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Correlation and correlation coefficient of generalized orthopair fuzzy sets
Author(s) -
Du Wen Sheng
Publication year - 2019
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22065
Subject(s) - mathematics , fuzzy logic , fuzzy set , bounded function , correlation , correlation coefficient , range (aeronautics) , membership function , measure (data warehouse) , fuzzy number , computer science , statistics , mathematical analysis , data mining , artificial intelligence , geometry , materials science , composite material
Generalized orthopair fuzzy sets are extensions of ordinary fuzzy sets by relaxing restrictions on the degrees of support for and support against. Correlation analysis is to measure the statistical relationships between two samples or variables. In this paper, we propose a function measuring the interrelation of two q ‐rung orthopair fuzzy sets, whose range is the unit interval [ 0 , 1 ] . First, the correlation and correlation coefficient of q ‐rung orthopair membership grades are presented, and their basic properties are investigated. Second, these concepts are extended to q ‐rung orthopair fuzzy sets on discrete universes. Then, we discuss their applications in cluster analysis under generalized orthopair fuzzy environments. And, a real‐world problem involving the evaluation of companies is used to illustrate the detailed processes of the clustering algorithm. Finally, we introduce the correlation and correlation coefficient of q ‐rung orthopair fuzzy sets on both bounded and unbounded continuous universes and provide some numerical examples to substantiate such arguments.