Some construction approaches for t-norms and t-conorms on bounded lattices

AŞICI E., Mesiar R.

Aequationes Mathematicae, vol.96, no.5, pp.955-979, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1007/s00010-022-00885-3
  • Journal Name: Aequationes Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.955-979
  • Keywords: T-norms, T-conorms, Bounded lattices, TRIANGULAR NORMS, ORDINAL SUMS, SEMIGROUPS
  • Karadeniz Technical University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.In this paper, we introduce some new ordinal sum constructions of t-norms and t-conorms on an appropriate bounded lattice. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar (Int J Intell Syst 30: 807–817, 2015) and Aşıcı, Mesiar (Int J General Syst 49: 143–160, 2020) as results. Also, for clarity we give some illustrative examples. Furthermore, we show that the new construction methods can be generalized by induction to a modified ordinal sum for t-norms and t-conorms on an appropriate bounded lattice, respectively.