ON FUZZIFYING TOPOLOGICAL STRUCTURES

Abstract

In this thesis, the new concepts of a fuzzifying proximity, (Fuzzifying EF- proximity), fuzzifying proximal neighbourhood system, fuzzifying filter, fuzzifying grill, fuzzifying ultrafilter, fuzzifying net and fuzzifying basic proximity II are introduced and developed . How to generate a fuzzifying topology from a fuzzifying proximity, how to obtain a fuzzifying proximity from old ones and how to introduce a fuzzifying filter from a fuzzifying net are also investigated . Some other fundamental properties for fuzzifying proximity spaces are proved . Using two defined operators, some relations between fuzzifying filters, • fuzzifying grills and ultrafilters on a fixed set are obtained . The relations between these concepts and the fuzzifying basic proximity II are also studied . The thesis is included by introducing the concepts offuzzifying f- proximities . Using the concepts offuzzifying filters, fuzzifying grills, and different choices of f , we obtain different types of fuzzifying • proximities such as a fuzzifying EF- proximity, a fuzzifying RH­ proximity and a fuzzifying basic proximity .