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

ERTUĞRUL Ü. , KARAÇAL F. , MESIAR R.

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, cilt.30, sa.7, ss.807-817, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Konu: 7
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1002/int.21713
  • Dergi Adı: INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
  • Sayfa Sayıları: ss.807-817

Özet

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.