An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making
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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.
KeywordsSet pair analysis Connection number Similarity measure Intuitionistic fuzzy set Decision-making process
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Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Arora R, Garg H (2018a) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Sci Iran 25(1):466–482Google Scholar
- ChangJian W (2007) Application of the set pair analysis theory in multiple attribute decision-making. J Mech Strength 6(029):1009–1012Google Scholar
- Ejegwa PA, Modom ES (2015) Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets. Int J Fuzzy Math Arch 8(1):1–7Google Scholar
- Liu C, Zhang L, Yang A (2013) The fundamental operation on connection number and its applications. J Theor Appl Inf Technol 49(2):618–623Google Scholar
- Lü WS, Zhang B (2012) Set pair analysis method of containing target constraint mixed interval multi-attribute decision-making. Appl Mech Mater Trans Tech Publ 226:2222–2226Google Scholar
- Xie Z, Zhang F, Cheng J, Li L (2013) Fuzzy multi-attribute decision making methods based on improved set pair analysis, vol 2. In: Sixth international symposium on computational intelligence and design, pp 386–389Google Scholar
- Yang Y, Yang S, Zhang R, Jiao Y (2014) On interval arithmetic method of connection number a+bi. J Chem Pharm Res 6(3):225–229Google Scholar
- Zhao K (1989) Set pair and set pair analysis-a new concept and systematic analysis method. In: Proceedings of the national conference on system theory and regional planning, pp 87–91Google Scholar