Soft Computing

, Volume 22, Issue 15, pp 4959–4970 | Cite as

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

  • Harish GargEmail author
  • Kamal Kumar


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.


Set pair analysis Connection number Similarity measure Intuitionistic fuzzy set Decision-making process 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsThapar Institute of Institute and Technology (Deemed University)PatialaIndia

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