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L -Fuzzy Sub-Effect Algebras

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yan-Yan Dong & Fu-Gui Shi, 2021. "L -Fuzzy Sub-Effect Algebras," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1596-:d:589920
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    References listed on IDEAS

    as
    1. Fu-Gui Shi & Zhen-Yu Xiu, 2014. "A New Approach to the Fuzzification of Convex Structures," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, August.
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