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

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.

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O. Sayed, "A Unified Theory (I) for Neighborhood Systems and Basic Concepts on Fuzzifying Topological Spaces," *Applied Mathematics*, Vol. 3 No. 9, 2012, pp. 983-996. doi: 10.4236/am.2012.39146.

Conflicts of Interest

The authors declare no conflicts of interest.

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