Intuitionistic fuzzy generators. Application to intuitionistic fuzzy complementation
The concept of an intuitionistic fuzzy generator \(\varphi: [0,1]\to[0,1]\) is introduced by \(\varphi(x)\leq 1-x\) for all \(x\in[0,1]\). It can be continuous, decreasing or increasing. Some properties of the new concept are studied and characterization theorems for it are proved. One of the most important results is: Theorem 25. Let \(A=\{\langle x,\mu_A(x) \rangle:x\in X\}\) be a fuzzy set on the referential set \(X\neq\emptyset\), and let \(\varphi\) be an intuitionistic fuzzy generator. The set \(\overline A=\{\langle x,\mu_A (x), \varphi(\mu_A(x)) \rangle:x\in X\}\) is an intuitionistic fuzzy set on \(X\) [see \textit{K. T. Atanassov}, ``Intuitionistic fuzzy sets'', Fuzzy Sets Syst. 20, 87-96 (1986; Zbl 0631.03040); Intuitionistic fuzzy sets. Theory and applications. Physica-Verlag, Heidelberg (1999; Zbl 0939.03057)].
scientific article; zbMATH DE number 1517326
scientific article