Characterizing idempotent nullnorms on a special class of bounded lattices


Wu X., Liang S., ÇAYLI G. D.

FUZZY SETS AND SYSTEMS, vol.427, pp.161-173, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 427
  • Publication Date: 2022
  • Doi Number: 10.1016/j.fss.2020.11.016
  • Title of Journal : FUZZY SETS AND SYSTEMS
  • Page Numbers: pp.161-173
  • Keywords: Lattice, Nullnorm, Idempotent nullnorm, Zero element, T-NORMS, UNINORMS, DISTRIBUTIVITY, OPERATORS, CONSTRUCTION, EQUATIONS, CONORMS

Abstract

Nullnorms with a zero element being at any point of a bounded lattice are an important generalization of triangular norms and triangular conorms. This paper obtains an equivalent characterization for the existence of idempotent nullnorms with the zero element a on any bounded lattice containing only two distinct elements incomparable with a. Furthermore, some basic properties for the bounded lattice containing only two distinct elements incomparable with a are presented. (c) 2020 Elsevier B.V. All rights reserved.