Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices

AŞICI E.

IRANIAN JOURNAL OF FUZZY SYSTEMS, vol.19, no.1, pp.125-140, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.22111/ijfs.2022.6556
  • Journal Name: IRANIAN JOURNAL OF FUZZY SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.125-140
  • Keywords: Bounded lattice, t-norms, t-conorms, TRIANGULAR NORMS, ORDINAL SUMS
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods by Ertugrul, Karacal, Mesiar [15] and Cayli [8] as results. Also, we give some illustrative examples. Finally, we show that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices. This paper has further constructed the t-norms and t-conorms on bounded lattices from a mathematical viewpoint.