Reference : Symmetric approximations of pseudo-Boolean functions with applications to influence inde...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/122347
Symmetric approximations of pseudo-Boolean functions with applications to influence indexes
English
Marichal, Jean-Luc mailto [University of Luxembourg > Mathematics Research Unit > > Professor >]
Mathonet, Pierre mailto [University of Luxembourg > Mathematics research unit > > >]
2012
Applied Mathematics Letters
Elsevier
25
8
1121-1126
Yes (verified by ORBi)
International
0893-9659
[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.
University of Luxembourg Mathematics resaech unit
Internal project F1R-MTH-PUL-09MRDO of the University of Luxembourg
Researchers
http://hdl.handle.net/2268/122347
10.1016/j.aml.2012.02.017

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