Affiliations: Department of Mathematics, Recep Tayyip Erdogan University, Rize, Turkey
Correspondence:
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Corresponding author. M. Nesibe Kesicioğlu, Department of Mathematics, Recep Tayyip Erdogan University, 53100 Rize, Turkey. Tel.: +90 464-2236126; Fax: +90 464-2234019. E-mail: [email protected].
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.
