On the optimal consistent approximation to pairwise comparison matrices
نویسندگان
چکیده
منابع مشابه
On the Optimal Consistent Approximation to Pairwise Comparison Matrices
Consistency retrieval from a biased relative preference table is an imperative task in decision theory This paper considers the least squares approximation of a pairwise comparison matrix by consistent matrices It is observed that the highly nonlinear manifold of consistent matrices can be changed into a linear subspace by the component wise logarithmic transformation A rst order optimality con...
متن کاملA method for approximating pairwise comparison matrices by consistent matrices
In several methods of multiattribute decision making, pairwise comparison matrices are applied to derive implicit weights for a given set of decision alternatives. A class of the approaches is based on the approximation of the pairwise comparison matrix by a consistent matrix. In the paper this approximation problem is considered in the least-squares sense. In general, the problem is nonconvex ...
متن کاملOn optimal completions of incomplete pairwise comparison matrices
An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uni...
متن کاملOn optimal completion of incomplete pairwise comparison matrices
An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uni...
متن کاملAn Algorithm for the Optimal Consistent Approximation to a Pairwise Comparisons Matrix by Orthogonal Projections
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comaprisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. Orthogonal basis is introduced in the vector space. The orthogonal projection of the transformed matrix onto the space formed by the images of consistent matrices is ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)00329-7