# An Integrated Intuitionistic Fuzzy Closeness Coefficient-Based OCRA Method for Sustainable Urban Transportation Options Selection

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## Abstract

**:**

## 1. Introduction

#### 1.1. Needs of the Paper

- i.
- Distance measures are essential tools for IFSs. In the literature, several distance measures have been introduced by the researchers. However, there is a need to develop an improved intuitionistic fuzzy distance measure for the betterment of existing measures.
- ii.
- To evade the redundant influence of subjective DEs’ significances on the decision result, there is an urgent need to derive the weights of the DEs’ opinions.
- iii.
- In the context of intuitionistic fuzzy MADA tools, most of the earlier studies have discussed either objective weighting methods or subjective weighting methods. To avoid the shortcomings of objective or subjective weighting models, there is a need to present a weighting model for finding the indicator weights. However, extant subjective weighting tools hardly consider the relative closeness coefficient degree as a degree for weighting from an intuitionistic fuzzy setting.
- iv.
- There is no study to present the operational competitiveness rating (OCRA) method from an intuitionistic fuzzy perspective to determine the MADA problems.
- v.
- In the literature, a single article [1] has implemented the choquet integral-TOPSIS method in the evaluation of SUT options over a finite number of criteria. However, this method has limitations in solving the multiple criteria SUT assessment problem under an intuitionistic fuzzy environment.

#### 1.2. Research Contributions

- To measure the degree of discrimination, a new IF-distance measure was proposed with enviable properties with the use of flexible parameters.
- For the first time, this paper proposed a generalized score value and rank sum model-based weighting approach to derive the DEs’ weights within the IFS environment.
- In order to consider the relative closeness coefficient of indicators, this paper presented a new intuitionistic fuzzy divergence measure-based model and further used it to compute the weights of the indicators.
- The present study proposed an OCRA model based on a combination of a distance measure and relative closeness coefficient, which can better describe the uncertainty of practical decision-making problems.
- This study implements the proposed IF-closeness coefficient-OCRA method on a case study of SUT assessment problems within the IFS context.

#### 1.3. Organizations of This Study

## 2. Literature Review

#### 2.1. Sustainable Transportation and Alternative Fuel Technologies

#### 2.2. MADA Methods with Uncertainties

## 3. IFSs and Parametric Distance Measure

#### 3.1. Preliminaries

**Definition**1.

**.**An IFS L on $O=\left\{{o}_{1},{o}_{2},\dots ,{o}_{t}\right\}$ is given by

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

#### 3.2. Proposed Parametric IF-Distance Measure

_{p}-norm, t, a and b signify the uncertainty level with the condition $a+b\le t+1,0\le a,b\le t+1,t0.$

**Theorem 1.**

**Proof.**

**(d1).**

**(d2).**It is easy to prove that $d\left(A,B\right)=d\left(B,A\right).$

**(d3).**

**(d4).**For $A,B,C\in IFSs\left(O\right),$

## 4. Proposed IF-Closeness Coefficient-OCRA Model

_{i}with regard to r

_{j}and is further converted into an “intuitionistic fuzzy-decision matrix (IF-DM)” using Table 1.

^{th}criterion. Each weight is normalized as follows:

## 5. Case Study: Prioritization of SUT Options

_{1}), hybrid electric vehicles (HEVs) (T

_{2}), Diesel engines (DIE) (T

_{3}), CNG (T

_{4}), and electric buses with exchangeable batteries (EEB) (T

_{5}).

_{1}, g

_{2}, g

_{3}, and g

_{4}) was created. These DEs were from various disciplines comprising researchers on gerontechnology groups/classes, stockholders, professors, and managers. The respondent of each technology group/class assessed the following criteria using an 11-stage scale, where AL means absolutely low and AH means absolutely high. In the study, buses with AFVs were considered and assessed in terms of sustainability perspectives. Corresponding to the assessment, the appropriate option will be chosen with the consideration of various, occasionally conflicting indicators. Apparently, no one option can instantaneously fulfill all decision indicators, which creates the problem of an appropriate choice for the utilization of multi-attribute assessment. Owing to the consequence of a sustainability perspectives of the SUT options, the DEs were invited by the Delhi municipality, India, to do this assessment over sustainability indicators. A wide-ranging literature study and DEs’ thoughts were assembled to evaluate the considered indicators. A wider range of indicators could be related with fuel types in sustainability perspectives. However, DEs defined the range of indicators so the most significant indicators could be engaged for the 11 assessment indicators, which were nominated by the DEs [3,4,5,23,32,58,59]. These indicators were then assembled into economical, technical, environmental, and social pillars. Brief explanations of these indicators are given in Table 2.

_{9}) with a weight of value 0.1008 came out to be the most important parameter for prioritizing SUT options. Road capacity (r

_{6}), with a weight of 0.0973, was the second-most significant criterion. Operating cost (r

_{4}) was third with a weight value of 0.0954. Acquisition cost (r

_{3}) was ranked fourth with a weight of 0.0943, fifth was social impact (r

_{11}) with a weight of 0.0917, and others were considered crucial criteria for the assessment of SUT options.

_{4}) is the best SUT option with the highest OPR.

#### 5.1. Comparison with Other Models

#### 5.1.1. The IF-TOPSIS Tool

_{4}) has a higher degree of RCC.

#### 5.1.2. The IF-COPRAS Tool

_{4}) was obtained as the suitable SUT option with the highest RD (0.7029).

#### 5.1.3. The IF-WASPAS Tool

_{4}) is a suitable choice with maximum UD.

#### 5.1.4. The IF-CoCoSo Tool

_{4}) is the best SUT alternative for prioritizing SUT options.

_{4}(CNG) for prioritizing SUT options using almost all MCDM tools. The advantages of the developed IF-relative closeness coefficient-OCRA model are presented as follows:

- The proposed method utilizes the linear normalization procedure and relative closeness coefficient, while the IF-COPRAS method utilizes only the vector normalization procedure, where IF-WASPAS, IF-TOPSIS, and IF-CoCoSo use only the linear normalization procedure. Thus, the proposed method avoids the information loss and provides more accurate decision results by means of different criteria.
- The IF-WASPAS, IF-CoCoSo, and the proposed method associate the WSM and WPM to enhance the accuracy of outcomes. In IF-COPRAS, the IFWA operator, utility degrees of options are obtained. In IF-TOPSIS, the closeness coefficients based on the distance measure of each option are estimated, while the IF–closeness coefficient–OCRA utilizes the performance of independent assessment of options over benefit and cost indicators and combines these two APRs so as to determine OPRs, which supports DEs not to misplace information during the MADA process.
- The systematic assessment of DEs’ weights using the IF-score value and IF-rank sum model reduce the imprecision and biases in the MADA procedure.
- The developed method determines the criteria weights by using the IF–relative closeness coefficient-based tool. In contrast, in IF-WASPAS, the criteria weight is obtained with a similarity measure-based tool, in IF-CoCoSo, the criteria weight is obtained using divergence measure and the score function-based approach, and in IF-COPRAS and IF-TOPSIS, the criteria weight is chosen randomly.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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

Absolutely high (AH) | (0.95, 0.05) |

Very very high (VVH) | (0.85, 0.1) |

Very high (VH) | (0.8, 0.15) |

High (H) | (0.7, 0.2) |

Slightly high (MH) | (0.6, 0.3) |

Average (A) | (0.5, 0.4) |

Slightly low (ML) | (0.4, 0.5) |

Low (L) | (0.3,0.6) |

Very very low (VL) | (0.2, 0.7) |

Very low (VVL) | (0.1, 0.8) |

Absolutely low (AL) | (0.05, 0.95) |

Indicators | Sub-Criteria | Type |
---|---|---|

Economical (I_{1}) | Energy availability (r_{1}) | Max |

Energy efficiency (r_{2}) | Max | |

Acquisition cost (r_{3}) | Min | |

Operating cost (r_{4}) | Min | |

Technical (I_{2}) | Vehicle capacity (r_{5}) | Max |

Road capacity (r_{6}) | Max | |

Flow conformance(r_{7}) | Max | |

Environmental factor (I_{3}) | Noise pollution (r_{8}) | Min |

Air pollution (r_{9}) | Min | |

Social (I_{4}) | Passenger comfort (r_{10}) | Max |

Social impact (r_{11}) | Max |

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

Ratings | VVH (0.85, 0.10) | VH (0.80, 0.15) | AH (0.95, 0.05) | H (0.7, 0.20) |

rank | 2 | 3 | 1 | 4 |

${\lambda}_{k}$ | 0.2793 | 0.2217 | 0.3376 | 0.1615 |

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

r_{1} | (H,VH,MH,H) | (AH,H,H,VH) | (H, MH,A,H) | (AH,H,H,VH) | (H,H,ML,VH) |

r_{2} | (MH,H,A,VH) | (H,H,VVH,MH) | (A,H,MH,ML) | (VH,H,MH,AH) | (VH,MH,H,A) |

r_{3} | (L,VL,ML,ML) | (AL,L,L,VL) | (ML, ML,VL,L) | (VL,ML,L,L) | (VL,L,ML,ML) |

r_{4} | (ML,ML,A,L) | (L,L,VL,ML) | (VVL,A,ML,ML) | (A,VL,ML,ML) | (VL,L,ML,VL) |

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

r_{6} | (AH, MH,VH,A) | (ML,H,A,VH) | (VH,MH,A,H) | (AH,H,A,VH) | (VH,H,MH,A) |

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

r_{8} | (AL,L,ML,VL) | (ML,L,ML,ML) | (VL,L,A,ML) | (AL,VVL,A,L) | (A,VL,VVL,L) |

r_{9} | (VL,L,A,L) | (A,VL,L,VVL) | (AL,MH,VL,L) | (L,AL,VL,ML) | (A,L,VL,VL) |

r_{10} | (A,MH,AH,VH) | (AH,H,H,MH) | (MH,ML,VH,H) | (MH,MH,ML,H) | (VH,A,MH,MH) |

r_{11} | (VH,H,MH,H) | (MH,H,VH,MH) | (ML,H,AH,H) | (H,MH,H,VH) | (A,A,VH,VVH) |

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

r_{1} | (0.698, 0.215, 0.087) | (0.830, 0.130, 0.041) | (0.620, 0.276, 0.103) | (0.830, 0.130, 0.041) | (0.645, 0.260, 0.095) |

r_{2} | (0.638, 0.270, 0.092) | (0.751, 0.169, 0.080) | (0.574, 0.323, 0.104) | (0.779, 0.169, 0.052) | (0.690, 0.226, 0.084) |

r_{3} | (0.315, 0.584, 0.101) | (0.221, 0.699, 0.080) | (0.322, 0.577, 0.101) | (0.298, 0.602, 0.101) | (0.327, 0.572, 0.101) |

r_{4} | (0.384, 0.478, 0.139) | (0.286, 0.614, 0.101) | (0.355, 0.543, 0.103) | (0.392, 0.506, 0.102) | (0.295, 0.604, 0.101) |

r_{5} | (0.575, 0.321, 0.104) | (0.632, 0.285, 0.083) | (0.614, 0.283, 0.103) | (0.847, 0.123, 0.030) | (0.703, 0.210, 0.087) |

r_{6} | (0.816, 0.151, 0.033) | (0.595, 0.312, 0.094) | (0.661, 0.255, 0.084) | (0.798, 0.164, 0.039) | (0.679, 0.237, 0.084) |

r_{7} | (0.618, 0.293, 0.088) | (0.621, 0.296, 0.084) | (0.698, 0.230, 0.072) | (0.712, 0.204, 0.084) | (0.689, 0.224, 0.087) |

r_{8} | (0.261, 0.658, 0.082) | (0.379, 0.521, 0.100) | (0.367, 0.530, 0.102) | (0.281, 0.634, 0.085) | (0.286, 0.611, 0.104) |

r_{9} | (0.330, 0.567, 0.103) | (0.316, 0.581, 0.103) | (0.296, 0.616, 0.088) | (0.236, 0.679, 0.085) | (0.319, 0.579, 0.103) |

r_{10} | (0.811, 0.159, 0.030) | (0.809, 0.145, 0.046) | (0.669, 0.249, 0.082) | (0.562, 0.334, 0.104) | (0.654, 0.263, 0.083) |

r_{11} | (0.705, 0.212, 0.084) | (0.703, 0.217, 0.080) | (0.801, 0.162, 0.037) | (0.701, 0.209, 0.091) | (0.698, 0.230, 0.072) |

Criteria | g_{1} | g_{2} | g_{3} | g_{4} | AIF-DM | ${\mathit{p}}_{\mathit{i}\mathit{j}}^{+}$ | ${\mathit{p}}_{\mathit{i}\mathit{j}}^{-}$ | $\mathit{r}{\mathit{c}}_{\mathit{j}}$ | ${\mathit{w}}_{\mathit{j}}$ |
---|---|---|---|---|---|---|---|---|---|

r_{1} | H | VH | H | A | (0.702, 0.210, 0.088) | 0.257 | 0.743 | 0.743 | 0.0893 |

r_{2} | MH | A | VH | MH | (0.667, 0.253, 0.080) | 0.295 | 0.705 | 0.705 | 0.0847 |

r_{3} | VH | ML | VVH | H | (0.753, 0.179, 0.068) | 0.215 | 0.785 | 0.785 | 0.0943 |

r_{4} | A | A | VVH | AH | (0.770, 0.179, 0.051) | 0.206 | 0.794 | 0.794 | 0.0954 |

r_{5} | MH | ML | MH | AH | (0.687, 0.252, 0.061) | 0.284 | 0.716 | 0.716 | 0.0860 |

r_{6} | H | ML | AH | A | (0.793, 0.172, 0.036) | 0.191 | 0.809 | 0.809 | 0.0973 |

r_{7} | VH | MH | ML | VH | (0.662, 0.263, 0.075) | 0.303 | 0.697 | 0.697 | 0.0838 |

r_{8} | ML | VH | MH | VVH | (0.672, 0.248, 0.079) | 0.291 | 0.709 | 0.709 | 0.0852 |

r_{9} | VH | MH | AH | ML | (0.826, 0.147, 0.028) | 0.161 | 0.839 | 0.839 | 0.1008 |

r_{10} | A | VH | VVH | A | (0.728, 0.202, 0.070) | 0.239 | 0.761 | 0.761 | 0.0915 |

r_{11} | VVH | MH | H | MH | (0.724, 0.192, 0.084) | 0.237 | 0.763 | 0.763 | 0.0917 |

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

r_{1} | 0.759 | 0.863 | 0.684 | 0.863 | 0.706 |

r_{2} | 0.697 | 0.811 | 0.633 | 0.819 | 0.748 |

r_{3} | 0.347 | 0.239 | 0.355 | 0.328 | 0.360 |

r_{4} | 0.437 | 0.314 | 0.391 | 0.432 | 0.325 |

r_{5} | 0.635 | 0.684 | 0.677 | 0.872 | 0.764 |

r_{6} | 0.843 | 0.651 | 0.716 | 0.828 | 0.736 |

r_{7} | 0.673 | 0.672 | 0.748 | 0.771 | 0.749 |

r_{8} | 0.282 | 0.417 | 0.405 | 0.305 | 0.315 |

r_{9} | 0.364 | 0.349 | 0.322 | 0.256 | 0.352 |

r_{10} | 0.836 | 0.846 | 0.724 | 0.621 | 0.708 |

r_{11} | 0.764 | 0.759 | 0.831 | 0.764 | 0.748 |

Options | ${\mathit{P}}_{\mathit{i}}$ | ${\overline{\mathit{P}}}_{\mathit{i}}$ | ${\mathit{Q}}_{\mathit{i}}$ | ${\overline{\mathit{Q}}}_{\mathit{i}}$ | ${\mathit{O}}_{\mathit{i}}$ | Ranking |
---|---|---|---|---|---|---|

T_{1} | 0.3354 | 0.0698 | 0.1881 | 0.0306 | 0.0556 | 2 |

T_{2} | 0.3064 | 0.0408 | 0.1881 | 0.0305 | 0.0266 | 3 |

T_{3} | 0.2656 | 0.0000 | 0.2023 | 0.0447 | 0.0000 | 5 |

T_{4} | 0.4287 | 0.1631 | 0.1576 | 0.0000 | 0.1184 | 1 |

T_{5} | 0.2938 | 0.0282 | 0.1967 | 0.0392 | 0.0227 | 4 |

Alternative | $\mathit{D}\left({\mathit{\xi}}_{\mathit{i}\mathit{j}},{\mathbf{N}}_{\mathit{j}}^{+}\right)$ | $\mathit{D}\left({\mathit{\xi}}_{\mathit{i}\mathit{j}},{\mathbf{N}}_{\mathit{j}}^{-}\right)$ | CC_{i} | Ranks |
---|---|---|---|---|

T_{1} | 0.288 | 0.208 | 0.4201 | 3 |

T_{2} | 0.234 | 0.257 | 0.5229 | 2 |

T_{3} | 0.357 | 0.134 | 0.2736 | 5 |

T_{4} | 0.157 | 0.333 | 0.6792 | 1 |

T_{5} | 0.287 | 0.203 | 0.4142 | 4 |

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

T_{1} | (0.540, 0.389, 0.071) | 0.575 | (0.137, 0.807, 0.055) | 0.165 | 0.7040 | 100.00 |

T_{2} | (0.544, 0.378, 0.078) | 0.583 | (0.126, 0.826, 0.048) | 0.150 | 0.7039 | 99.99 |

T_{3} | (0.501, 0.419, 0.080) | 0.541 | (0.142, 0.808, 0.050) | 0.167 | 0.7003 | 99.47 |

T_{4} | (0.591, 0.344, 0.065) | 0.623 | (0.127, 0.826, 0.046) | 0.150 | 0.7029 | 99.84 |

T_{5} | (0.509, 0.414, 0.077) | 0.548 | (0.129, 0.820, 0.051) | 0.154 | 0.6966 | 98.95 |

Options | ${\mathit{S}}_{\mathit{i}}^{(1)}$ | ${\mathit{S}}_{\mathit{i}}^{(2)}$ | $\mathbb{S}\left({\mathit{S}}_{\mathit{i}}^{(1)}\right)$ | $\mathbb{S}\left({\mathit{S}}_{\mathit{i}}^{(2)}\right)$ | ${\mathit{Q}}_{\mathit{i}}\left(\mathit{\hslash}\right)$ |
---|---|---|---|---|---|

T_{1} | (0.666, 0.254, 0.080) | (0.642, 0.268, 0.090) | 0.706 | 0.687 | 0.6965 |

T_{2} | (0.683, 0.238, 0.079) | (0.661, 0.255, 0.084) | 0.722 | 0.703 | 0.7128 |

T_{3} | (0.637, 0.277, 0.086) | (0.624, 0.286, 0.091) | 0.680 | 0.669 | 0.6743 |

T_{4} | (0.713, 0.234, 0.054) | (0.685, 0.237, 0.078) | 0.740 | 0.724 | 0.7317 |

T_{5} | (0.649, 0.260, 0.091) | (0.644, 0.264, 0.092) | 0.694 | 0.690 | 0.6923 |

Options | ${\mathit{Q}}_{\mathit{i}}^{\left(1\right)}$ | ${\mathit{Q}}_{\mathit{i}}^{\left(2\right)}$ | ${\mathit{Q}}_{\mathit{i}}^{\left(3\right)}$ | ${\mathit{Q}}_{\mathit{i}}$ |
---|---|---|---|---|

T_{1} | 0.1986 | 2.0657 | 0.9525 | 1.8033 |

T_{2} | 0.2032 | 2.1139 | 0.9746 | 1.8453 |

T_{3} | 0.1922 | 2.0000 | 0.9211 | 1.7453 |

T_{4} | 0.2086 | 2.1701 | 1.0000 | 1.8941 |

T_{5} | 0.1974 | 2.0534 | 0.9447 | 1.7913 |

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## Share and Cite

**MDPI and ACS Style**

Mishra, A.R.; Rani, P.; Cavallaro, F.; Hezam, I.M.; Lakshmi, J.
An Integrated Intuitionistic Fuzzy Closeness Coefficient-Based OCRA Method for Sustainable Urban Transportation Options Selection. *Axioms* **2023**, *12*, 144.
https://doi.org/10.3390/axioms12020144

**AMA Style**

Mishra AR, Rani P, Cavallaro F, Hezam IM, Lakshmi J.
An Integrated Intuitionistic Fuzzy Closeness Coefficient-Based OCRA Method for Sustainable Urban Transportation Options Selection. *Axioms*. 2023; 12(2):144.
https://doi.org/10.3390/axioms12020144

**Chicago/Turabian Style**

Mishra, Arunodaya Raj, Pratibha Rani, Fausto Cavallaro, Ibrahim M. Hezam, and Jyoti Lakshmi.
2023. "An Integrated Intuitionistic Fuzzy Closeness Coefficient-Based OCRA Method for Sustainable Urban Transportation Options Selection" *Axioms* 12, no. 2: 144.
https://doi.org/10.3390/axioms12020144