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On Lipschitz properties of generated aggregation functions
journal contributionposted on 2010-05-01, 00:00 authored by Gleb BeliakovGleb Beliakov, T Calvo, Simon JamesSimon James
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[.
JournalFuzzy sets and systems
Pagination1437 - 1447
NotesReproduced with the specific permission of the copyright owner.
Publication classificationC1 Refereed article in a scholarly journal; C Journal article
Copyright notice2009, Elsevier B.V.
aggregation functionsgenerated aggregation functionsk-Lipschitz aggregation functionstriangular normsquasi-arithmetic meansuninormsnullnormsstabilityScience & TechnologyTechnologyPhysical SciencesComputer Science, Theory & MethodsMathematics, AppliedStatistics & ProbabilityComputer ScienceMathematicsOPERATORSArtificial Intelligence and Image Processing