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On Lipschitz properties of generated aggregation functions

Authors :
Beliakov, Gleb
Calvo, Tomasa
James, Simon
Beliakov, Gleb
Calvo, Tomasa
James, Simon
Publication Year :
2010

Abstract

This article discusses Lipschitz properties of generated aggregation functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provide verifiable sufficient conditions to determine when a generated aggregation function holds the k-Lipschitz property, and calculate the Lipschitz constants of power means. We also establish sufficient conditions which guarantee that a generated aggregation function is not Lipschitz. We found the only 1-Lipschitz generated function with a neutral element e ∈]0, 1[.

Details

Database :
OAIster
Notes :
11 p., English
Publication Type :
Electronic Resource
Accession number :
edsoai.ocn945707836
Document Type :
Electronic Resource