Divergence-based distance for picture fuzzy sets and its application to multi-attribute decision-making

As a direct extension of intuitionistic fuzzy sets, picture fuzzy sets have a powerful ability to deal with vague, uncertain and inconsistent information. The distance between picture fuzzy sets is an effective mathematical tool to distinguish the difference between objects. Although various distanc...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 28; no. 1; pp. 253 - 269
Main Authors: Luo, Minxia, Zhang, Guofeng
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024
Subjects:
Artificial Intelligence
Computational Intelligence
Control
Engineering
Mathematical Logic and Foundations
Mechatronics
Robotics
Soft Computing in Decision Making and in Modeling in Economics
Divergence
Multi-attribute decision-making
Distance
Picture fuzzy sets
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary:As a direct extension of intuitionistic fuzzy sets, picture fuzzy sets have a powerful ability to deal with vague, uncertain and inconsistent information. The distance between picture fuzzy sets is an effective mathematical tool to distinguish the difference between objects. Although various distances have been proposed, there are some distances that do not meet the axiomatic definition of distance or some distances that induce counter-intuitive results. To address the above defects, this paper gives a new distance between picture fuzzy sets by aggregating three-dimensional divergence, due to the capability of divergence to distinguish information. This new distance not only satisfies the axiomatic definition, but also overcomes the counter-intuitive defects. Furthermore, the proposed distance is applied to solve the multi-attribute decision-making problem. Through comparison and analysis of decision results, this distance not only provides reasonable decision results, but also has high degree of confidence.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-09205-6