Construction methods for idempotent nullnorms on bounded lattices

ÇAYLI G. D.

APPLIED MATHEMATICS AND COMPUTATION, vol.366, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 366
  • Publication Date: 2020
  • Doi Number: 10.1016/j.amc.2019.124746
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Keywords: Bounded lattice, Construction method, Idempotent nullnorm, Nullnorm, Zero element, TRIANGULAR NORMS, T-OPERATORS, DISTRIBUTIVITY, UNINORMS, EQUATIONS
  • Karadeniz Technical University Affiliated: Yes

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.