Ordinal Sum of Two Binary Operations Being a T-Norm on Bounded Lattice

Wu X., Zhang Q., Zhang X., Cayl G. D., Wang L.

IEEE TRANSACTIONS ON FUZZY SYSTEMS, vol.30, no.6, pp.1762-1772, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1109/tfuzz.2021.3066120
  • Journal Name: IEEE TRANSACTIONS ON FUZZY SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1762-1772
  • Keywords: Lattices, Petroleum, Proposals, Upper bound, Technological innovation, Set theory, Probabilistic logic, Incomparability, lattice, ordinal sum, triangular norm, TRIANGULAR NORMS, CONORMS, CONSTRUCTION, EXTENSIONS
  • Karadeniz Technical University Affiliated: Yes

Abstract

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm. Some necessary and sufficient conditions are presented in this article for ensuring that an ordinal sum on a bounded lattice of two binary operations is, in fact, a t-norm. In particular, the results presented here provide an answer to an open problem put forward by Ertugrul and Yesilyurt, ordinal sums of triangular norms on bounded lattices, Inf. Sci., vol. 517, (2020) 198-216.