A new approach to lattice-valued convergence groups via ⊤-filters

Zhang, Lin; Pang, Bin

doi:10.1016/j.fss.2022.06.026

Cited by 7 publications

(3 citation statements)

References 42 publications

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“…Since Zadeh [32] introduced fuzzy sets, many mathematical structures have been combined with fuzzy set theory, such as fuzzy topology [1,6,19,31], fuzzy order [29,30], fuzzy convergence [3,4,[33][34][35][36] and so on. Convex structures have also been generalized to the fuzzy case.…”

Section: Introductionmentioning

confidence: 99%

Further research on separated degrees of M-fuzzifying convex spaces

Huang,

Xiu

2024

Hacettepe Journal of Mathematics and Statistics

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Section: Introductionmentioning

confidence: 99%

Further research on separated degrees of M-fuzzifying convex spaces

Huang,

Xiu

2024

Hacettepe Journal of Mathematics and Statistics

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“…In 1965, Zadeh [42] introduced the notion of fuzzy sets, which plays an important role in the development of fuzzy set theory. Many mathematical structures were endowed with fuzzy set theory, such as fuzzy ideals and fuzzy filters [41], fuzzy convergence structures [12,47,48], fuzzy convex structures [24,26,33] and so on. A nonempty set with an equivalence relation on it is called an approximation space [28].…”

Section: Introductionmentioning

confidence: 99%

Degrees of compatible L-subsets and compatible mappings

Shi,

Sun

2024

Kybernetika

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Based on a completely distributive lattice L, degrees of compatible L-subsets and compatible mappings are introduced in an L-approximation space and their characterizations are given by four kinds of cut sets of L-subsets and L-equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible L-subsets and compatible degrees of L-subsets. Finally, the notion of complete L-sublattices is introduced and it is shown that the product of complete L-sublattices is still a complete L-sublattice and the compatible degree of an L-subset is a complete L-sublattice.

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“…Recently, Pang and Wu investigated many characterizations of (L, M )-fuzzy convex spaces [10,24,25]. Now, these fuzzy forms of convex structures have been being applied to many fuzzy mathematical structures such as fuzzy topology [6,22,25], fuzzy convergence [31,37] and fuzzy matroid [23,33].…”

Section: Introductionmentioning

confidence: 99%

Characterizations of $L$-concavities and $L$-convexities via derived relations

2023

Hacettepe Journal of Mathematics and Statistics

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This paper is to characterize L-concavities and L-convexities via some derived forms of relations and operators. Specifically, notions of L-concave derived internal relation space and L-concave derived hull space are introduced. It is proved that the category of L-concave derived internal relation spaces and the category of L-concave derived hull spaces are isomorphic to the category of L-concave spaces. Also, notions of L-convex derived enclosed relation space and L-convex derived hull space are introduced. It is proved that the category of L-convex derived enclosed relation spaces and the category of L-convex derived hull spaces are isomorphic to the category of L-convex spaces.

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A new approach to lattice-valued convergence groups via ⊤-filters

Cited by 7 publications

References 42 publications

Further research on separated degrees of M-fuzzifying convex spaces

Further research on separated degrees of M-fuzzifying convex spaces

Degrees of compatible L-subsets and compatible mappings

Characterizations of $L$-concavities and $L$-convexities via derived relations

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