Construction methods for the smallest and largest uni-nullnorms on bounded lattices


Wu X., Liang S., Luo Y., ÇAYLI G. D.

FUZZY SETS AND SYSTEMS, vol.427, pp.132-148, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 427
  • Publication Date: 2022
  • Doi Number: 10.1016/j.fss.2021.02.010
  • Title of Journal : FUZZY SETS AND SYSTEMS
  • Page Numbers: pp.132-148
  • Keywords: Lattice, Triangular norm, Nullnorm, Uninorm, Uni-nullnorm, T-NORMS, TRIANGULAR NORMS, ORDINAL SUMS, UNINORMS, DISTRIBUTIVITY, OPERATORS, CONORMS

Abstract

This paper continues to study the construction of uni-nullnorms on bounded lattices. At first, we introduce a new method for constructing the smallest uni-nullnorm on an arbitrary bounded lattice L having the elements e, a is an element of L, based on the existence of a uninorm on [0, a](2) with the neutral element e and a triangular norm on [a, 1](2). And then, we propose another new approach to obtain the largest uni-nullnorm on L via a uninorm on [0, a)(2) with the neutral element e and a triangular norm on [a, 1](2). Furthermore, we provide some corresponding examples to illustrate that our construction methods differ from the existing ones. (C) 2021 Elsevier B.V. All rights reserved.