Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms

ERTUĞRUL Ü.

FUZZY SETS AND SYSTEMS, vol.334, pp.94-109, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 334
  • Publication Date: 2018
  • Doi Number: 10.1016/j.fss.2017.07.020
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.94-109
  • Keywords: Equivalence relation, Nullnorm, Partial order, TRIANGULAR NORMS, UNINORMS, DISTRIBUTIVITY, EQUATIONS
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this study, we present two methods for the construction of nullnorms on bounded lattices based on the existence of t-norms as well as t-conorms on an arbitrary bounded lattice L. We demonstrate that these methods differ from the existing approaches mainly because of their more generalized structures. An equivalence relation is also defined based on a class of nullnorms and some properties of this relation are examined. (c) 2017 Elsevier B.V. All rights reserved.