Open Access

ARTICLE

Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control

Fangwei Zhang^1,2, Yi Zhao^3,*, Jun Ye⁴, Shuhong Wang⁵, Jingyi Hu⁶
1 Naval Architecture and Port Engineering College, Shandong Jiaotong University, Weihai, 264209, China
2 College of Transport and Communications, Shanghai Maritime University, Shanghai, 201306, China
3 College of Automotive and Traffic Engineering, Nanjing Forestry University, Nanjing, 210037, China
4 School of Civil and Environmental Engineering, Ningbo University, Ningbo, 315211, China
5 School of Business, National University of Singapore, 118414, Singapore
6 Durham Law School, Durham University, Durham, DH1 3LE, UK
* Corresponding Author: Yi Zhao. Email:
(This article belongs to this Special Issue: Decision making Modeling, Methods and Applications of Advanced Fuzzy Theory in Engineering and Science)

Computer Modeling in Engineering & Sciences 2023, 135(2), 1589-1602. https://doi.org/10.32604/cmes.2022.022431

Received 09 March 2022; Accepted 07 June 2022; Issue published 27 October 2022

Abstract

The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets (HFSs). The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements (HFEs) in a special way. Firstly, a probability density function is assigned for any given HFE. Thereafter, equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function. The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs, the higher the credibility of the mentioned membership degrees is, then, the bigger the probability density values for them are. According to this transformation technique, a set of novel distance measures on HFSs is provided. Finally, an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures. The example also shows that this study is a good complement to operation theories on HFSs.

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Keywords

Hesitant fuzzy sets; equal-probability mapping; distance measure; intersection traffic control; cardinality theory

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