Bases and Transforms of Set Functions
نویسنده
چکیده
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 duality 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.
منابع مشابه
Solution of Harmonic Problems with Weak Singularities Using Equilibrated Basis Functions in Finite Element Method
In this paper, Equilibrated Singular Basis Functions (EqSBFs) are implemented in the framework of the Finite Element Method (FEM), which can approximately satisfy the harmonic PDE in homogeneous and heterogeneous media. EqSBFs are able to automatically reproduce the terms consistent with the singularity order in the vicinity of the singular point. The newly made bases are used as the compliment...
متن کاملApplication of some integral transforms and multiple hypergeometric functions in modeling randomly weighted average of some random variables
This article has no abstract.
متن کاملFekete-Szegö coefficient functional for transforms of universally prestarlike functions
Universally prestarlike functions of order $alphaleq 1$ in the slit domain $Lambda=mathbb{C}setminus [1,infty)$ have been recently introduced by S. Ruscheweyh.This notion generalizes the corresponding one for functions in the unit disk $Delta$ (and other circular domains in $mathbb{C}$). In this paper, we obtain the Fekete-Szegö coefficient functional for transforms of such f...
متن کاملAutoconvolution equations and generalized Mittag-Leffler functions
This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...
متن کامل