New constructions of triangular norms and triangular conorms on an arbitrary bounded lattice


AŞICI E. , Mesiar R.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol.49, no.2, pp.143-160, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1080/03081079.2019.1668385
  • Title of Journal : INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Page Numbers: pp.143-160
  • Keywords: Bounded lattices, t-norms, t-conorms, ordinal sum, ORDINAL SUMS, UNINORMS, NULLNORMS

Abstract

The ordinal sum of triangular norms on the real unit interval has been used to construct other triangular norms. But, in general, the standard approach to the ordinal sum construction of triangular norms and triangular conorms may not work on an arbitrary bounded lattice. In this study, we introduce a new ordinal sum construction of triangular norms and triangular conorms on an arbitrary bounded lattice. Also, we give some illustrative examples for the clarity.