Abstract
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.
Highlights
Combining with fuzzy set theory, Chang [1] introduced the concept of fuzzy topology together with the definition of compactness by means of open cover in 1968
We introduce and characterize the degree of countable RL-fuzzy compactness and the RL-Lindelof property of an L-subset in RL-fuzzy topology based on the concepts of pseudocomplement of L-subsets and the implication operator
Since L-fuzzy topology in the sense of Kubiak and Sostak is a special case of RL-fuzzy topology, the degrees of RL-fuzzy compactness and the RL-Lindelof property are generalization of the corresponding degrees in L-fuzzy topology
Summary
Combining with fuzzy set theory, Chang [1] introduced the concept of fuzzy topology together with the definition of compactness by means of open cover in 1968. We introduce and characterize the degree of countable RL-fuzzy compactness and the RL-Lindelof property of an L-subset in RL-fuzzy topology based on the concepts of pseudocomplement of L-subsets and the implication operator. Let λ ∈ VLX, μ ∈ VLY, and fL⟶ ,λ : λ ⟶ μ be RL-fuzzy mapping from λ to μ, and c ∈ FLX(λ). A relative L-topology κ on an L-subset λ is a subcollection on FLX(λ) that satisfies the following conditions:. An RL-fuzzy topology on λ is a mapping κ: FLX(λ) ⟶ L such that κ satisfying the following statements:. An L-subset μ ∈ FLX(λ) is said to be an RL-fuzzy compact with respect to κ if for each P⊆FLX(λ), the following inequality holds:. (2) If μ1, μ2 ∈ FLX(λ) such that μ1 is an RL-fuzzy compact with respect to κ and μ2 is an RL-closed subset, μ1∧μ2 is an RL-fuzzy compact. Μ is the RL-fuzzy compact in RL-ts κ iff cχκ(μ) 1
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