On Properties of Internal Uninorms on Bounded Lattices
10th International Summer School on Aggregation Functions (AGOP), Olomouc, Czech Republic, 1 - 04 July 2019, vol.981, pp.115-128, (Full Text)
- 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
- Karadeniz Technical University Affiliated: Yes
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.