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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1080/03081079.2019.1668385
  • Journal Name: INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, Sociological abstracts, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.143-160
  • Keywords: Bounded lattices, t-norms, t-conorms, ordinal sum, ORDINAL SUMS, UNINORMS, NULLNORMS
  • Karadeniz Technical University Affiliated: Yes

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.