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On Weakly Smooth Uninorms on Finite Chain
Author(s) -
Li Gang,
Liu HuaWen,
Fodor János
Publication year - 2015
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21694
Subject(s) - unary operation , chain (unit) , mathematics , class (philosophy) , product (mathematics) , pure mathematics , t norm , discrete mathematics , fuzzy logic , fuzzy set , computer science , artificial intelligence , geometry , physics , astronomy , fuzzy classification
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 .