}}_{\mathit{k}}^{-}$ | ${\mathit{\psi}}_{\mathit{k}}^{*}$ | ${\mathit{\psi}}_{\mathit{k}}^{-}$ | |

${A}_{1}$ | 1.1497 | 0.2323 | 1.12186 | 0.2634 | 1.12795 | 0.2683 |

${A}_{2}$ | 0.7583 | 0.2426 | 0.7681 | 0.2334 | 0.6631 | 0.3387 |

${A}_{3}$ | 1.1883 | 0.2119 | 1.1731 | 0.2156 | 1.1762 | 0.2300 |

Experts | Relative Weight | Normalized Weights |
---|---|---|

${\mathit{\tau}}_{\mathit{k}}$ | ${\mathit{\varpi}}_{\mathit{k}}$ | |

${\mathrm{DM}}_{1}$ | 0.1815 | 0.31 |

${\mathrm{DM}}_{2}$ | 0.1887 | 0.32 |

${\mathrm{DM}}_{3}$ | 0.2201 | 0.37 |

Alternatives | ${\mathrm{DM}}_{1}$ | ${\mathrm{DM}}_{2}$ | ${\mathrm{DM}}_{3}$ | ||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{\gamma}}_{\mathit{j}}^{*\mathit{k}}$ | ${\mathit{\gamma}}_{\mathit{j}}^{-\mathit{k}}$ | ${\mathit{S}}_{\mathit{j}}^{\mathit{k}}$ | ${\mathit{\gamma}}_{\mathit{j}}^{*\mathit{k}}$ | ${\mathit{\gamma}}_{\mathit{j}}^{-\mathit{k}}$ | ${\mathit{S}}_{\mathit{j}}^{\mathit{k}}$ | ${\mathit{\gamma}}_{\mathit{j}}^{*\mathit{k}}$ | ${\mathit{\gamma}}_{\mathit{j}}^{-\mathit{k}}$ | ${\mathit{S}}_{\mathit{j}}^{\mathit{k}}$ | |

${A}_{1}$ | 0.4536 | 0.3378 | 0.42 | 0.4385 | 0.3621 | 0.45 | 0.4734 | 0.3964 | 0.46 |

${A}_{2}$ | 0.4993 | 0.3092 | 0.38 | 0.5214 | 0.3132 | 0.37 | 0.5044 | 0.2903 | 0.37 |

${A}_{3}$ | 0.4307 | 0.4066 | 0.48 | 0.3940 | 0.3913 | 0.49 | 0.4168 | 0.4385 | 0.51 |

**Table 16.**Comparison of energy usage and pollutants [60].

Technology | Emission Factor (g/kg of Fired Brick) | SEC (MJ/kg Fired Brick) | ||||
---|---|---|---|---|---|---|

CO | CO_{2} | SO_{2} | PM2.5 | SPM | ||

ZZK | 1.47 | 103 | 0.32 | 0.13 | 0.26 | 1.13 |

VSBK | 1.84 | 70 | 0.54 | 0.09 | 0.11 | 0.91 |

TK | 2.45 | 166 | 0.72 | 0.18 | 0.31 | 1.48 |

Alternative | Proposed Approach | Dinmohammadi and Shafiee [39] | ||
---|---|---|---|---|

Similarity Index | Rank | Similarity Index | Rank | |

${A}_{1}$ | 0.4538 | 2 | 0.4087 | 2 |

${A}_{2}$ | 0.3521 | 3 | 0.3217 | 3 |

${A}_{3}$ | 0.5103 | 1 | 0.4492 | 1 |

$\mathrm{Standard}\mathrm{deviation}\left({\sigma}_{j}\right)$ | 0.0801 | 0.0651 |

Comparison Parameters | Results | Superiority of Proposed Method | ||
---|---|---|---|---|

Lose | Adequate | Overcome | ||

Group decision-making | The experts take part in the decision-making processes in these two methods. As a result, they utilize the experts’ opinions to evaluate candidates. | √ | ||

Criteria’s weights | The proposed approach calculated the weights of the criteria. In other words, The DMs expressed their viewpoint about the significance of evaluation criteria. Consequently, the proposed approach leads to an accurate solution in the compassion of the Dinmohammadi and Shafiee [39] method, which did not consider the criteria weight in the decision-making processes. | √ | ||

Modeling uncertainty | The proposed methodology is utilized fuzzy concepts. Hence, it is appropriate to deal with vague and imprecise data in technology selection problems. In contrast, the Dinmohammadi and Shafiee [39] method could not reflect the experts’ preferences appropriately. | √ | ||

Experts’ weights | Because experts have different attitudes and interests, determining the experts’ weights is a key part of group decision-making problems. To address this issue, the proposed methodology calculates the weight of each expert. Therefore, the proposed framework leads to a more precise solution. | √ | ||

Last aggregation tactic | The last aggregation of DMs’ opinions is considered in the proposed methodology to avoid information loss. Thus, the proposed methodology leads to a more precise solution versus the Dinmohammadi and Shafiee [39] method, which did not consider this concept. | √ | ||

Time complexity | Computing the weights of criteria, experts’ weights, and considering the last aggregation in the proposed methodology takes time and leads to more computations. As a result, the method of Dinmohammadi and Shafiee [39] method has less time complexity in comparison with the proposed methodology. | √ |

Expert No. | Definition | Overall Score | Ranking | ||
---|---|---|---|---|---|

A_{1} | A_{2} | A_{3} | |||

1 | ${W}_{c1-c5}=\left(1/3,2/5,1/2\right)$ | 0.343 | 0.322 | 0.361 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

2 | ${W}_{c1-c5}=\left(2/5,1/2,2/3\right)$ | 0.352 | 0.331 | 0.378 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

3 | ${W}_{c1-c5}=\left(1/2,2/3,1\right)$ | 0.367 | 0.351 | 0.388 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

4 | ${W}_{c1-c5}=\left(2/3,1,1\right)$ | 0.381 | 0.369 | 0.401 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

5 | ${W}_{c1-c5}=\left(1,1,3/2\right)$ | 0.395 | 0.380 | 0.418 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

6 | ${W}_{c1-c5}=\left(1,3/2,2\right)$ | 0.401 | 0.392 | 0.426 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

7 | ${W}_{c1-c5}=\left(3/2,2,5/2\right)$ | 0.421 | 0.404 | 0.449 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

8 | ${W}_{c1-c5}=\left(2,5/2,3\right)$ | 0.438 | 0.424 | 0.457 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

9 | ${W}_{c1}=\left(2,5/2,3\right),{W}_{c2-c5}=\left(1/3,2/5,1/2\right)$ | 0.417 | 0.351 | 0.473 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

10 | ${W}_{c2}=\left(2,5/2,3\right),{W}_{c1,c3-c5}=\left(1/3,2/5,1/2\right)$ | 0.523 | 0.423 | 0.333 | ${A}_{1}>{A}_{2}>{A}_{3}$ |

11 | ${W}_{c3}=\left(2,5/2,3\right),{W}_{c1-c2,c4-c5}=\left(1/3,2/5,1/2\right)$ | 0.441 | 0.483 | 0.412 | ${A}_{2}>{A}_{1}>{A}_{3}$ |

12 | ${W}_{c4}=\left(2,5/2,3\right),{W}_{c1-c3,c5}=\left(1/3,2/5,1/2\right)$ | 0.431 | 0.374 | 0.463 | ${A}_{3}>{A}_{1}>{A}_{2}$ |

13 | ${W}_{c5}=\left(2,5/2,3\right),{W}_{c1-c4}=\left(1/3,2/5,1/2\right)$ | 0.440 | 0.512 | 0.401 | ${A}_{2}>{A}_{1}>{A}_{3}$ |

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**MDPI and ACS Style**

Solgi, E.; Gitinavard, H.; Tavakkoli-Moghaddam, R.
Sustainable High-Tech Brick Production with Energy-Oriented Consumption: An Integrated Possibilistic Approach Based on Criteria Interdependencies. *Sustainability* **2022**, *14*, 202.
https://doi.org/10.3390/su14010202

**AMA Style**

Solgi E, Gitinavard H, Tavakkoli-Moghaddam R.
Sustainable High-Tech Brick Production with Energy-Oriented Consumption: An Integrated Possibilistic Approach Based on Criteria Interdependencies. *Sustainability*. 2022; 14(1):202.
https://doi.org/10.3390/su14010202

**Chicago/Turabian Style**

Solgi, Ehsan, Hossein Gitinavard, and Reza Tavakkoli-Moghaddam.
2022. "Sustainable High-Tech Brick Production with Energy-Oriented Consumption: An Integrated Possibilistic Approach Based on Criteria Interdependencies" *Sustainability* 14, no. 1: 202.
https://doi.org/10.3390/su14010202