An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making

Set pair analysis (SPA) is an updated theory for dealing with the uncertainty, which overlaps with the other existing theories such as vague, fuzzy, intuitionistic fuzzy set (IFS). Keeping the advantages of it, in this paper, we propose some novel similarity measures to measure the relative strength...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 22; no. 15; pp. 4959 - 4970
Main Authors: Garg, Harish, Kumar, Kamal
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018
Springer Nature B.V
Subjects:
Artificial Intelligence
Computational Intelligence
Control
Decision analysis
Decision making
Decision theory
Engineering
Entropy
Focus
Fuzzy sets
Mathematical functions
Mathematical Logic and Foundations
Mechatronics
Medical diagnosis
Preferences
Robotics
Similarity
Similarity measures
Connection number
Intuitionistic fuzzy set
Set pair analysis
Decision-making process
Similarity measure
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary:Set pair analysis (SPA) is an updated theory for dealing with the uncertainty, which overlaps with the other existing theories such as vague, fuzzy, intuitionistic fuzzy set (IFS). Keeping the advantages of it, in this paper, we propose some novel similarity measures to measure the relative strength of the different intuitionistic fuzzy sets (IFSs) after pointing out the weakness of the existing measures. For it, a connection number, the main component of SPA theory is formulated in the form of the degrees of identity, discrepancy, and contrary. Then, based on it some new similarity and weighted similarity measures between the connection number sets are defined. A comparative analysis of the proposed and existing measures are formulated in terms of the counter-intuitive cases for showing the validity of it. Finally, an illustrative example is provided to demonstrate it.
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-018-3202-1