Aggregation-based extensions of fuzzy measures

作者：Kolesarova Anna^*; Stupnanova Andrea; Beganova Juliana

来源：Fuzzy Sets and Systems, 2012, 194: 1-14.

DOI：10.1016/j.fss.2011.11.003

• Aggregation function
• Choquet integral
• Fuzzy measure
• Utility function
• Quasi-copula
• Copula
• n-monotone function

We present a method extending fuzzy measures on N = {1, ... , n} (represented as Boolean utility functions) to n-ary aggregation functions (utility functions) by means of a suitable n-ary aggregation function and the Mobius transform of the considered fuzzy measure. The method generalizes the well-known Lovasz and Owen extensions of nondecreasing pseudo-Boolean functions linked to fuzzy measures. All n-ary aggregation functions suitable for the proposed construction are completely characterized, including. among others, all n-ary copulas. Associative extended aggregation functions applicable in the case of an arbitrary arity are also completely characterized.

• 出版日期2012-5-1
• 单位中国人民解放军信息工程大学