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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Official URL: http://www.sciencedirect.com/science/article/pii/S0165011408004600

## 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 |
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Uncontrolled Keywords: | Aggregation functions; Migrativity; Associativity; Bisymmetry; T-norms; Uninorms; Nullnorms |

Subjects: | Sciences > Computer science > Artificial intelligence |

ID Code: | 16182 |

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Deposited On: | 11 Sep 2012 07:43 |

Last Modified: | 06 Feb 2014 10:39 |

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