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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1109/tfuzz.2021.3066120
  • Title of Journal : IEEE TRANSACTIONS ON FUZZY SYSTEMS
  • 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

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.