On Lipschitz properties of generated aggregation functions
Data(s) |
01/05/2010
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Resumo |
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 <i>k</i>-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[.<br /> |
Identificador | |
Idioma(s) |
eng |
Publicador |
Elsevier |
Relação |
http://dro.deakin.edu.au/eserv/DU:30028315/beliakov-onlipschitzproperties-2009.pdf http://dro.deakin.edu.au/eserv/DU:30028315/beliakov-onlipschitzpropertiesof-2010.pdf http://dx.doi.org/10.1016/j.fss.2009.06.017 |
Direitos |
2009, Elsevier B.V. |
Palavras-Chave | #aggregation functions #generated aggregation functions #k-Lipschitz aggregation functions #triangular norms #quasi-arithmetic means #uninorms #nullnorms #stability |
Tipo |
Journal Article |