Medians and nullnorms on bounded lattices

Ince M. A., KARAÇAL F., MESIAR R.

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

  • Publication Type: Article / Article
  • Volume: 289
  • Publication Date: 2016
  • Doi Number: 10.1016/j.fss.2015.05.015
  • Journal Name: FUZZY SETS AND SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.74-81
  • Keywords: Nullnorm, Median, Idempotent nullnorm, Distributive bounded lattice, Triangular norm, Triangular conorm, DISTRIBUTIVE T-NORMS, PRODUCT LATTICES, OPERATORS, UNINORMS
  • Recep Tayyip Erdoğan University Affiliated: Yes

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.