Equivalent representations of set functions

被引：123

作者：

Grabisch, M

Marichal, JL

Roubens, M

机构：

[1] Univ Paris 06, LIP6, F-75015 Paris, France

[2] Univ Liege, FEGSS, Dept Management, B-4000 Liege, Belgium

[3] Univ Liege, Inst Math, B-4000 Liege, Belgium

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2000年 / 25卷 / 02期

关键词：

set function; pseudo-Boolean function; Mobius inversion formula; Shapley and Banzhaf values; interaction indices; game theory; multicriteria decision making;

D O I：

10.1287/moor.25.2.157.12225

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper introduces four alternative representations of a set function: the Mobius transformation, the co-Mobius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.

引用

页码：157 / 178

页数：22

共 24 条

[1]

Abramowitz M., 1970, HDB MATH FUNCTIONS F

[2]

Aumann R. J., 1974, Values of Non-Atomic Games

[3]

Banzhaf JF, 1965, Rutgers Law Review, V19, P317

[4] Interaction transform of set functions over a finite set [J].