Many-valued partial orders in a closed monoidal category

DEMİRCİ M.

Fuzzy Sets and Systems, vol.468, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 468
  • Publication Date: 2023
  • Doi Number: 10.1016/j.fss.2023.108591
  • Journal Name: Fuzzy Sets and Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, zbMATH
  • Keywords: Categorical many-valued partial order, Fuzzy partial order, L-set, Lattice-valued partial order, Many-valued partial order, Monoidal relation system, Partially ordered monoidal relation system, Quantale-valued partial order
  • Akdeniz University Affiliated: Yes

Abstract

This paper introduces partially ordered Ω-monoidal relation systems on a category C endowed with a closed monoidal structure, and therewith explores a categorical theory of many-valued partial orders in C. For a fixed C-object Ω and a partially ordered Ω-monoidal relation system ϒ on C, the notion of a many-valued preordered (resp. many-valued partially ordered) C-object is formulated as a ϒ-preordered (resp. ϒ-partially ordered) C-object. Furthermore, the category of ϒ-preordered (resp. ϒ-partially ordered) C-objects is constructed and applied to quantale-valued preorders (resp. partial orders) on ordinary sets as well as on L-sets.