Generalized convex combination of triangular norms on bounded lattices

KARAÇAL F., Nesibe Kesicioglu M., ERTUĞRUL Ü.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol.49, no.3, pp.277-301, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1080/03081079.2020.1730358
  • 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.277-301
  • Keywords: Triangular norm, triangular conorm, linear combination, convex combination, bounded lattice, ORDINAL SUMS, OPERATORS
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we introduce the notions of the linear and generalized convex combination (shortly, g-convex combination) for triangular norms on bounded lattices. We investigate the conditions for the g-convex combination to be a triangular norm again. We introduce a triangular norm defined on a bounded lattice of equivalence classes and investigate some basic properties of the introduced triangular norm.