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Migrativity of aggregation functions.

Bustince, H. and Montero de Juan, Francisco Javier and Mesiar, R. (2009) Migrativity of aggregation functions. Fuzzy Sets and Systems, 160 (6). pp. 799-777. ISSN 0165-0114

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Aggregation functions; Migrativity; Associativity; Bisymmetry; T-norms; Uninorms; Nullnorms
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:16182
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