Construction of nullnorms on some special classes of bounded lattices


ÇAYLI G. D.

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol.134, pp.111-128, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 134
  • Publication Date: 2021
  • Doi Number: 10.1016/j.ijar.2021.04.005
  • Title of Journal : INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
  • Page Numbers: pp.111-128
  • Keywords: Bounded lattice, Nullnorm, Closure operator, Interior operator, T-norm, T-conorm, T-NORMS, TRIANGULAR NORMS, ORDINAL SUMS, UNINORMS, DISTRIBUTIVITY, OPERATORS, EQUATIONS, CONORMS

Abstract

This paper continues to study the construction of nullnorms on bounded lattices. We first propose two new construction methods of nullnorms derived from an arbitrary t norm (resp. an arbitrary t-conorm) using a closure operator (resp. an interior operator) on bounded lattices, where some sufficient and necessary conditions are considered. Then, we introduce two other methods to obtain nullnorms based on a closure operator (an interior operator) on bounded lattices with some constraints. In particular, we obtain some new classes of idempotent nullnorms on bounded lattices. Moreover, we provide some examples for a better understanding of new classes of nullnorms on bounded lattices. (C) 2021 Elsevier Inc. All rights reserved.