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A New Approach to the Fuzzification of Convex Structures

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  • Fu-Gui Shi
  • Zhen-Yu Xiu

Abstract

A new approach to the fuzzification of convex structures is introduced. It is also called an -fuzzifying convex structure. In the definition of -fuzzifying convex structure, each subset can be regarded as a convex set to some degree. An -fuzzifying convex structure can be characterized by means of its -fuzzifying closure operator. An -fuzzifying convex structure and its -fuzzifying closure operator are one-to-one corresponding. The concepts of -fuzzifying convexity preserving functions, substructures, disjoint sums, bases, subbases, joins, product, and quotient structures are presented and their fundamental properties are obtained in -fuzzifying convex structure.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:249183
    DOI: 10.1155/2014/249183
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    Cited by:

    1. Yan-Yan Dong & Fu-Gui Shi, 2021. "L -Fuzzy Sub-Effect Algebras," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    2. Faisal Mehmood & Fu-Gui Shi & Khizar Hayat & Xiao-Peng Yang, 2020. "The Homomorphism Theorems of M -Hazy Rings and Their Induced Fuzzifying Convexities," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    3. Faisal Mehmood & Fu-Gui Shi, 2021. "M -Hazy Vector Spaces over M -Hazy Field," Mathematics, MDPI, vol. 9(10), pages 1-13, May.
    4. Yu Zhong & Xin Wu & Alexander Šostak & Fu-Gui Shi, 2022. "( L , M )-Fuzzy k -Pseudo Metric Space," Mathematics, MDPI, vol. 10(7), pages 1-17, April.

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