کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
420835 683991 2008 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Approximations of Lovász extensions and their induced interaction index
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Approximations of Lovász extensions and their induced interaction index
چکیده انگلیسی

The Lovász extension of a pseudo-Boolean function f:{0,1}n→Rf:{0,1}n→R is defined on each simplex of the standard triangulation of [0,1]n[0,1]n as the unique affine function f^:[0,1]n→R that interpolates f   at the n+1n+1 vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses f  . In this paper we investigate the least squares approximation problem of an arbitrary Lovász extension f^ by Lovász extensions of (at most) a specified degree. We derive explicit expressions of these approximations. The corresponding approximation problem for pseudo-Boolean functions was investigated by Hammer and Holzman [Approximations of pseudo-Boolean functions; applications to game theory, Z. Oper. Res. 36(1) (1992) 3–21] and then solved explicitly by Grabisch et al. [Equivalent representations of set functions, Math. Oper. Res. 25(2) (2000) 157–178], giving rise to an alternative definition of Banzhaf interaction index. Similarly we introduce a new interaction index from approximations of f^ and we present some of its properties. It turns out that its corresponding power index identifies with the power index introduced by Grabisch and Labreuche [How to improve acts: an alternative representation of the importance of criteria in MCDM, Internat. J. Uncertain. Fuzziness Knowledge-Based Syst. 9(2) (2001) 145–157].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 156, Issue 1, 1 January 2008, Pages 11–24
نویسندگان
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