A note on the Sobol' indices and interactive criteria

Michel Grabisch and Christophe Labreuche ()
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Christophe Labreuche: Thales Research and Technology [Palaiseau] - THALES [France]

PSE-Ecole d'économie de Paris (Postprint) from HAL

Abstract: 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 gives 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.

Keywords: capacity; interaction index; Sobol' index; multilinear extension; Fourier transform (search for similar items in EconPapers)
Date: 2017-05
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03220838v1
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Published in Fuzzy Sets and Systems, 2017, 315, pp.99-108. ⟨10.1016/j.fss.2016.05.009⟩

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Related works:
Working Paper: A note on the Sobol' indices and interactive criteria (2017)
Working Paper: A note on the Sobol' indices and interactive criteria (2017)
Working Paper: A note on the Sobol' indices and interactive criteria (2016)
Working Paper: A note on the Sobol' indices and interactive criteria (2016)
Working Paper: A note on the Sobol' indices and interactive criteria (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-03220838

DOI: 10.1016/j.fss.2016.05.009

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