On the structure of the k-additive fuzzy measures

被引：15

作者：

Combarro, Elias F. ^{[2
]}

Miranda, Pedro ^{[1
]}

机构：

[1] Univ Complutense Madrid, Dept Stat & Operat Res, E-28040 Madrid, Spain

[2] Univ Oviedo, Ctr Artificial Intelligence, Gijon 33204, Spain

来源：

FUZZY SETS AND SYSTEMS | 2010年 / 161卷 / 17期

关键词：

Fuzzy measures; k-Additive measures; Vertices; MODEL;

D O I：

10.1016/j.fss.2010.03.016

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we present some results concerning the vertices of the set of fuzzy measures being at most k-additive. We provide an algorithm to compute them. We give some examples of the results obtained with this algorithm and give lower bounds on the number of vertices for the (n - 1)-additive case, proving that it grows much faster than the number of vertices of the general fuzzy measures. The results in the paper suggest that the structure of k-additive measures might be more complex than expected from their definition and, in particular, that they are more complex than general fuzzy measures. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2314 / 2327

页数：14

共 30 条

[11] A CLASS OF FUZZY MEASURES BASED ON TRIANGULAR NORMS - A GENERAL FRAMEWORK FOR THE COMBINATION OF UNCERTAIN-INFORMATION [J].

DUBOIS, D ;

PRADE, H .

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 1982, 8 (01) :43-61

[12] Alternative representations of discrete fuzzy measures for decision making [J].

Grabisch, M .

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 1997, 5 (05) :587-607

[13] k-order additive discrete fuzzy measures and their representation [J].

Grabisch, M .

FUZZY SETS AND SYSTEMS, 1997, 92 (02) :167-189

[14]

Grabisch M., 1996, P 6 INT C INF PROC M, P1345

[15] A SIMPLIFIED BARGAINING MODEL FOR THE NORMAL-PERSON COOPERATIVE GAME [J].

HARSANYI, JC .

INTERNATIONAL ECONOMIC REVIEW, 1963, 4 (02) :194-220

[16]

Holland J.H., 1992, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence

[17]

Karkishchenko AN, 1996, 1996 BIENNIAL CONFERENCE OF THE NORTH AMERICAN FUZZY INFORMATION PROCESSING SOCIETY - NAFIPS, P588, DOI 10.1109/NAFIPS.1996.534802

[18]

Korshunov A.D., 1981, Problemy Kibernetiki, V38, P5

[19] Monotone Boolean functions [J].

Korshunov, AD .

RUSSIAN MATHEMATICAL SURVEYS, 2003, 58 (05) :929-1001

[20] Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral [J].

Marichal, JL .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2004, 155 (03) :771-791

← 1 2 3 →