Reference : Symmetric approximations of pseudo-Boolean functions with applications to influence i...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/1459
Symmetric approximations of pseudo-Boolean functions with applications to influence indexes
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre mailto [University of Liège > Department of Mathematics]
Aug-2012
Applied Mathematics Letters
Pergamon Press - An Imprint of Elsevier Science
25
8
1121-1126
Yes (verified by ORBilu)
International
0893-9659
Oxford
United Kingdom
[en] Pseudo-Boolean function ; Least squares approximation ; Symmetric function ; Cooperative game theory ; System reliability ; System signature ; Cardinality index
[en] We introduce an index for measuring the influence of the $k$th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear combinations of order statistic functions. We give explicit expressions for both the index and the approximation and discuss some properties of the index. Finally, we show that this index subsumes the concept of system signature in engineering reliability and that of cardinality index in decision making.
Mathematics Research Unit
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/1459
10.1016/j.aml.2012.02.017
http://arxiv.org/abs/1004.2593

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