Construction methods for idempotent nullnorms on bounded lattices


ÇAYLI G. D.

APPLIED MATHEMATICS AND COMPUTATION, vol.366, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 366
  • Publication Date: 2020
  • Doi Number: 10.1016/j.amc.2019.124746
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Keywords: Bounded lattice, Construction method, Idempotent nullnorm, Nullnorm, Zero element, TRIANGULAR NORMS, T-OPERATORS, DISTRIBUTIVITY, UNINORMS, EQUATIONS

Abstract

In this paper, we discuss the presence of idempotent nullnorms on bounded lattices and investigate some properties of these operators. We introduce two new methods for constructing idempotent nullnorms on bounded lattices for a zero element under a constraint that all elements incomparable with the zero element are comparable with each other. In order to stress the role of this constraint satisfying that our constructions yield an idempotent nullnorm, some illustrative examples are added. (C) 2019 Elsevier Inc. All rights reserved.