Correlation coefficients in T-spherical fuzzy environment using statistical viewpoint and their applications

Dinesh K. Sharma, Surender Singh and Abdul Haseeb Ganie

International Journal of Operational Research, 2023, vol. 47, issue 3, 384-411

Abstract: A T-spherical fuzzy set (T-SFS) is a generalisation of spherical fuzzy sets (SFSs), picture fuzzy sets (SFSs), intuitionistic fuzzy sets (IFSs), and fuzzy sets (FSs) in which the sum of the q^th power of membership, the q^th power of non-membership and q^th power of neutrality values is at most one. The correlation coefficient is a crucial tool in fuzzy/non-standard fuzzy theory and has been applied in various fields such as clustering, pattern recognition, medical diagnosis, decision-making, etc. However, the existing correlation coefficients for T-SFSs give only the degree of correlation between two T-SFSs but do not tell us the nature of correlation (negative or positive). In this study, we propose two correlation coefficients for T-SFSs, which not only give the strength of correlation between two T-SFSs but also tell us whether the two T-SFSs are positively correlated or negatively correlated. We also discuss several properties of these correlation coefficients. We apply these correlation coefficients to solve a pattern recognition problem in the T-spherical fuzzy environment and compare the results with some existing measures. Further, by considering linguistic hedges, we theoretically and empirically contrast the performance of the proposed coefficients of correlation for T-SFSs with several existing measures.

Keywords: correlation coefficient; picture fuzzy set; PIFS; linguistic hedges; spherical fuzzy set; pattern recognition; T-spherical fuzzy set; T-SFS. (search for similar items in EconPapers)
Date: 2023
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