A Unified Theory (I) for Neighborhood Systems and Basic Concepts on Fuzzifying Topological Spaces

Osama Rashed Sayed

Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.

DOI: 10.4236/am.2012.39146                

Abstract

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying. It investigates topological notions defined by means of -open sets when these are planted into the frame-work of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying operations from P(X) to , where (X, τ) is a fuzzifying topological space. By making use of them we contract neighborhood structures, derived sets, closure operations and interior operations.

Keywords

Lukasiewicz Logic; Semantics; Fuzzifying Topology

Conflicts of Interest

The authors declare no conflicts of interest.

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