Topological Approach to Fuzzy Sets and Fuzzy Logic

We show how fuzzy set theory and fuzzy logic can be described by classical topology. The basic concepts are filter and ideal bases and morphisms on these. Logics are introduced as hierarchies of valuated objects and the valuations are uniformly topologized to represent approximations to logical terms. As selected applications we consider contractive mappings, roundings, hierarchical filter bases (“pyramids”), adaptable networks.