Article: Correlation coefficients in T-spherical fuzzy environment using statistical viewpoint and their applications Journal: International Journal of Operational Research (IJOR) 2023 Vol.47 No.3 pp.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 qth power of membership, the qth power of non-membership and qth 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. Inderscience Publishers - linking academia, business and industry through research

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

Authors: Dinesh K. Sharma; Surender Singh; Abdul Haseeb Ganie

Addresses: Department of Business, Management and Accounting, University of Maryland Eastern Shore, Princess Anne, Maryland, USA ' School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, India ' School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, India

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.

DOI: 10.1504/IJOR.2023.132256

International Journal of Operational Research, 2023 Vol.47 No.3, pp.384 - 411

Received: 02 Sep 2020
Accepted: 07 Dec 2020
Published online: 14 Jul 2023 *

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

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