Many valued topologies on L-sets

DEMİRCİ M.

Fuzzy Sets and Systems, cilt.437, ss.97-113, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 437
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.fss.2021.07.010
  • 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, Computer & Applied Sciences, INSPEC, zbMATH
  • Sayfa Sayıları: ss.97-113
  • Anahtar Kelimeler: Category of L-sets, Fuzzy topology, L-set, Lattice-valued topology, Many valued topology, Monadic topology
  • Akdeniz Üniversitesi Adresli: Evet

Özet

© 2021 Elsevier B.V.Many valued topologies on L-sets, providing a common framework for fuzzy topologies on fuzzy sets and the fixed-basis lattice-valued topologies on ordinary sets, are the main subject of the present study. In this paper, we have introduced many valued topological L-set-spaces, referring to L-sets equipped with many valued topologies, in an axiomatic way and focused on the vindication of their axiomatization in a categorical framework. In order to attain this objective, we apply the theory of Höhle of topological space objects formulated in terms of a partially ordered monad on an abstract category, and show that the category of many valued topological L-set-spaces is isomorphic to the category of topological space objects with respect to a partially ordered monad on a category of L-sets.