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On left and right uninorms on a finite chain. (English) Zbl 1045.03029
Summary: The main concern of this paper is to introduce and characterize the class of operators on a finite chain $$L$$ having the same properties as pseudosmooth uninorms but without commutativity. Moreover, in this case we only require the existence of a one-side neutral element. These operators are characterized as combinations of AND and OR operators of directed algebras (smooth t-norms and smooth t-conorms) and the case of pseudosmooth uninorms is retrieved for the commutative case.

##### MSC:
 03B52 Fuzzy logic; logic of vagueness 03E72 Theory of fuzzy sets, etc.
##### Keywords:
t-norm; t-conorm; uninorm; non-commutativity; smoothness; finite chain
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##### References:
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