Hull operators and interval operators in (L,M)-fuzzy convex spaces

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Abstract

Considering L being a continuous lattice and M being a completely distributive De Morgan algebra, several basic notions with respect to (L,M)-fuzzy convex structures in the sense of Shi and Xiu are introduced and their relationship with (L,M)-fuzzy convex structures are studied. Firstly, an equivalent form of (L,M)-fuzzy convex structures in the sense of Shi and Xiu is provided. Secondly, two types of fuzzy hull operators are introduced, which are called (L,M)-fuzzy hull operators and (L,M)-fuzzy restricted hull operators, respectively. It is shown that they can be used to characterize (L,M)-fuzzy convex structures. Finally, fuzzy counterparts of interval operators in the (L,M)-fuzzy case are proposed, which are called (L,M)-fuzzy interval operators. It is proved that there is a Galois correspondence between the category of (L,M)-fuzzy interval spaces and that of (L,M)-fuzzy convex spaces and further the category of arity 2 (L,M)-fuzzy convex spaces can be embedded in the category of (L,M)-fuzzy interval spaces as a fully reflective subcategory.

Original languageEnglish
Pages (from-to)106-127
Number of pages22
JournalFuzzy Sets and Systems
Volume405
DOIs
Publication statusPublished - 15 Feb 2021

Keywords

  • Fuzzy closure operator
  • Fuzzy convex structure
  • Fuzzy hull operator
  • Fuzzy interval operator

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Pang, B. (2021). Hull operators and interval operators in (L,M)-fuzzy convex spaces. Fuzzy Sets and Systems, 405, 106-127. https://doi.org/10.1016/j.fss.2019.11.010