Bases and Transforms of Set Functions

Grabisch, Michel

Bases and Transforms of Set Functions

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: 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.

Keywords: set function; capacity; basis; transform; Moebius transform; Choquet integral (search for similar items in EconPapers)
Date: 2016
New Economics Papers: this item is included in nep-gth and nep-hpe
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Published in S. Saminger-Platz and R. Mesiar. On Logical, Algebraic and Probabilistic Aspects of Fuzzy Set Theory, 2016, ⟨10.1007/978-3-319-28808-6_13⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-01302376

DOI: 10.1007/978-3-319-28808-6_13

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