A Note on Fixed Fuzzy Points for Fuzzy Mappings

After the introduction of the concept of a fuzzy set by Zadeh, several researches were conducted on the generalizations of the concept of a fuzzy set. The idea of intuitionistic fuzzy set is due to Atanassov [1], [2], [3] and recently Çoker [4] has defined the concept of intuitionistic fuzzy topological space which generalizes the concept of fuzzy topological space introduced by Chang [5]. Heilpern [6] introduced the concept of a fuzzy mapping and proved a fixed point theorem for fuzzy contraction mappings which is a generalization of the fixed point theorem for multivalued mappings of Nadler [7]. In this paper we give a fixed fuzzy point theorem for fuzzy contraction mappings over a complete metric space, which is a generalization of the given by S. Heilpern for fixed points. Then, we introduce the concept