Fuzzy set-valued mappings and fixed point theorems
A fuzzy-set valued mapping \(R\) is a function from a set \(X\) to \([0,1]^ X\). A fixed point of \(R\) is a point \(x_ 0\) of \(X\) such that \(R(x_ 0;x_ 0)\geq R(x_ 0;x)\) for any \(x\in X\). The problem of the existence of the fixed points for fuzzy-set valued mappings arises in game theory [cf. the reviewer, Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Sér. 23(71), 29-35 (1979; Zbl 0398.90115)] and in other fields. Some existence criteria for fixed points of fuzzy-set valued mappings are proved and their applications to fuzzy games are pointed out.
scientific article; zbMATH DE number 3897817
Fixed point theorems for fuzzy mappings