Characterizing Ordinal Sum for t-norms and t-conorms on Bounded Lattices


ÇAYLI G. D.

10th Conference of the European-Society-for-Fuzzy-Logic-and-Technology (EUSFLAT) / 16th International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets (IWIFSGN), Warszawa, Poland, 11 - 15 September 2017, vol.641, pp.443-454 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 641
  • Doi Number: 10.1007/978-3-319-66830-7_40
  • City: Warszawa
  • Country: Poland
  • Page Numbers: pp.443-454

Abstract

The ordinal sum of triangular norms on the unit interval has been proposed to construct new triangular norms. However, considering general bounded lattices, the ordinal sum of triangular norms and conorms may not generate triangular norms and conorms. In this paper, we study and propose some new construction methods yielding triangular norms and conorms on general bounded lattices. Moreover, we generalize these construction methods by induction to a ordinal sum construction for triangular norms and conorms, applicable on any bounded lattice. And some illustrative examples are added for clarity.