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Cauchy-like functional equation based on a class of uninorms

Feng Qin — 2015

Kybernetika

Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting n -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that the unary...

Migrativity properties of 2-uninorms over semi-t-operators

Ying Li-Jun;  Qin Feng — 2022

Kybernetika

In this paper, we analyze and characterize all solutions about α -migrativity properties of the five subclasses of 2-uninorms, i. e. C k , C k 0 , C k 1 , C 1 0 , C 0 1 , over semi-t-operators. We give the sufficient and necessary conditions that make these α -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for G ∈ C k , the α -migrativity of G over a semi-t-operator F μ , ν is closely related to the α -section of F μ , ν or the ordinal sum representation of t-norm...

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