منابع مشابه
Median hyperplanes in normed spaces
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In this survey we deal with the location of hyperplanes in n{ dimensional normed spaces, i.e., we present all known results and a unifying approach to the so-called median hyperplane problem in Minkowski spaces. We describe how to nd a hyperplane H minimizing the weighted sum f(H) of distances to a given, nite set of demand points. In robust statistics and operations research such an optimal hy...
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In this paper we will extend two known location problems from Euclidean n-space to all n-dimensional normed spaces, n¿ 2. Let X be a "nite set of weighted points whose a2ne hull is n-dimensional. Our "rst objective is to "nd a hyperplane minimizing (among all hyperplanes) the sum of weighted distances with respect to X. Such a hyperplane is called a median hyperplane with respect to X, and we w...
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In this paper we consider a problem of distance selection in the arrangement of hyperplanes induced by n given points. Given a set of n points in d-dimensional space and a number k, 1 k (n d ) , determine the hyperplane that is spanned by d points and at distance ranked by k from the origin. For the planar case we present an O(n log2 n) runtime algorithm using parametric search partly different...
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In this paper, the fuzzy scalar median (FSM) is proposed, defined by using ordering of fuzzy numbers based on fuzzy minimum and maximum operations defined by using the extension principle. Alternatively, the FSM is defined from the minimization of a fuzzy distance measure, and the equivalence of the two definitions is proven. Then, the fuzzy vector median (FVM) is proposed as an extension of ve...
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ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2001
ISSN: 0022-3239,1573-2878
DOI: 10.1023/a:1017551731021