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Migrativity of aggregation functions. (English) Zbl 1186.68459

Summary: We introduce a slight modification of the definition of migrativity for aggregation functions that allows useful characterization of this property. Among other things, in this context we prove that there are no \(t\)-conorms, uninorms or nullnorms that satisfy migrativity (with the product being the only migrative \(t\)-norm, as already shown by other authors) and that the only migrative idempotent aggregation function is the geometric mean. The \(k\)-Lipschitz migrative aggregation functions are also characterized and the product is shown to be the only 1-Lipschitz migrative aggregation function. Similarly, it is the only associative migrative aggregation function possessing a neutral element. Finally, the associativity and bisymmetry of migrative aggregation functions are discussed.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
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