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2016
- handle: 10670/1.dm1b83
- hal: hal-01302376
- doi: 10.1007/978-3-319-28808-6_13
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info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-28808-6_13
info:eu-repo/semantics/OpenAccess
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Amusements Children--Recreation Games for children Pastimes Primitive games Recreations Games, Primitive Children's gamesCiter ce document
Michel Grabisch, « Bases and Transforms of Set Functions », Archive Ouverte d'INRAE, ID : 10.1007/978-3-319-28808-6_13
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The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic dual-ity between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral.