Symmetric approximations of pseudo-Boolean functions with applications to influence indexes
نویسندگان
چکیده
We consider the approximation problem of a pseudo-Boolean function by a symmetric pseudo-Boolean function in the sense of weighted least squares. We give explicit expressions for the approximation and provide interpretations and properties of its L-statistic representation. We also discuss applications of these expressions in cooperative game theory and engineering reliability.
منابع مشابه
Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified degree. We first observe that this property still holds if we consider approximations by pseudo-Boolean functions depending only on specified variables. We ...
متن کاملApproximations of pseudo-Boolean functions; applications to game theory
This paper studies the approximation of pseudo-Boolean functions by linear functions and more generally by functions of (at most) a specified degree. Here a pseudo-Boolean function means a real valued function defined on {0, 1} n, and its degree is that of the unique multilinear polynomial that expresses it; linear functions are those of degree at most one. The approximation consists in choosin...
متن کاملWeighted Banzhaf power and interaction indexes through weighted approximations of games
The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo-Boolean functions. Considerin...
متن کاملThe influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making
The power of players in a collective decision process is a central issue in game theory. For this reason, the concept of influence of players on a simple game has been introduced. More generally, the influence of variables on Boolean functions has been defined and studied. We extend this concept to pseudo-Boolean functions, thus making it possible to appraise the degree of influence of any coal...
متن کاملThreshold and Symmetric Functions over Bitmaps
Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (and, or, not). However, less is known about the application of bitmap indexes to more advanced queries. We want to extend the applicability of bitmap indexes. As a starting point, we consider symmetric Boolean...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 25 شماره
صفحات -
تاریخ انتشار 2012