On Weakly Smooth Uninorms on Finite Chain |
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| Authors: | Gang Li Hua‐Wen Liu János Fodor |
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| Affiliation: | 1. School of Mathematics, Shandong University, Ji'nan, Shandong, People's Republic of China;2. Faculty of Science, Qilu University of Technology, Ji'nan, Shandong, People's Republic of China |
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| 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. |
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