Convexity on fuzzy partially ordered sets

In this paper, we generalize a series of research work about convexity on classical partially ordered sets to fuzzy partially ordered sets (L-posets). Taking a complete Heyting algebra as the truth value structure, we propose an L-ordered L-convex structure on an L-poset and give its corresponding L...

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Bibliographic Details
Published inJournal of intelligent & fuzzy systems Vol. 36; no. 4; pp. 3607 - 3617
Main Authors Liu, Hongping, Wang, Shuang, Fan, WenPing
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2019
Subjects
Convexity
Fuzzy sets
Hulls
Set theory
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Summary:In this paper, we generalize a series of research work about convexity on classical partially ordered sets to fuzzy partially ordered sets (L-posets). Taking a complete Heyting algebra as the truth value structure, we propose an L-ordered L-convex structure on an L-poset and give its corresponding L-convex hulls. We characterize the L-ordered L-convex sets in terms of four kinds of cut sets of L-subsets, and discuss the product of L-ordered L-convex sets. We also discuss L-convexity-preserving (resp.,L-convex-to-convex) mappings. After that, with a consideration of the degree to which an L-subset is an L-ordered L-convex set, an L-ordered (L, L)-fuzzy convex structure is introduced. The properties such as equivalent descriptions, the product and (L, L)-fuzzy convexity-preserving mappings are analyzed.
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-18170