Abstract
We introduce fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological space in view of the definition of Šostak, and study some of their properties. Also, we investigate the behavior of fuzzy compactness under several types of fuzzy continuous mappings.
Highlights
Introduction and preliminariesThe concept of a fuzzy set was introduced by Zadeh [13], and later Chang [3] defined fuzzy topological spaces
We introduce fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological space in view of the definition of Sostak, and study some of their properties
We investigate the behavior of fuzzy compactness under several types of fuzzy continuous mappings
Summary
Introduction and preliminariesThe concept of a fuzzy set was introduced by Zadeh [13], and later Chang [3] defined fuzzy topological spaces. Suppose that the IFTS (X,τ) is (α,β)-intuitionistic fuzzy nearly compact, for every family {Gi : i ∈ J} in {G : G ∈ ζX , τ(G) > α, β }, where α ∈ I0, β ∈ I1 with α + β ≤ 1, there exists a finite subset J0 of J such that ∪i∈J0 intα,β(clα,β Gi) = 1∼ since, Gi = intα,β Gi ⊆ intα,β clα,β Gi ⊆ clα,β Gi for each i ∈ J 1∼ = ∪i∈J0 intα,β clα,β Gi ⊆ ∪i∈J0 clα,β Gi. ∪i∈J0 clα,β Gi = 1∼.
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