Characterization of uninorms on bounded lattices


KARAÇAL F. , ERTUĞRUL Ü. , Mesiar R.

FUZZY SETS AND SYSTEMS, vol.308, pp.54-71, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 308
  • Publication Date: 2017
  • Doi Number: 10.1016/j.fss.2016.05.014
  • Title of Journal : FUZZY SETS AND SYSTEMS
  • Page Numbers: pp.54-71

Abstract

In this paper, we propose a characterization of uninorms on a general bounded lattice L by means of a sextuple of a triangular norm, a triangular conorm, and four aggregation functions on L. Observe that in the case when L is a chain, it is enough to consider a triple consisting of a t-norm, a t-conorm and an averaging aggregation function. An example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown (note that this cannot happen if we consider uninorms acting on a chain). Two general constructions of uninorms on L are added, letting a t-norm (a t-conorm) linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions. (C) 2016 Elsevier B.V. All rights reserved.