The Relation Between F-partial Order and Distributivity Equation

AŞICI E., Mesiar R.

10th International Summer School on Aggregation Functions (AGOP), Olomouc, Czech Republic, 1 - 04 July 2019, vol.981, pp.106-114 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 981
  • Doi Number: 10.1007/978-3-030-19494-9_10
  • City: Olomouc
  • Country: Czech Republic
  • Page Numbers: pp.106-114
  • Karadeniz Technical University Affiliated: Yes


The notations of the order induced by triangular norms, null-norms and uninorms have been studied widely. Nullnorms have been produced from triangular norms and triangular conorms with a zero element in the interior of the unit interval. They have been proved to be useful in several fields like expert systems, neural networks, fuzzy quantifiers. Also, the distributivity equation has been studied involving different classes of aggregation functions from triangular norms and triangular conorms to nullnorms. So, the study of the distributive property becomes very interesting, since nullnorms have been used several fields. In this paper we investigate distributivity equation for nullnorms on the unit interval [0, 1] and we give sufficient condition for two nullnorms to be equivalent.