Ordering based on uni-nullnorms


KESİCİOĞLU M. N., Samli E.

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, vol.39, no.1, pp.645-663, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.3233/jifs-191583
  • Journal Name: JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.645-663
  • Keywords: Uninorm, bounded lattice, partial order, uni-nullnorm, SEMI-T-OPERATORS, UNINORMS, EQUIVALENCE, DISTRIBUTIVITY, NORMS
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

In this paper, orders based on uni-nullnorms on bounded lattices are introduced and discussed. By this way, the existing orders in the literature induced by t-norms, t-conorms, uninorms and nullnorms are extended to much more general form. The relationships between the orders induced by uni-nullnorms and the orders induced by their underlying t-norms, t-conorms, uninorms and nullnorms are presented. A necessary and sufficient condition making a bounded lattice again a lattice with respect to the orders based on uni-nullnorms is given. Also, the relationships between the partially ordered sets based on the orders induced by t-norms and induced by their N-dual t-conorms and conjugate t-norms, which are special uni-nullnorms, are investigated.