Idempotent nullnorms on bounded lattices

ÇAYLI G. D., KARAÇAL F.

INFORMATION SCIENCES, vol.425, pp.154-163, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 425
  • Publication Date: 2018
  • Doi Number: 10.1016/j.ins.2017.10.003
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.154-163
  • Keywords: Bounded lattice, Idempotent nullnorm, Zero element, Nullnorm, TRIANGULAR NORMS, T-OPERATORS, UNINORMS, DISTRIBUTIVITY, CONORMS
  • Karadeniz Technical University Affiliated: Yes

Abstract

Nullnorms are generalizations of triangular norms and triangular conorms with a zero element to be an arbitrary point from a bounded lattice. In this paper, we study and discuss the existence of idempotent nullnorms on bounded lattices. Considering an arbitrary distributive bounded lattice L, we show that there exists a unique idempotent nullnorm on L. We prove that an idempotent nullnorm may not always exist on an arbitrary bounded lattice. Furthermore, we propose a construction method to obtain idempotent nullnorms on a bounded lattice L with an additional constraint on a for the given zero element a is an element of L\ {0, 1}. (C) 2017 Elsevier Inc. All rights reserved.