Aggregation-based extensions of fuzzy measures

被引：26

作者：

Kolesarova, Anna ^{[1
]}

Stupnanova, Andrea ^{[2
]}

Beganova, Juliana ^{[2
]}

机构：

[1] Slovak Univ Technol Bratislava, Inst Informat Engn Automat & Math, Bratislava 81237, Slovakia

[2] Slovak Univ Technol Bratislava, Fac Civil Engn, Bratislava 81368, Slovakia

来源：

FUZZY SETS AND SYSTEMS | 2012年 / 194卷

关键词：

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

D O I：

10.1016/j.fss.2011.11.003

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：1 / 14

页数：14

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