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M -Hazy Vector Spaces over M -Hazy Field

Author

Listed:
  • Faisal Mehmood

    (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

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M -hazy vector spaces over M -hazy field. Some fundamental properties of M -hazy field, M -hazy vector spaces, and M -hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M -hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M -fuzzifying convex spaces are induced by an M -hazy subspace of M -hazy vector space.

Suggested Citation

  • Faisal Mehmood & Fu-Gui Shi, 2021. "M -Hazy Vector Spaces over M -Hazy Field," Mathematics, MDPI, vol. 9(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1118-:d:554974
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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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