A note on the Sobol' indices and interactive criteria

Grabisch Michel; Labreuche Christophe

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A note on the Sobol' indices and interactive criteria

机译：A note on the Sobol' indices and interactive criteria

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The Choquet integral and the Owen extension (or multilinear extension) are the most popular tools in multicriteria decision making to take into account the interaction between criteria. It is known that the interaction transform and the Banzhaf interaction transform arise as the average total variation of the Choquet integral and multilinear extension respectively. We consider in this note another approach to define interaction, by using the Sobol' indices which are related to the analysis of variance of a multivariate model. We prove that the Sobol' indices of the multilinear extension give the square of the Fourier transform, a well-known concept in computer sciences. We also relate the latter to the Banzhaf interaction transform and compute the Sobol' indices for the 2-additive Choquet integral. (C) 2016 Elsevier B.V. All rights reserved.

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《Fuzzy sets and systems》 |2017年第15期|99-108|共10页
作者
Grabisch Michel; Labreuche Christophe;
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作者单位

Thales Res & Technol, 1 Ave Augustin Fresnel, F-91767 Palaiseau, France;

Univ Paris 01, Paris Sch Econ, 106-112 Bd Hop, F-75013 Paris, France;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
中图分类数学;
关键词
Capacity; Interaction index; Sobol' index; Multilinear extension; Fourier transform;

A note on the Sobol' indices and interactive criteria

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