Smooth Fuzzy Topology on Crisp Sets

Murugesan Shakthiganesan, Ramachandran Vembu

Abstract

In almost all examples available in the literature, while introducing fuzzy concepts, certain properties like intelligence and beauty are considered on objects like students and flowers. The properties are fuzzy in nature whereas the objects are crisp in nature. The motive for introducing fuzzy mathematics is to discuss about the fuzzy properties on crisp objects. But no significant separate theory of fuzzy properties on crisp objects is available in the literature. In this paper we develop a theory named co-smooth fuzzy theory  exclusively to study fuzzy properties of crisp objects. We define co-smooth fuzzy topology, basis, sub-basis, product topology and discuss Hausdorffness in the new context.