A new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness in L-fuzzy pretopological spaces

Ghareeb, A.; Al-Saadi, Hanan; Khalil, O. H.

doi:10.1515/math-2019-0047

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…In an L-fuzzy topology, open L-subsets are not crisp subset, and topology comprising those open L-subsets is an L-subset of L X . In the setting of L-fuzzy topologies, many researchers have also made plentiful investigations on the notion of compactness ( [12][13][14][15][16][17][18][19][20][21][22][23][24][25]).…”

Section: Introductionmentioning

confidence: 99%

Measurement of Countable Compactness and Lindelöf Property in RL‐Fuzzy Topological Spaces

2021

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Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

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Section: Introductionmentioning

confidence: 99%

Measurement of Countable Compactness and Lindelöf Property in RL‐Fuzzy Topological Spaces

2021

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“…Moreover, the new operator is used to introduce a new form of F-compactness. Recently, we used the new operators to generalize several kinds of functions between L-fuzzy topological spaces [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces

2021

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In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-compactness of an L-fuzzy set in RL-fuzzy bitopological spaces are given and characterized. As RL-fuzzy bitopology is a generalization of L-bitopology, RL-bitopology, L-fuzzy bitopology, and RL-fuzzy topology, the results of our paper are more general.

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A New Approach to Concavity Fuzzification

Alshammari

Alghamdi

Ghareeb

2021

Journal of Mathematics

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In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, the degree of L , M -fuzzy concavity is introduced and characterized as a generalization of L -concave structure and L , M -fuzzy concave structure. Based on that, the degree of L , M -fuzzy concavity preserving and L , M -fuzzy concave-to-concave of a function are defined. Some properties and relationships between the degree of L , M -fuzzy concavity preserving and L , M -fuzzy concave-to-concave functions are discussed.

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A new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness in L-fuzzy pretopological spaces

Cited by 3 publications

References 16 publications

Measurement of Countable Compactness and Lindelöf Property in RL‐Fuzzy Topological Spaces

Measurement of Countable Compactness and Lindelöf Property in RL‐Fuzzy Topological Spaces

A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces

A New Approach to Concavity Fuzzification

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