Order-equivalent triangular norms

Kesicioglu M. N., KARAÇAL F., MESIAR R.

FUZZY SETS AND SYSTEMS, vol.268, pp.59-71, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 268
  • Publication Date: 2015
  • Doi Number: 10.1016/j.fss.2014.10.006
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.59-71
  • Keywords: Triangular norm, Bounded lattice, T-partial order, Divisibility, DISTRIBUTIVE T-NORMS, PRODUCT LATTICES, DIRECT DECOMPOSABILITY
  • Recep Tayyip Erdoğan University Affiliated: Yes


In this paper, an equivalence relation on the class of t-norms induced by a T-partial order is provided and discussed. The equivalence classes linked to some special t-norms are characterized as well as some properties preserved by the introduced equivalence. Defining the set of incomparable elements with respect to the T-partial order, this set is deeply investigated. Finally, we give an answer to a recently posed open problem. (C) 2014 Elsevier B.V. All rights reserved.