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.
Highlights
In the last few years fuzzy topology, as an important research field in fuzzy set theory, has been developed into a quite mature discipline [1,2,3,4,5,6]
In contrast to classical topology, fuzzy topology is endowed with richer structure, to a certain extent, which is manifested with different ways to generalize certain classical concepts
According to Ref. [2], the kind of topologies defined by Chang [7] and Goguen [8] is called the topologies of fuzzy subsets, and further is naturally called L-topological spaces if a lattice L of membership values has been chosen
Summary
A basic structure of this paper is as follows: First, in Section 2 we offer some definition and results which will be needed in this paper. We fill a gap in the existing literature on fuzzifying topology.
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