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Interval Operators and Preorders in Strong L -Fuzzy Convex Structures

Author

Listed:
  • Sen Zhao

    (School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

  • Fangfang Zhao

    (School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

Abstract

In this paper, the relationship between strong L -fuzzy convex structures and L -fuzzifying interval operators are investigated. It is proved that there is a Galois correspondence between the category of strong L -fuzzy convex spaces and that of L -fuzzifying interval spaces. Also, the concept of arity 2 strong L -fuzzy convex structures is presented, which can be reflectively embedded into the category of L -fuzzifying interval spaces. Finally, the ways of L -fuzzy preorders inducing strong L -fuzzy convex structures and strong L -fuzzy convex structures inducing L -fuzzy preorders are given. It is shown that a strong L -fuzzy convex structure generated by an L -fuzzy preorder is an arity 2 strong L -fuzzy convex structure.

Suggested Citation

  • Sen Zhao & Fangfang Zhao, 2025. "Interval Operators and Preorders in Strong L -Fuzzy Convex Structures," Mathematics, MDPI, vol. 13(15), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2365-:d:1708469
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