Ordering based on uni-nullnorms


KESİCİOĞLU M. N. , Samli E.

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, cilt.39, sa.1, ss.645-663, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 39 Konu: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3233/jifs-191583
  • Dergi Adı: JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
  • Sayfa Sayıları: ss.645-663

Özet

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.