Medians and nullnorms on bounded lattices


Ince M. A. , KARAÇAL F., MESIAR R.

FUZZY SETS AND SYSTEMS, vol.289, pp.74-81, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 289
  • Publication Date: 2016
  • Doi Number: 10.1016/j.fss.2015.05.015
  • Title of Journal : FUZZY SETS AND SYSTEMS
  • Page Numbers: pp.74-81

Abstract

Nullnorms are generalizations of triangular norms and triangular conorms with a zero element in the interior of the unit interval. In this paper, we work on nullnorms which are defined on an arbitrary bounded lattice. We introduce a general median-based method for constructing nullnorms by means of triangular norms and triangular conorms. Furthermore, we highlight a significant difference between the (existence and representation of) (idempotent) nullnorms on chains, distributive bounded lattices and general bounded lattices. (C) 2015 Elsevier B.V. All rights reserved.