Correlation of intuitionistic fuzzy sets by centroid method
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.
interval-valued intuitionistic fuzzy set
scientific article; zbMATH DE number 1867084