On Properties of Internal Uninorms on Bounded Lattices


ÇAYLI G. D.

10th International Summer School on Aggregation Functions (AGOP), Olomouc, Czech Republic, 1 - 04 July 2019, vol.981, pp.115-128 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 981
  • Doi Number: 10.1007/978-3-030-19494-9_11
  • City: Olomouc
  • Country: Czech Republic
  • Page Numbers: pp.115-128
  • Keywords: Bounded lattice, Internal uninorm, Neutral element, Uninorm, t-norm, t-conorm, IDEMPOTENT UNINORMS, ORDER

Abstract

In this paper, we study internal uninorms on bounded lattices. We show that an internal uninorm on a bounded lattice L for the chosen neutral element e is an element of L\{0, 1} does not always exist. We introduce two new construction methods for uninorms on a bounded lattice L based on the existence of a t-norm and a t-conorm, where some necessary and sufficient conditions on its neutral element e is an element of L\{0, 1} are required. These methods also show the existence of internal uninorms on some special bounded lattices.