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It is well known that the main tool for finding dependencies among data is the linear regression model, which expresses one or several variables in term of a linear combination of the others. Linear regression is based on the least square principle, and has been studied at length, its statistical performance are well known. In real situations however, the… (More)

Until now, decision under uncertainty and multicriteria decision making have been investigated separately and almost independently, although there is a close link between both fields. Decision theory is also closely related to measurement theory. Besides, it is well known that additive representations in decision making are not sufficient to avoid paradoxes… (More)

- MlCHEL GRABISCH
- 2007

We present a survey of various approaches for the refinement of the Sugeno integral, based on the lexicographic order or the principle of discarding common values between acts. We try to relate these different approaches and compare their merits.

It is a very natural process for the mind to order objects of a set. To achieve this, we intuitively assign values (they can be real values, qualitative values like "good", "bad" or more generally lattice values) that are easy to handle and to compare. The general theory for this is measurement theory that aims to give general conditions on the set X of… (More)

- Fabien Lange, MlCHEL GRABISCH
- 2007 5th International Symposium on Intelligent…
- 2007

We propose a new axiomatization of the Shapley value for cooperative games, where symmetry and efficiency can be discarded and replaced with new natural axioms. From any game, an excluded-player game is built by discarding all coalitions that contain a fixed player. Then it is shown that the Shapley value is the unique value satisfying the linearity axiom,… (More)

- MlCHEL GRABISCH
- 2009

Nota: this compilation of various results has been intended primarily for my personal use, hence its very rough form. It is just a quick reference compilation of results. It is far to be complete, and does not intend to be so especially for references, and I update it from time to time. All comments, discovered mistakes, etc. are welcome. Please be kind… (More)

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital… (More)

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