An alternative construction of uninorms on bounded lattices

ÇAYLI G. D.

International Journal of General Systems, vol.52, no.5, pp.574-596, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.1080/03081079.2023.2196421
  • Journal Name: International Journal of General Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.574-596
  • Keywords: Bounded lattice, closure operator, interior operator, t-norm, t-conorm, uninorm, T-NORMS, TRIANGULAR NORMS, ORDINAL SUM
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this article, we first introduce a method for obtaining uninorms on a bounded lattice (Formula presented.) with the identity element (Formula presented.) using an interior operator on (Formula presented.) and a t-conorm on (Formula presented.) Next, based on a closure operator on (Formula presented.) and a t-norm on (Formula presented.) a construction method for uninorms on (Formula presented.) with the identity element (Formula presented.) is proposed. Furthermore, we state that these methods are generalizations of those described in [Çaylı, G. D. 2018. “A Characterization of Uninorms on Bounded Lattices by Means of Triangular Norms and Triangular Conorms.” International Journal of General Systems 47: 772–793. doi:10.1080/03081079.2018.1513929; Dan, Y., and B. Q. Hu. 2020. “A New Structure for Uninorms on Bounded Lattices.” Fuzzy Sets and Systems 386: 77–94. doi:10.1016/j.fss.2019.02.001.]. Some corresponding examples are also provided to illustrate that our methods differ from the existing ones.