Interval Operators and Preorders in Strong L -Fuzzy Convex Structures

Sen Zhao and Fangfang Zhao ()
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Sen Zhao: School of Mathematics and Statistics, Linyi University, Linyi 276005, China
Fangfang Zhao: School of Mathematics and Statistics, Linyi University, Linyi 276005, China

Mathematics, 2025, vol. 13, issue 15, 1-18

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.

Keywords: strong L-fuzzy convex structure; L-fuzzifying interval operator; L-fuzzy preorder; Galois correspondence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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