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A generalization of the migrativity property of aggregation functions. (English) Zbl 1248.62003

Summary: This paper gives a generalization of the migrativity property of aggregation functions, suggested in earlier work of some of the present authors by imposing the \(\alpha\)-migrativity property of Durante and Sarkoci for all values of \(\alpha\) instead of a single one. Replacing the algebraic product by an arbitrary aggregation function \(B\) naturally leads to the properties of \(\alpha\)-\(B\)-migrativity and \(B\)-migrativity. This generalization establishes a link between migrativity and a particular case of Aczel’s general associativity equation, already considered by Cutello and Montero as a recursive formula for aggregation. Following a basic investigation, emphasis is put on aggregation functions that can be represented in terms of an additive generator, more specifically, strict \(t\)-norms, strict \(t\)-conorms and representable uninorms.

MSC:

62A99 Foundational topics in statistics
62H99 Multivariate analysis
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