On a new class of uninorms on bounded lattices

ÇAYLI G. D., KARAÇAL F., Mesiar R.

INFORMATION SCIENCES, vol.367, pp.221-231, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 367
  • Publication Date: 2016
  • Doi Number: 10.1016/j.ins.2016.05.036
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.221-231
  • Keywords: Bounded lattice, Idempotent uninorm, Neutral element, Uninorm, FUZZY-SET THEORY, TRIANGULAR NORMS, OPERATORS, OPERATIONS, UNIFORMS, CONORMS
  • Karadeniz Technical University Affiliated: Yes

Abstract

We study and propose some new construction methods to obtain uninorms on bounded lattices. Considering an arbitrary bounded lattice L, we show the existence of idempotent uninorms on L for any element e is an element of L\{0, 1} playing the role of a neutral element. By our construction method, we obtain the smallest idempotent uninorm and the greatest idempotent uninorm with the neutral element e is an element of L\{0, 1}. We see that the obtained uninorms are conjunctive and disjunctive uninorms, respectively. On the other hand, if L is not a chain, we also provide an example of an idempotent uninorm which is neither conjunctive nor disjunctive. (C) 2016 Elsevier Inc. All rights reserved.