An application of the theory of categorical many-valued partial orders to sets with fuzzy equalities

DEMİRCİ M.

Fuzzy Sets and Systems, cilt.502, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 502
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.fss.2024.109219
  • Dergi Adı: Fuzzy Sets and Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Anahtar Kelimeler: Categorical many-valued partial order, Fuzzy equality, Fuzzy partial order, Global L-valued equality, Global L-valued set, Lattice-valued partial order
  • Akdeniz Üniversitesi Adresli: Evet

Özet

A recently proposed theory of categorical many-valued partial orders suggests a new approach to fuzzy equality-based fuzzy partial orders. The present study applies the theory to the category GL-SET of global L-valued sets for a fixed strictly two-sided, commutative quantale L. For a special global L-valued set Ω, we construct a partially ordered Ω-monoidal relation system ϒG, containing an Ω-monoidal relation system G, on GL-SET and formulate fuzzy equality-based fuzzy partial orders on sets as ϒG-partial orders on global L-valued sets in this paper. It is then shown that the category of fuzzy equality-based fuzzy partially ordered sets can be presented as the category of ϒG-partially ordered global L-valued sets. Furthermore, we give explicit characterizations of the Kleisli and Eilenberg-Moore categories of the Ω-monoidal power object monad associated with G.