# A Hybrid Intuitionistic Fuzzy-MEREC-RS-DNMA Method for Assessing the Alternative Fuel Vehicles with Sustainability Perspectives

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## Abstract

**:**

_{2}), hybrid electric vehicles (G

_{1}), and hydrogen vehicles (G

_{3}) achieve higher overall performance compared to the other technologies available in India. The assessment outcomes prove that electric vehicles can serve as a valuable alternative for decreasing carbon emissions and negative effects on the environment. This technology contributes to transportation sector development and job creation in less developed areas of the country. Moreover, a comparison with existing studies and a sensitivity investigation are conferred to reveal the robustness and stability of the developed framework.

## 1. Introduction

_{2}emissions. This transportation fuel is mainly based on the combustion of fossil fuels, making it one of the key sources of air pollution in both the urban and regional areas [4,5].

- We identify the parameters for selecting AFVs for sustainable road transportation, using a survey approach based on the literature and interviews with the experts.
- We present a comprehensive procedure to evaluate and analyze the related parameters of AFV selection for sustainable road transportation with a hybrid decision support method.
- We propose a weighting procedure called the intuitionistic fuzzy subjective objective integrated approach, using the IF-MEREC and RS method to obtain the parameters weights of selecting AFVs for sustainable road transportation.
- The IF-DNMA method on IFSs is discussed using the IF-generalized Dombi operator and the IF-MEREC-RS method, with the aim of ranking AFVs for sustainable road transportation.
- We present sensitivity and comparison analyses to validate the integrated IF-MEREC-RS-DNMA approach.

## 2. Preliminaries

#### 2.1. AFVs Assessment and Selection

#### 2.2. Intuitionistic Fuzzy Set (IFS)

#### 2.3. DNMA Method

## 3. Proposed IF-Generalized Dombi Weighted AOs

#### 3.1. Basic Concepts

**Definition**

**1**

**[29].**

**Definition**

**2**

**[60].**

**Definition**

**3**

**[61].**

**Definition**

**4**

**[60].**

**Definition**

**5**

**[62].**

#### 3.2. Generalized-Dombi Operations on IFNs

**Definition**

**6.**

**Theorem**

**1.**

- (i)
- ${\omega}_{1}\tilde{\oplus}{\omega}_{2}={\omega}_{2}\tilde{\oplus}{\omega}_{1};$
- (ii)
- ${\omega}_{1}\tilde{\otimes}{\omega}_{2}={\omega}_{2}\tilde{\otimes}{\omega}_{1};$
- (iii)
- $\zeta ({\omega}_{1}\tilde{\oplus}{\omega}_{2})=(\zeta {\omega}_{1})\tilde{\oplus}(\zeta {\omega}_{2});$
- (iv)
- ${({\omega}_{1}\tilde{\otimes}{\omega}_{2})}^{\zeta}=({\omega}_{1}^{\zeta})\tilde{\otimes}({\omega}_{2}^{\zeta});$
- (v)
- $({\zeta}_{1}+{\zeta}_{2}){\omega}_{1}=({\zeta}_{1}{\omega}_{1})\tilde{\oplus}({\zeta}_{2}{\omega}_{1});$
- (vi)
- ${({\omega}_{1})}^{{\zeta}_{1}+{\zeta}_{2}}=({\omega}_{1}^{{\zeta}_{1}})\tilde{\otimes}({\omega}_{1}^{{\zeta}_{2}}).$

**Proof.**

#### 3.3. IF-Generalized-Dombi Weighted Averaging (IFGDWA) Operator

**Definition**

**7.**

**Theorem**

**2.**

**Proof.**

- (i)
- For $p=1,q=1,$ the IFGDWA diminishes to the IFWA operator.
- (ii)
- For $p=1,q=2,$ the IFGDWA concerts to the “intuitionistic fuzzy Einstein weighted averaging (IFEWA)” operator; and
- (iii)
- For $q=1,$ the IFGDWA operator reduces to the “intuitionistic fuzzy Hamacher weighted averaging (IFHWA)” operator.

**Theorem**

**3**

**(Shift**

**invariance).**

**Theorem**

**4.**

**Theorem**

**5**

**(Boundedness).**

**Theorem**

**6**

**(Monotonicity).**

#### 3.4. IF-Generalized-Dombi Weighted Geometric (IFGDWG) Operator

**Definition**

**8.**

**Theorem**

**7.**

**Proof.**

- (i)
- For $p=1,q=1,$ the IFGDWG operator moderates to the IFWG operator.
- (ii)
- For $p=1,q=2,$ the IFGDWG operator reduces to the “intuitionistic fuzzy Einstein weighted averaging (IFEWG)” operator; and
- (iii)
- For $q=1,$ the IFGDWG operator reduces to the “intuitionistic fuzzy Hamacher weighted averaging (IFHWG)” operator.

**Theorem**

**8**

**(Shift**

**invariance).**

**Theorem**

**9.**

**Theorem**

**10**

**(Boundedness).**

**Theorem**

**11**

**(Monotonicity).**

## 4. Proposed IF-MEREC-RS-DNMA Method

_{i}over attribute C

_{j}given by kth expert, and further, converted into IF-DM.

_{b}and C

_{n}represent the benefit and cost-type attributes, respectively.

_{j}symbolizes the rank of each attribute, where $j=1\left(1\right)n.$

## 5. Case Study: Assessment of Alternative Fuel Vehicles (AFVs)

_{1}), electric vehicles (G

_{2}), hydrogen vehicles (G

_{3}), natural gas vehicles (G

_{4}), and biofuel vehicles (G

_{5}). In addition, open interviews and literature reviews facilitated us to recognize global AFVs. On account of the initial analysis, extant literature, and discussion with experts, 15 attributes have been recognized, as shown in Table 1. Afterward, DEs are invited to give their opinions and experiences, both to weigh the evaluation criteria and to score the candidate AFVs by means of each criterion. As per their domain knowledge, DEs express their preferences in the form of LVs.

_{i}over the different attributes. From Equation (18) and Table 5, the AIF-DM is computed (taking p = 1 and q = 1) and shown in Table 6.

_{1}= 0.370, S

_{2}= 0.353, S

_{3}= 0.404, S

_{4}= 0.358 and S

_{5}= 0.389. By means of Equation (21), the overall performance of each option by removing each attribute is computed and shown in Table 7. Next, we derive the removal effect of each attribute on the overall performance of the options using Equation (22). Furthermore, we calculate the final attributes’ weights for AFV selection by utilizing Equations (23) and (24), and given in last column of Table 7. The resultant values are in depicted in Figure 2.

_{j}= (0.0473, 0.0670, 0.0570, 0.0669, 0.0500, 0.0949, 0.0576, 0.0530, 0.0610, 0.0876, 0.0520, 0.0702, 0.0770, 0.0755, 0.0830).

_{6}), with a weight value of 0.0949, have been determined to be the most important parameter in AFV selection. Fueling/charging infrastructure (C

_{11}), with a weight value of 0.0876, is the second most important parameter in AFV selection. Financial incentives (C

_{15}), with a significance value of 0.0830, is the third most significant parameter in AFV selection, and others are considered as crucial parameters in AFV selection for sustainable road transportation.

_{2}is with a highest UD of appropriateness of options.

#### 5.1. Comparative Study

#### 5.1.1. IF-COPRAS Method

_{2}is obtained to be the most appropriate AFV, as it has the highest relative weight value (0.2933).

#### 5.1.2. IF-WASPAS Method

_{2}is with higher degree of appropriateness of the selection AFVs.

- The presented methodology estimates the attribute weights with the use of a combined IF-MEREC-RS process, which achieves more accurate attributes’ weights, while in IF-WASPAS, only the objective weight of criteria is estimated with the use of a similarity measure, and in IF-COPRAS, the weight of criteria is assumed by experts.
- According to the computation procedures of the three methods, we can find the subordinate utility degrees and rank the options by using the IF-DNMA method, which can not only ensure that the selected alternative performs excellently in total, but also avoids the bad performance under each criterion. To this point, the IF-MEREC-RS-DNMA can provide experts with a more robust reference compared with the IF-WASPAS method and IF-COPRAS.
- Aggregation functions used in the IF-MEREC-RS-DNMA model have both the linear and vector normalizations, while the IF-COPRAS model uses vector normalization, and the IF-WASPAS model utilizes the linear normalization. So, the IF-MEREC-RS-DNMA method is more reliable and flexible than extant methods.
- The proposed methodology is applied in the IF-DNMA method to increase the robustness of the fuzzy-DNMA model. Compared to the extant utility based ranking method (namely MULTIMOORA [84], VIKOR [85], TOPSIS [86], ELECTRE [87], COPRAS [81], WASPAS [83], CoCoSo [88], and others), the key benefit of the DNMA approach is that it is considered by two normalization procedures (namely target-based linear and vector normalization). Moreover, DNMA approach gives the DEs to adjust the weight of subordinate models (namely CCM, UCM, and ICM) to reveal their preferences on the “group utility” values and the “individual regret” values of options. Thus, the proposed hybrid DNMA approach is fulfilling the existing gap in the study of AFV assessment.

#### 5.2. Sensitivity Investigation

_{2}is at the top of the ranking, while the G

_{5}has the last rank for ϑ = 0.0 to ϑ = 0.8 and the G

_{3}is at the top of the ranking and G

_{5}has the last rank for ϑ = 0.9 to ϑ = 1.0. Therefore, it is observable that the developed method possesses adequate stability with numerous parameter values. As shown clearly in Table 15, the developed IF-MEREC-RS-DNMA methodology is capable of generating stable and, at the same time, flexible preference results in a variety of utility parameter. This property is of high importance for MCDM procedures and decision-making reality.

_{1}= 0.604, G

_{2}= 0.704, G

_{3}= 0.631, G

_{4}= 0.655, and G

_{5}= 0.631, and the prioritization of the following AFVs:${G}_{2}\succ {G}_{4}\succ {G}_{3}\approx {G}_{5}\succ {G}_{1}.$ Applying the RS method, the OUD of the AFVs is as follows: G

_{1}= 0.618, G

_{2}= 0.675, G

_{3}= 0.638, G

_{4}= 0.690 and G

_{5}= 0.582 and the prioritization of AFVs as follows:${G}_{4}\succ {G}_{2}\succ {G}_{3}\succ {G}_{1}\succ {G}_{5}.$ In the aforementioned discussion, we observe that the diverse parameter values will recover the steadiness of the IF-MEREC-RS-DNMA method.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AIF-DM | Aggregated intuitionistic fuzzy-decision matrix |

AFVs | Alternative fuel vehicles |

AHP | Analytic hierarchy process |

ANP | Analytical network process |

AOs | Aggregation operators |

CCM | Complete compensatory method |

CCRP | Cardinal consensus reaching process |

CRITIC | Criteria importance through inter-criteria correlation |

DEs | Decision experts |

DEMATEL | Decision making trial and evaluation laboratory |

DMs | Decision matrices |

DNMA | Double normalization-based multi-aggregation |

DST | Dempster–Shafer theory |

EVs | Electric vehicles (EVs) |

ELECTRE | Elimination et choix traduisant la realité |

FST | Fuzzy set theory |

FUCOM-F | Fuzzy full consistency method |

GD | Generalized-Dombi |

GHGs | Greenhouse gases |

HFLTSs | Hesitant fuzzy linguistic term sets |

ICM | Incomplete compensatory method |

IFGDWA | Intuitionistic fuzzy generalized Dombi weighted averaging |

IFGDWG | Intuitionistic fuzzy generalized Dombi weighted geometric |

IF | Indeterminacy function |

IF-COPRAS | Intuitionistic fuzzy complex proportional assessment |

IF-DM | Intuitionistic fuzzy-decision matrix |

IFEWA | Intuitionistic fuzzy Einstein weighted averaging |

IFEWG | Intuitionistic fuzzy Einstein weighted averaging |

IFHWA | Intuitionistic fuzzy Hamacher weighted averaging |

IFHWG | Intuitionistic fuzzy Hamacher weighted averaging |

IFI | Intuitionistic fuzzy information |

IF-MEREC-RS-DNMA | Intuitionistic fuzzy-MEREC-RS-DNMA |

IFN | Intuitionistic fuzzy number |

IFS | intuitionistic fuzzy set |

IFWA | Intuitionistic fuzzy weighted averaging |

IF-WASPAS | Intuitionistic fuzzy weighted aggregated sum product assessment |

IFWG | Intuitionistic fuzzy weighted geometric |

LDM | Linguistic decision-matrix |

LVs | Linguistic variables |

MADA | Multi-attribute decision-analysis |

MARCOS | Measurement alternatives and ranking according to the compromise solution |

MEREC | Method based on the removal effects of criteria |

MF | Membership function |

NF | Non-membership function |

OUD | Overall utility degree |

PROMETHEE | Preference ranking organization method for enrichment of evaluation |

q-ROFSs | q-rung orthopair fuzzy sets |

RD | Relative degree |

RESs | Renewable energy sources |

RS | ranking sum |

SCM | supply chain management |

TOPSIS | Technique for order performance by similarity to ideal solution |

UCM | Un-compensatory method |

UDs | Utility degrees |

VIKOR | Vlsekriterijumska optimizcija I kompromisno resenje |

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Dimension | Criteria | Meaning | References |
---|---|---|---|

Economic (L_{1}) | Purchase cost (C_{1}) | The marketing cost of a specific vehicle (containing taxes) | [2,65,66,67,68,69] |

Energy cost (C_{2}) | Energy generation and supply cost | [42,65,66,67,70,71] | |

Maintenance cost (C_{3}) | The cost needed for systematic maintenance of the vehicle | [1,2,43,71] | |

Social (L_{2}) | Sense of comfort (C_{4}) | The consumer’s consideration to the comfort and accessories of the vehicle | [5,72] |

Job creation (C_{5}) | The formation of new workplaces | [1,5,71,73] | |

Social benefits (C_{6}) | The increase in the level of welfare and lifestyle of the society | [42,71,74] | |

Social acceptability (C_{7}) | The choice of a client for purchasing a particular vehicle | [1,65,74,75,76] | |

Environmental (L_{3}) | Noise pollution (C_{8}) | Noise when the vehicle is operating | [73,75,77] |

Environmental-friendly technology (C_{9}) | The degree of option fuel usability while driving the vehicle | [65,78,79] | |

Technological (L_{4}) | Fueling/charging Infrastructure (C_{10}) | AFV fuel station sites | [42,66,72,73,74] |

Driving range (C_{11}) | Range that can be reached from a single charge | [2,42,68,69,72] | |

Energy efficiency (C_{12}) | Efficiency of fuel energy | [70,73,80] | |

Political (L_{5}) | Energy security (C_{13}) | Dependence on non-fossil methods | [5,71,74] |

Policy support (C_{14}) | Flexible policy procedures and guidelines | [65,71] | |

Financial incentives (C_{15}) | Government aids | [1,5,42] |

LVs | IFNs |
---|---|

Extremely Significance | (0.90, 0.10) |

Very Significance | (0.80, 0.15) |

Significance | (0.70, 0.25) |

Moderate | (0.50, 0.45) |

Insignificance | (0.40, 0.55) |

Very Insignificance | (0.20, 0.75) |

Extremely Insignificance | (0.10, 0.90) |

LVs | IFNs |
---|---|

Extremely good/high (EH) | (0.95, 0.05) |

Very very good//high (VVH) | (0.85, 0.10) |

Very good/high (VH) | (0.80, 0.15) |

Good/high (H) | (0.70, 0.20) |

Slightly good/high (MH) | (0.60, 0.30) |

Average (A) | (0.50, 0.40) |

Slightly low (ML) | (0.40, 0.50) |

Low (L) | (0.30, 0.60) |

Very very low (VL) | (0.20, 0.70) |

Very low (VVL) | (0.10, 0.80) |

Extremely low (EL) | (0.05, 0.95) |

DEs | D_{1} | D_{2} | D_{3} | D_{4} |
---|---|---|---|---|

LVs | VS (0.80, 0.15) | S (0.70, 0.25) | M (0.50, 0.45) | ES (0.90, 0.10) |

Weight | 0.2800 | 0.2450 | 0.1750 | 0.3000 |

Criteria | G_{1} | G_{2} | G_{3} | G_{4} | G_{5} |
---|---|---|---|---|---|

C_{1} | (L, VL, VL, ML) | (L, ML, VL, L) | (A, ML, A, L) | (ML, ML, A, L) | (A, A, ML, ML) |

C_{2} | (ML, L, A, L) | (VL, L, VL, ML) | (MH, A, ML, A) | (VL, L, ML, L) | (VVL, L, ML, ML) |

C_{3} | (L, L, L, VL) | (VL, ML, VL, A) | (A, L, A, ML) | (ML, L, A, A) | (A, A, ML, L) |

C_{4} | (A, MH, MH, H) | (H, H, H, MH) | (MH, MH, A, H) | (H, ML, VH, VH) | (MH, A, MH, ML) |

C_{5} | (MH, H, A, MH) | (VH, H, VH, A) | (ML, MH, A, MH) | (VH, ML, A, MH) | (MH, MH, H, VH) |

C_{6} | (A, ML, VH, A) | (L, ML, A, H) | (H, VH, A, MH) | (A, MH, A, H) | (MH, A, ML, A) |

C_{7} | (MH, L, A, VVH) | (A, L, ML, MH) | (MH, A, VH, H) | (VVH, H, A, MH) | (VVH, A, H, VH) |

C_{8} | (VL, L, A, ML) | (A, VL, L, ML) | (A, MH, VL, L) | (VL, ML, VL, ML) | (A, ML, ML, L) |

C_{9} | (A, H, MH, H) | (VVH, H, H, A) | (MH, H, A, H) | (MH, H, A, MH) | (ML, A, MH, VH) |

C_{10} | (VVH, H, A, MH) | (MH, H, VH, H) | (ML, MH, A, VH) | (H, ML, A, H) | (MH, H, VH, VH) |

C_{11} | (ML, A, VL, ML) | (A, ML, MH, H) | (H, A, H, VVH) | (MH, ML, A, VH) | (A, A, MH, H) |

C_{12} | (H, ML, A, MH) | (VH, MH, A, MH) | (VH, A, MH, ML) | (ML, MH, VH, H) | (VH, VH, H, MH) |

C_{13} | (VH, H, VH, A) | (H, VH, VH, MH) | (MH, ML, A, MH) | (MH, VH, MH, H) | (A, ML, MH, VH) |

C_{14} | (A, H, MH, H) | (H, H, VVH, A) | (VH, MH, A, H) | (VHH, A, ML, ML) | (ML, A, MH, MH) |

C_{15} | (H, MH, A, VH) | (VH, H, MH, MH) | (ML, H, A, A) | (VH, H, A, H) | (MH, ML, H, A) |

Criteria | G_{1} | G_{2} | G_{3} | G_{4} | G_{5} |
---|---|---|---|---|---|

C_{1} | (0.342, 0.578, 0.080) | (0.340, 0.575, 0.086) | (0.444, 0.473, 0.083) | (0.411, 0.504, 0.086) | (0.460, 0.445, 0.094) |

C_{2} | (0.398, 0.523, 0.078) | (0.341, 0.580, 0.079) | (0.517, 0.386, 0.096) | (0.327, 0.588, 0.084) | (0.362, 0.555, 0.083) |

C_{3} | (0.286, 0.618, 0.096) | (0.417, 0.514, 0.069) | (0.446, 0.469, 0.085) | (0.448, 0.467, 0.085) | (0.451, 0.466, 0.083) |

C_{4} | (0.606, 0.292, 0.102) | (0.672, 0.227, 0.101) | (0.616, 0.282, 0.102) | (0.699, 0.228, 0.074) | (0.527, 0.379, 0.094) |

C_{5} | (0.610, 0.288, 0.101) | (0.700, 0.222, 0.077) | (0.538, 0.368, 0.095) | (0.613, 0.306, 0.081) | (0.685, 0.230, 0.084) |

C_{6} | (0.549, 0.366, 0.085) | (0.524, 0.394, 0.082) | (0.669, 0.299, 0.031) | (0.590, 0.308, 0.102) | (0.517, 0.386, 0.096) |

C_{7} | (0.637, 0.286, 0.076) | (0.495, 0.422, 0.083) | (0.650, 0.258, 0.092) | (0.695, 0.217, 0.088) | (0.742, 0.186, 0.072) |

C_{8} | (0.397, 0.530, 0.073) | (0.418, 0.507, 0.075) | (0.477, 0.453, 0.070) | (0.366, 0.553, 0.081) | (0.424, 0.492, 0.084) |

C_{9} | (0.632, 0.265, 0.103) | (0.701, 0.211, 0.088) | (0.641, 0.256, 0.102) | (0.610, 0.288, 0.101) | (0.606, 0.315, 0.079) |

C_{10} | (0.695, 0.217, 0.088) | (0.694, 0.215, 0.091) | (0.612, 0.308, 0.080) | (0.608, 0.292, 0.100) | (0.727, 0.198, 0.075) |

C_{11} | (0.424, 0.491, 0.085) | (0.568, 0.335, 0.098) | (0.714, 0.199, 0.087) | (0.618, 0.302, 0.080) | (0.584, 0.315, 0.102) |

C_{12} | (0.576, 0.327, 0.098) | (0.649, 0.265, 0.085) | (0.598, 0.322, 0.080) | (0.630, 0.282, 0.088) | (0.731, 0.197, 0.073) |

C_{13} | (0.700, 0.222, 0.077) | (0.720, 0.202, 0.078) | (0.543, 0.361, 0.095) | (0.686, 0.227, 0.088) | (0.608, 0.312, 0.080) |

C_{14} | (0.632, 0.265, 0.103) | (0.681, 0.225, 0.094) | (0.679, 0.235, 0.086) | (0.595, 0.325, 0.080) | (0.530, 0.375, 0.095) |

C_{15} | (0.681, 0.234, 0.085) | (0.688, 0.227, 0.086) | (0.536, 0.368, 0.096) | (0.702, 0.212, 0.086) | (0.551, 0.352, 0.097) |

Criteria | $\left({\mathit{S}}_{\mathit{i}\mathit{j}}^{\prime}\right)\mathbf{Values}$ | V_{j} | w_{j} | ||||
---|---|---|---|---|---|---|---|

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

C_{1} | 0.347 | 0.330 | 0.375 | 0.329 | 0.357 | 0.136 | 0.0863 |

C_{2} | 0.343 | 0.330 | 0.367 | 0.336 | 0.366 | 0.133 | 0.0840 |

C_{3} | 0.351 | 0.324 | 0.374 | 0.326 | 0.358 | 0.141 | 0.0891 |

C_{4} | 0.350 | 0.337 | 0.386 | 0.343 | 0.364 | 0.093 | 0.0588 |

C_{5} | 0.350 | 0.339 | 0.380 | 0.338 | 0.375 | 0.092 | 0.0583 |

C_{6} | 0.345 | 0.326 | 0.388 | 0.337 | 0.363 | 0.116 | 0.0732 |

C_{7} | 0.351 | 0.323 | 0.388 | 0.343 | 0.378 | 0.090 | 0.0568 |

C_{8} | 0.343 | 0.324 | 0.372 | 0.333 | 0.361 | 0.141 | 0.0894 |

C_{9} | 0.352 | 0.339 | 0.388 | 0.338 | 0.370 | 0.088 | 0.0554 |

C_{10} | 0.356 | 0.339 | 0.385 | 0.338 | 0.377 | 0.079 | 0.0502 |

C_{11} | 0.334 | 0.330 | 0.392 | 0.338 | 0.369 | 0.112 | 0.0706 |

C_{12} | 0.348 | 0.335 | 0.384 | 0.339 | 0.377 | 0.090 | 0.0570 |

C_{13} | 0.356 | 0.340 | 0.381 | 0.343 | 0.370 | 0.085 | 0.0540 |

C_{14} | 0.352 | 0.338 | 0.390 | 0.336 | 0.364 | 0.094 | 0.0593 |

C_{15} | 0.355 | 0.338 | 0.380 | 0.344 | 0.366 | 0.091 | 0.0577 |

Criteria | D_{1} | D_{2} | D_{3} | D_{4} | Aggregated IFNs | $\mathbf{Crisp}\mathbf{Values}{\mathbb{S}}^{*}\left({\tilde{\mathit{\xi}}}_{\mathit{k}\mathit{j}}\right)$ | Rank of Challenges | $\mathbf{Weight}{\mathit{w}}_{\mathit{j}}^{\mathit{s}}$ |
---|---|---|---|---|---|---|---|---|

C_{1} | MH | A | ML | MH | (0.548, 0.355, 0.097) | 0.403 | 15 | 0.0083 |

C_{2} | A | A | ML | L | (0.451, 0.466, 0.083) | 0.508 | 10 | 0.0500 |

C_{3} | A | MH | L | A | (0.509, 0.401, 0.090) | 0.446 | 13 | 0.0250 |

C_{4} | MH | L | ML | A | (0.493, 0.424, 0.083) | 0.534 | 7 | 0.0750 |

C_{5} | L | MH | L | ML | (0.453, 0.476, 0.071) | 0.488 | 11 | 0.0417 |

C_{6} | A | H | MH | A | (0.572, 0.326, 0.101) | 0.623 | 2 | 0.1167 |

C_{7} | ML | A | H | L | (0.490, 0.472, 0.038) | 0.509 | 9 | 0.0583 |

C_{8} | MH | A | L | MH | (0.544, 0.366, 0.090) | 0.411 | 14 | 0.0167 |

C_{9} | A | ML | MH | ML | (0.477, 0.432, 0.091) | 0.522 | 8 | 0.0667 |

C_{10} | H | ML | A | MH | (0.576, 0.327, 0.098) | 0.624 | 1 | 0.1250 |

C_{11} | L | VL | MH | ML | (0.431, 0.504, 0.064) | 0.464 | 12 | 0.0333 |

C_{12} | ML | MH | MH | A | (0.525, 0.381, 0.095) | 0.572 | 6 | 0.0833 |

C_{13} | H | ML | L | MH | (0.560, 0.352, 0.088) | 0.604 | 4 | 0.1000 |

C_{14} | H | L | ML | MH | (0.558, 0.356, 0.086) | 0.601 | 5 | 0.0917 |

C_{15} | MH | H | L | A | (0.567, 0.341, 0.092) | 0.613 | 3 | 0.1083 |

Criteria | G_{1} | G_{2} | G_{3} | G_{4} | G_{5} |
---|---|---|---|---|---|

C_{1} | (0.228, 0.713, 0.059) | (0.226, 0.710, 0.064) | (0.304, 0.630, 0.066) | (0.279, 0.654, 0.067) | (0.317, 0.606, 0.077) |

C_{2} | (0.274, 0.665, 0.061) | (0.231, 0.709, 0.059) | (0.368, 0.549, 0.083) | (0.221, 0.716, 0.063) | (0.247, 0.690, 0.063) |

C_{3} | (0.201, 0.726, 0.074) | (0.302, 0.642, 0.056) | (0.325, 0.604, 0.071) | (0.326, 0.602, 0.071) | (0.329, 0.601, 0.070) |

C_{4} | (0.496, 0.404, 0.099) | (0.559, 0.336, 0.105) | (0.505, 0.395, 0.100) | (0.586, 0.337, 0.077) | (0.423, 0.490, 0.087) |

C_{5} | (0.502, 0.399, 0.099) | (0.590, 0.329, 0.081) | (0.434, 0.478, 0.088) | (0.504, 0.417, 0.079) | (0.575, 0.338, 0.088) |

C_{6} | (0.420, 0.503, 0.077) | (0.399, 0.528, 0.073) | (0.531, 0.438, 0.031) | (0.457, 0.446, 0.096) | (0.393, 0.521, 0.086) |

C_{7} | (0.546, 0.378, 0.076) | (0.412, 0.511, 0.077) | (0.558, 0.348, 0.094) | (0.603, 0.305, 0.092) | (0.652, 0.270, 0.078) |

C_{8} | (0.259, 0.686, 0.055) | (0.274, 0.669, 0.057) | (0.319, 0.625, 0.056) | (0.237, 0.703, 0.060) | (0.279, 0.656, 0.064) |

C_{9} | (0.525, 0.372, 0.103) | (0.593, 0.313, 0.093) | (0.534, 0.363, 0.103) | (0.504, 0.396, 0.100) | (0.500, 0.422, 0.077) |

C_{10} | (0.596, 0.311, 0.092) | (0.596, 0.308, 0.096) | (0.516, 0.406, 0.078) | (0.512, 0.390, 0.098) | (0.630, 0.289, 0.081) |

C_{11} | (0.342, 0.583, 0.075) | (0.470, 0.437, 0.093) | (0.612, 0.295, 0.093) | (0.517, 0.404, 0.079) | (0.485, 0.416, 0.098) |

C_{12} | (0.482, 0.424, 0.094) | (0.553, 0.361, 0.086) | (0.503, 0.419, 0.078) | (0.534, 0.378, 0.088) | (0.635, 0.287, 0.078) |

C_{13} | (0.599, 0.320, 0.081) | (0.619, 0.298, 0.083) | (0.448, 0.462, 0.090) | (0.584, 0.324, 0.091) | (0.509, 0.413, 0.078) |

C_{14} | (0.517, 0.381, 0.102) | (0.565, 0.338, 0.097) | (0.563, 0.348, 0.089) | (0.482, 0.441, 0.077) | (0.423, 0.490, 0.087) |

C_{15} | (0.573, 0.339, 0.088) | (0.580, 0.331, 0.089) | (0.436, 0.475, 0.090) | (0.594, 0.315, 0.091) | (0.450, 0.459, 0.091) |

Criteria | G_{1} | G_{2} | G_{3} | G_{4} | G_{5} |
---|---|---|---|---|---|

C_{1} | (0.3800, 0.4995, 0.1205) | (0.3774, 0.4965, 0.1261) | (0.4931, 0.4087, 0.0983) | (0.4565, 0.4349, 0.1087) | (0.5116, 0.3845, 0.1039) |

C_{2} | (0.4508, 0.4402, 0.1089) | (0.3861, 0.4877, 0.1262) | (0.5855, 0.3248, 0.0898) | (0.3704, 0.4949, 0.1347) | (0.4095, 0.4669, 0.1236) |

C_{3} | (0.3088, 0.5415, 0.1497) | (0.4505, 0.4504, 0.0991) | (0.4810, 0.4114, 0.1075) | (0.4832, 0.4096, 0.1072) | (0.4866, 0.4085, 0.1049) |

C_{4} | (0.4327, 0.4547, 0.1126) | (0.4792, 0.3538, 0.1669) | (0.4395, 0.4400, 0.1205) | (0.4986, 0.3549, 0.1466) | (0.3759, 0.5904, 0.0337) |

C_{5} | (0.4318, 0.4481, 0.1201) | (0.4955, 0.3454, 0.1590) | (0.3803, 0.5714, 0.0482) | (0.4337, 0.4749, 0.0913) | (0.4850, 0.3574, 0.1576) |

C_{6} | (0.4284, 0.4641, 0.1075) | (0.4094, 0.4993, 0.0914) | (0.5227, 0.3793, 0.0980) | (0.4609, 0.3901, 0.1489) | (0.4040, 0.4892, 0.1068) |

C_{7} | (0.4390, 0.4478, 0.1131) | (0.3409, 0.6508, 0.0083) | (0.4478, 0.4035, 0.1488) | (0.4786, 0.3401, 0.1813) | (0.5114, 0.2904, 0.1981) |

C_{8} | (0.4251, 0.4663, 0.1086) | (0.4469, 0.4467, 0.1065) | (0.5101, 0.3989, 0.0909) | (0.3916, 0.4863, 0.1221) | (0.4539, 0.4329, 0.1132) |

C_{9} | (0.4424, 0.4405, 0.1171) | (0.4906, 0.3499, 0.1595) | (0.4488, 0.4258, 0.1254) | (0.4270, 0.4790, 0.0940) | (0.4240, 0.5223, 0.0536) |

C_{10} | (0.4644, 0.3887, 0.1469) | (0.4639, 0.3840, 0.1520) | (0.4093, 0.5508, 0.0399) | (0.4065, 0.5226, 0.0708) | (0.4861, 0.3535, 0.1604) |

C_{11} | (0.3220, 0.6429, 0.0351) | (0.4311, 0.4385, 0.1304) | (0.5422, 0.2611, 0.1967) | (0.4690, 0.3956, 0.1354) | (0.4433, 0.4120, 0.1447) |

C_{12} | (0.4027, 0.5177, 0.0796) | (0.4545, 0.4199, 0.1256) | (0.4185, 0.5099, 0.0716) | (0.4410, 0.4458, 0.1132) | (0.5115, 0.3114, 0.1772) |

C_{13} | (0.4783, 0.3658, 0.1559) | (0.4915, 0.3331, 0.1755) | (0.3712, 0.5942, 0.0346) | (0.4683, 0.3731, 0.1586) | (0.4154, 0.5129, 0.0718) |

C_{14} | (0.4516, 0.4082, 0.1402) | (0.4866, 0.3465, 0.1669) | (0.4850, 0.3614, 0.1537) | (0.4249, 0.4996, 0.0754) | (0.3789, 0.5771, 0.0440) |

C_{15} | (0.4792, 0.3649, 0.1560) | (0.4838, 0.3538, 0.1623) | (0.3771, 0.5743, 0.0487) | (0.4937, 0.3311, 0.1753) | (0.3879, 0.5498, 0.0623) |

Options | $\mathbf{CCM}\left({\mathit{\mathbb{Q}}}_{1}\right)$ | $\mathbf{UCM}\left({\mathit{\mathbb{Q}}}_{2}\right)$ | $\mathbf{ICM}\left({\mathit{\mathbb{Q}}}_{3}\right)$ | |||
---|---|---|---|---|---|---|

${\mathit{\u2102}}_{1}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathbb{S}}^{*}\left({\mathit{\u2102}}_{1}\left({\mathit{G}}_{\mathit{i}}\right)\right)$ | ${\mathit{\u2102}}_{2}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathbb{S}}^{*}\left({\mathit{\u2102}}_{2}\left({\mathit{G}}_{\mathit{i}}\right)\right)$ | ${\mathit{\u2102}}_{3}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathbb{S}}^{*}\left({\mathit{\u2102}}_{3}\left({\mathit{G}}_{\mathit{i}}\right)\right)$ | |

G_{1} | (0.566, 0.350, 0.084) | 0.608 | (0.071, 0.913, 0.016) | 0.079 | (0.450, 0.426, 0.124) | 0.512 |

G_{2} | (0.581, 0.337, 0.082) | 0.622 | (0.079, 0.907, 0.014) | 0.086 | (0.462, 0.401, 0.137) | 0.530 |

G_{3} | (0.534, 0.386, 0.080) | 0.574 | (0.052, 0.933, 0.015) | 0.059 | (0.430, 0.468, 0.102) | 0.481 |

G_{4} | (0.571, 0.346, 0.083) | 0.613 | (0.081, 0.904, 0.015) | 0.088 | (0.456, 0.415, 0.129) | 0.521 |

G_{5} | (0.551, 0.368, 0.081) | 0.591 | (0.075, 0.910, 0.014) | 0.082 | (0.435, 0.449, 0.116) | 0.493 |

Options | $\mathbf{CCM}\left({\mathit{\mathbb{Q}}}_{1}\right)$ | $\mathbf{UCM}\left({\mathit{\mathbb{Q}}}_{2}\right)$ | $\mathbf{ICM}\left({\mathit{\mathbb{Q}}}_{3}\right)$ | ${\mathit{\mathbb{R}}}_{\mathit{i}}$$\left(\mathit{\xi}=0.5\right)$ | Final Ranking | |||
---|---|---|---|---|---|---|---|---|

${\mathit{\u2102}}_{1}^{\left(\mathit{N}\right)}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathit{\rho}}_{1}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathit{\u2102}}_{2}^{\left(\mathit{N}\right)}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathit{\rho}}_{2}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathit{\u2102}}_{3}^{\left(\mathit{N}\right)}\left({\mathit{G}}_{\mathit{i}}\right)$ | ${\mathit{\rho}}_{3}\left({\mathit{G}}_{\mathit{i}}\right)$ | |||

G_{1} | 0.452 | 3 | 0.444 | 2 | 0.451 | 3 | 0.654 | 2 |

G_{2} | 0.462 | 1 | 0.484 | 4 | 0.467 | 1 | 0.685 | 1 |

G_{3} | 0.427 | 5 | 0.332 | 1 | 0.423 | 5 | 0.638 | 3 |

G_{4} | 0.455 | 2 | 0.495 | 5 | 0.459 | 2 | 0.632 | 4 |

G_{5} | 0.439 | 4 | 0.462 | 3 | 0.434 | 4 | 0.610 | 5 |

Weight of aggregation model | ${w}_{1}=1/3$ | ${w}_{2}=1/3$ | ${w}_{3}=1/3$ |

Options | ${\mathit{\alpha}}_{\mathit{i}}$ | ${\mathbb{S}}^{*}\left({\mathit{\alpha}}_{\mathit{i}}\right)$ | ${\mathit{\beta}}_{\mathit{i}}$ | ${\mathbb{S}}^{*}\left({\mathit{\beta}}_{\mathit{i}}\right)$ | ${\mathit{\gamma}}_{\mathit{i}}$ | ${\mathit{\delta}}_{\mathit{i}}$ | Ranking |
---|---|---|---|---|---|---|---|

G_{1} | (0.433, 0.482, 0.085) | 0.475 | (0.061, 0.922, 0.018) | 0.069 | 0.2835 | 96.66% | 3 |

G_{2} | (0.457, 0.457, 0.086) | 0.500 | (0.065, 0.918, 0.017) | 0.074 | 0.2933 | 100.00% | 1 |

G_{3} | (0.428, 0.494, 0.078) | 0.467 | (0.087, 0.891, 0.023) | 0.098 | 0.2660 | 90.69% | 5 |

G_{4} | (0.448, 0.468, 0.084) | 0.490 | (0.067, 0.914, 0.019) | 0.076 | 0.2868 | 97.78% | 2 |

G_{5} | (0.433, 0.487, 0.080) | 0.473 | (0.074, 0.905, 0.021) | 0.085 | 0.2744 | 93.56% | 4 |

Options | ${\mathit{\wp}}_{\mathit{i}}^{(1)}$ | ${\mathit{\wp}}_{\mathit{i}}^{(2)}$ | ${\mathbb{S}}^{*}\left({\mathit{\wp}}_{\mathit{i}}^{(1)}\right)$ | ${\mathbb{S}}^{*}\left({\mathit{\wp}}_{\mathit{i}}^{(2)}\right)$ | ${\mathit{Q}}_{\mathit{i}}\left(\mathit{\u019b}\right)$ | Ranking Order |
---|---|---|---|---|---|---|

G_{1} | (0.566, 0.350, 0.084) | (0.545, 0.370, 0.085) | 0.608 | 0.588 | 0.5977 | 3 |

G_{2} | (0.581, 0.337, 0.082) | (0.564, 0.353, 0.083) | 0.622 | 0.605 | 0.6137 | 1 |

G_{3} | (0.534, 0.386, 0.080) | (0.527, 0.393, 0.080) | 0.574 | 0.567 | 0.5706 | 5 |

G_{4} | (0.571, 0.346, 0.083) | (0.559, 0.356, 0.085) | 0.613 | 0.601 | 0.6069 | 2 |

G_{5} | (0.551, 0.368, 0.081) | (0.531, 0.387, 0.083) | 0.591 | 0.572 | 0.5816 | 4 |

Θ | G_{1} | G_{2} | G_{3} | G_{4} | G_{5} | Ranking Order |
---|---|---|---|---|---|---|

ϑ = 0.0 | 0.633 | 0.700 | 0.533 | 0.600 | 0.533 | ${G}_{2}\succ {G}_{1}\succ {G}_{4}\succ {G}_{3}\succ {G}_{5}$ |

ϑ = 0.1 | 0.637 | 0.697 | 0.568 | 0.607 | 0.554 | ${G}_{2}\succ {G}_{1}\succ {G}_{4}\succ {G}_{3}\succ {G}_{5}$ |

ϑ = 0.2 | 0.641 | 0.694 | 0.591 | 0.613 | 0.571 | ${G}_{2}\succ {G}_{1}\succ {G}_{4}\succ {G}_{3}\succ {G}_{5}$ |

ϑ = 0.3 | 0.645 | 0.691 | 0.609 | 0.620 | 0.585 | ${G}_{2}\succ {G}_{1}\succ {G}_{4}\succ {G}_{3}\succ {G}_{5}$ |

ϑ = 0.4 | 0.649 | 0.688 | 0.624 | 0.626 | 0.598 | ${G}_{2}\succ {G}_{1}\succ {G}_{4}\succ {G}_{3}\succ {G}_{5}$ |

ϑ = 0.5 | 0.654 | 0.685 | 0.638 | 0.632 | 0.610 | ${G}_{2}\succ {G}_{1}\succ {G}_{3}\succ {G}_{4}\succ {G}_{5}$ |

ϑ = 0.6 | 0.658 | 0.682 | 0.651 | 0.638 | 0.621 | ${G}_{2}\succ {G}_{1}\succ {G}_{3}\succ {G}_{4}\succ {G}_{5}$ |

ϑ = 0.7 | 0.662 | 0.679 | 0.662 | 0.644 | 0.631 | ${G}_{2}\succ {G}_{1}\approx {G}_{3}\succ {G}_{4}\succ {G}_{5}$ |

ϑ = 0.8 | 0.666 | 0.676 | 0.673 | 0.650 | 0.641 | ${G}_{2}\succ {G}_{3}\succ {G}_{1}\succ {G}_{4}\succ {G}_{5}$ |

ϑ = 0.9 | 0.670 | 0.673 | 0.683 | 0.656 | 0.650 | ${G}_{3}\succ {G}_{2}\succ {G}_{1}\succ {G}_{4}\succ {G}_{5}$ |

ϑ = 1.0 | 0.675 | 0.671 | 0.693 | 0.661 | 0.658 | ${G}_{3}\succ {G}_{1}\succ {G}_{2}\succ {G}_{4}\succ {G}_{5}$ |

Weighting Procedure | Subordinate UDs of AFVs Options | Ranking Order | ||||
---|---|---|---|---|---|---|

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

MEREC method | 0.604 | 0.704 | 0.631 | 0.655 | 0.631 | ${G}_{2}\succ {G}_{4}\succ {G}_{3}\approx {G}_{5}\succ {G}_{1}$ |

RS method | 0.618 | 0.675 | 0.638 | 0.690 | 0.582 | ${G}_{4}\succ {G}_{2}\succ {G}_{3}\succ {G}_{1}\succ {G}_{5}$ |

Integrated method | 0.654 | 0.685 | 0.638 | 0.632 | 0.610 | ${G}_{2}\succ {G}_{1}\succ {G}_{3}\succ {G}_{4}\succ {G}_{5}$ |

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## Share and Cite

**MDPI and ACS Style**

Hezam, I.M.; Mishra, A.R.; Rani, P.; Cavallaro, F.; Saha, A.; Ali, J.; Strielkowski, W.; Štreimikienė, D.
A Hybrid Intuitionistic Fuzzy-MEREC-RS-DNMA Method for Assessing the Alternative Fuel Vehicles with Sustainability Perspectives. *Sustainability* **2022**, *14*, 5463.
https://doi.org/10.3390/su14095463

**AMA Style**

Hezam IM, Mishra AR, Rani P, Cavallaro F, Saha A, Ali J, Strielkowski W, Štreimikienė D.
A Hybrid Intuitionistic Fuzzy-MEREC-RS-DNMA Method for Assessing the Alternative Fuel Vehicles with Sustainability Perspectives. *Sustainability*. 2022; 14(9):5463.
https://doi.org/10.3390/su14095463

**Chicago/Turabian Style**

Hezam, Ibrahim M., Arunodaya Raj Mishra, Pratibha Rani, Fausto Cavallaro, Abhijit Saha, Jabir Ali, Wadim Strielkowski, and Dalia Štreimikienė.
2022. "A Hybrid Intuitionistic Fuzzy-MEREC-RS-DNMA Method for Assessing the Alternative Fuel Vehicles with Sustainability Perspectives" *Sustainability* 14, no. 9: 5463.
https://doi.org/10.3390/su14095463