The Fixed Point Property for Intuitionistic Fuzzy Lattices

Abstract

In this paper, based on the concept of intuitionistic fuzzy lattice previously introduced by Tripathy and his colleagues, a class of intuitionistic fuzzy complete lattices is proposed with some interesting characterizations given. In particular, we show the fixed point property for this proposed class. Conversely, we show that any intuitionistic fuzzy lattice is complete having its fixed point property. These results establish a criterion for completeness of intuitionistic fuzzy lattices in terms of the fixed points of their intuitionistic fuzzy monotone mappings.