Correlation of intuitionistic fuzzy sets by centroid method
type: Item
instance of: scholarly article
title: Correlation of intuitionistic fuzzy sets by centroid method
zbMATH Open document ID: 1013.03067
DOI: 10.1016/S0020-0255(02)00181-0
author: Yanyan Li
published in: Information Sciences
publication date: 2003-02-11T00:00:00Z
review text: Let \(X\) be a fixed set and \(A= \{\langle x,\mu_A(x),\nu_A(x)\rangle: x\in E\}\) be an intuitionistic fuzzy set (IFS, see the reviewer's paper ``Intuitionistic fuzzy sets'' [Fuzzy Sets Syst. 20, 87-96 (1986; Zbl 0631.03040)] and his book [Intuitionistic fuzzy sets. Theory and applications. Heidelberg: Physica-Verlag (1999; Zbl 0939.03057)]), where \(\mu_A(x)\) and \(\nu_A(x)\) are the degrees of membership and of nonmembership of \(x\in X\) with respect to \(A\) and \(\mu_A(x)\), \(\nu_A(x)\), \(\mu_A(x)+ \nu_A(x)\in [0,1]\). For two IFSs \(A\) and \(B\), four special numbers are defined: \(m(\mu_A)= {\int_X x \mu_A(x) dx\over\int_X \mu_A(x) dx}\) and \(m(\nu_A)= {\int_X x\nu_A(x) dx\over \int_X \nu_A(x) dx}\) are called centroids of \(\mu_A\) and \(\nu_A\), respectively; \(C(A,B)= m(\mu_A)m(\mu_B)+ m(\nu_A)m(\nu_B)\) and \(\rho(A,B)= {C(A,B)\over (C(A,A) C(B,B))^{1/2}}\) are called correlation formula and correlation coefficient of \(A\) and \(B\), respectively. Some properties of these numbers are discussed. Some examples are given.
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1867084
zbMATH Keywords: centroid
zbMATH Keywords: correlation coefficient
zbMATH Keywords: interval-valued intuitionistic fuzzy set
reviewed by: Krassimir Atanassov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1867084