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- Title
On Weakly Smooth Uninorms on Finite Chain.
- Authors
Li, Gang; Liu, Hua‐Wen; Fodor, János
- Abstract
In this paper, we characterize all weakly smooth uninorms (i.e., uninorms with smooth underlying operators) defined on a finite chain. It is proved that any such uninorm is determined by three unary functions and vice versa. As a by-product, we obtain the characterizations of smooth t-norms, smooth t-conorms through additive generators and show that on a finite chain, there exists no counterpart of the class of uninorms continuous in ]0, 1[2.
- Subjects
SMOOTHNESS of functions; OPERATOR theory; FINITE differences; CONTINUOUS groups; UNARY algebras
- Publication
International Journal of Intelligent Systems, 2015, Vol 30, Issue 4, p421
- ISSN
0884-8173
- Publication type
Article
- DOI
10.1002/int.21694