L -Fuzzy Sub-Effect Algebras

Yan-Yan Dong and Fu-Gui Shi
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Yan-Yan Dong: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China
Fu-Gui Shi: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China

Mathematics, 2021, vol. 9, issue 14, 1-14

Abstract: 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.

Keywords: effect algebra; L -fuzzy subalgebra degree; L -subalgebra; L -fuzzy convexity; L -convex hull formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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