Alternative approaches to obtain t-norms and t-conorms on bounded lattices


Aşıcı E. , Mesiar R.

IRANIAN JOURNAL OF FUZZY SYSTEMS, cilt.17, ss.121-138, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 17 Konu: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.22111/ijfs.2020.5410
  • Dergi Adı: IRANIAN JOURNAL OF FUZZY SYSTEMS
  • Sayfa Sayıları: ss.121-138

Özet

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for the clarity. Finally, we show that our construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on an arbitrary bounded lattice, respectively.