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

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DOI: 10.4236/am.2012.39146    3,084 Downloads   5,069 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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