Gradation of supra-openness

In this paper, we introduce the concepts of the degrees of compactness, countable compactness and Lindelöf property in L-fuzzy pretopological spaces by means of implication operator. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. The notions of pre-compactness and semi-compactness in L-fuzzy topological spaces can be viewed as special cases of compactness in L-fuzzy pretopological spaces. Their properties are investigated. Further when L is completely distributive, their characterizations are presented.

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“…Ghanim, O.A. Tantawy and Fawzia M. Selim introduced fuzzy supratopological spaces (L-fuzzy pretopological spaces) [4].…”

Section: Introductionmentioning

confidence: 99%

Measures of compactness in L-fuzzy pretopological spaces

Shi

Liang

2014

Journal of Intelligent &Amp; Fuzzy Systems

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“…A fuzzy set λ is quasi-coincident with a fuzzy set µ, denoted by λqµ, if there exists x ∈ X such that λ(x) + µ(x) > 1, if λ is not quasi-coincident with µ, we denote λqµ, λqµ if and only if λ ≤ 1 − µ [14]. Definition 1.1 ( [6,18]). A mapping τ : I X −→ I is called a supra fuzzy topology on X if it satisfies the following conditions:…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Bitopological Spaces in Šostak's Sense (Ii)

Ramadan¹,

Abbas²,

El-Latif³

2010

Communications of the Korean Mathematical Society

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Abstract. In this paper, we have use a fuzzy bitopological space (X, τ 1 , τ 2 ) to create a family τ s ij which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r − (τ i , τ j )-generalized fuzzy regular closed, r − (τ i , τ j )-generalized fuzzy strongly semi-closed and r − (τ i , τ j )-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense ofŠostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

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Fuzzy independent topological spaces generated by fuzzy $$\gamma ^{*}$$ γ ∗ -open sets and their applications

Bhattacharya

2017

Afr. Mat.

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Gradation of supra-openness

Cited by 14 publications

References 0 publications

Measures of compactness in L-fuzzy pretopological spaces

Measures of compactness in L-fuzzy pretopological spaces

On Fuzzy Bitopological Spaces in Šostak's Sense (Ii)

Fuzzy independent topological spaces generated by fuzzy $$\gamma ^{*}$$ γ ∗ -open sets and their applications

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