Ordering based on uni-nullnorms


KESİCİOĞLU M. N. , Samli E.

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

  • Publication Type: Article / Article
  • Volume: 39 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.3233/jifs-191583
  • Title of Journal : JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
  • Page Numbers: pp.645-663

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.