Characterizations of L-convex spaces via domain theory

Shen, Chong; Shi, Fu-Gui

doi:10.1016/j.fss.2019.02.009

Cited by 23 publications

(7 citation statements)

References 26 publications

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“…, respectively. We give some useful properties of the way below relation between L-subsets on X (refer to [15]).…”

Section: Preliminariesmentioning

confidence: 99%

“…In the theory of L-convex structures, we usually replace the points by fuzzy points and replace (finite) subsets by (finite) L-subsets. This results in the definition of restricted L-hull operators h : L (X) −→ L X in [15]. By the above-mentioned analysis, what is the fuzzy counterpart of a betweenness relation induced by a restricted L-hull operator?…”

Section: L-betweenness Relations From Restricted L-hull Operatorsmentioning

confidence: 99%

“…In particular, Shi and Li [16] extended the concept of restricted hull operators to the M-fuzzifying case, namely, restricted M-fuzzifying hull operators, to characterize M-fuzzifying convex structures. More recently, Shen and Shi [15] proposed the concept of restricted L-hull operators to characterize L-convex structures from a categorical aspect.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy points based betweenness relations in L-convex spaces

Yang

Pang

2021

Filomat

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As topology-like mathematical structures, convex structures can be characterized by betweenness relations via (restricted) hull operators in convex spaces. In a topological approach, the aim of this paper is to present the fuzzy counterpart of betweenness relations based on fuzzy points in fuzzy convex spaces. Concretely, the notion of L-betweenness relations via restricted L-hull operators is introduced. Firstly, it is proved that L-betweenness relations are categorically isomorphic to restricted L-hull operators and L-remotehood systems, respectively. Secondly, it is shown that L-betweenness relations from two perspectives of restricted L-hull operators and L-remotehood systems are unified. Finally, a new type of restricted L-hull operators in accordance with L-betweenness relations is proposed and the relationship between two types of restricted L-hull operators is displayed.

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“…, respectively. We give some useful properties of the way below relation between L-subsets on X (refer to [15]).…”

Section: Preliminariesmentioning

confidence: 99%

Section: L-betweenness Relations From Restricted L-hull Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fuzzy points based betweenness relations in L-convex spaces

Yang

Pang

2021

Filomat

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“…The L-convex hull operator with respect to the L-convex space (E, E L ) is as follows: [17], i.e., co(A) is the least L-subalgebra containing A. In the following, we will give the corresponding L-convex hull formula.…”

Section: Corollarymentioning

confidence: 99%

“…In 1994, Rosa [14] first proposed the notion of fuzzy convex structures with the unit interval [0, 1] as the lattice background. In 2009, Y. Maruyama [15] defined another more generalized fuzzy convex structure based on a completely distributive lattice L, which is called L-convex structure, some of the latest research related to L-convex structure can be found in [16][17][18][19][20][21]. In 2014, a new approach to the fuzzification of convex structures was introduced in [22].…”

Section: Introductionmentioning

confidence: 99%

L-Fuzzy Sub-Effect Algebras

Dong

Shi

2021

Mathematics

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In this paper, the notions of L-fuzzy subalgebra degree and L-subalgebras on an effect algebra are introduced and some characterizations are given. We use four kinds of cut sets of L-subsets to characterize the L-fuzzy subalgebra degree. We induce an L-fuzzy convexity by the L-fuzzy subalgebra degree, and we prove that a morphism between two effect algebras is an L-fuzzy convexity preserving mapping and a monomorphism is an L-fuzzy convex-to-convex mapping. Finally, it is proved that the set of all L-subalgebras on an effect algebra can form an L-convexity, and its L-convex hull formula is given.

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