Alternative approaches for generating uninorms on bounded lattices

ÇAYLI G. D.

INFORMATION SCIENCES, vol.488, pp.111-139, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 488
  • Publication Date: 2019
  • Doi Number: 10.1016/j.ins.2019.03.007
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.111-139
  • Keywords: Bounded lattice, Uninorms, Idempotent uninorm, Triangular norm, Triangular conorm, IDEMPOTENT UNINORMS, FUZZY, CONSTRUCTION, OPERATORS, SETS
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, uninorms on bounded lattices are studied. Based on the existence a t-norm T-e acting on [0, e] and a t-conorm S-e acting on [e, 1], we propose some construction methods for uninorms on a bounded lattice L, where some additional conditions on the element e is an element of L\{0, 1} considered as an identity are required. The role of these additional conditions is stressed, as then our constructions yield a uninorm only in particular cases. When the idempotent t-norm T-e and the idempotent t-conorm S-e are considered, our methods give new types of idempotent uninorms on L. (C) 2019 Elsevier Inc. All rights reserved.