A generalization of the migrativity property of aggregation functions

作者：Bustince H^*; De Baets B; Fernandez J; Mesiar R; Montero J

来源：Information Sciences, 2012, 191: 76-85.

DOI：10.1016/j.ins.2011.12.019

• Aggregation function
• Migrativity
• Associativity
• Additive generator
• t-Norm
• Uninorm

This paper brings 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%26apos;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.

• 出版日期2012-5-15