Modified Ordinal Sums of Triangular Norms and Triangular Conorms on Bounded Lattices

ERTUĞRUL Ü., KARAÇAL F., MESIAR R.

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, vol.30, no.7, pp.807-817, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 7
  • Publication Date: 2015
  • Doi Number: 10.1002/int.21713
  • Journal Name: INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.807-817
  • Karadeniz Technical University Affiliated: Yes

Abstract

Having in mind that ordinal sum construction of triangular norms (triangular conorms) may not work on bounded lattices, in general, we propose a modification of ordinal sums of t-norms (t-conorms) resulting to a t-norm (t-conorm) on an arbitrary bounded lattice. In particular, our method can be applied to define connectives for fuzzy sets type 2, interval-valued fuzzy sets, intuitionistic fuzzy sets, etc. Some illustrative examples are added, considering the interval lattice L([0, 1]), the intuitionistic lattice LI, and the diamond lattice.