Formulations of L-convex hulls on some algebraic structures

Zhong, Yu; Shi, Fu-Gui

doi:10.3233/jifs-161927

Cited by 15 publications

(2 citation statements)

References 19 publications

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“…e notions of M-fuzzifying convex structure and (L, M)-fuzzy convex structure are introduced by Shi and Xiu in [9,10]. Actually, fuzzy convexity exists in many mathematical research areas, such as fuzzy vector spaces, fuzzy groups, fuzzy lattices, and fuzzy topologies (see [7,8,[11][12][13][14][15][16][17][18][19][20][21][22][23][24]).…”

Section: Introductionmentioning

confidence: 99%

A Generalized Definition of Fuzzy Subrings

Shi

Wang

2022

Journal of Mathematics

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In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L -fuzzy subring measures are presented. The properties of L -fuzzy subring measures under these two kinds of product operations are further studied. In addition, an L -fuzzy convexity is directly induced by L -fuzzy subring measure, and it is pointed out that ring homomorphism can be regarded as L -fuzzy convex preserving mapping and L -fuzzy convex-to-convex mapping. Next, we give the definition and related properties of the measure of L -fuzzy quotient ring and give a new characterization of L -fuzzy quotient ring when the measure of L -fuzzy quotient ring is 1.

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Section: Introductionmentioning

confidence: 99%

A Generalized Definition of Fuzzy Subrings

Shi

Wang

2022

Journal of Mathematics

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“…For example, fuzzy convexity exists in so many mathematical areas, such as hazy lattices, hazy group, fuzzy algebras, and so on. Some more details can be found in [4][5][6][7][8]21].…”

Section: Introductionmentioning

confidence: 99%