Determination of the Smallest-Greatest Uni-Nullnorms and Null-Uninorms on an Arbitrary Bounded Lattice <i>L</i>

İNCE M. A., KARAÇAL F.

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol.31, no.1, pp.103-119, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1142/s0218488523500071
  • Journal Name: INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Compendex, Computer & Applied Sciences, zbMATH
  • Page Numbers: pp.103-119
  • Keywords: bounded lattice, null-uninorm, nullnorm, uni-nullnorm, Uninorm
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we study uni-nullnorms and null-uninorms on bounded lattices, which are generalizations of uninorms, nullnorms, t-norms and t-conorms. We construct two uni-nullnorms and two null-uninorms on a bounded lattice L. We determine the smallest-greatest uni-nullnorms with 2-neutral element {e, 1}(a) and the smallest-greatest null-uninorms with 2-neutral element {0,e}(a) by using these construction methods.