Construction methods for interval-valued t-norms on bounded lattices

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KARACAİR K., ERTUĞRUL Ü., KARAÇAL F., Qiao J.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.45, no.6, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 6
  • Publication Date: 2026
  • Doi Number: 10.1007/s40314-026-03641-4
  • Journal Name: COMPUTATIONAL & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, zbMATH
  • Keywords: Bounded lattices, Down-sets, Interval-valued t-conorms, Interval-valued t-norms, Up-sets
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, some construction methods for interval-valued t-norms (t-conorms) based on a down-set or an upset are presented. It is worth noting that the new construction methods do not have to be t-representable, which is a significant difference between the construction methods proposed in this paper and the commonly used construction methods of interval-valued t-norms (t-conorms) on other truth values sets. Some illustrative examples and remarks are also included to clarify the methods.