From lattice valued theories to lattice valued analysis

Abstract

We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core.We discuss the property of continuity of a fuzzy function in a lattice valued topology.