Deriving consistent pairwise comparison matrices in decision making methodologies based on linear programming method
نویسندگان
چکیده
منابع مشابه
A 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 کاملDeriving weights from general pairwise comparison matrices
The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matric...
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This paper addresses the Cook and Kress method regarding the use of mathematical programming to derive weights from pairwise comparison ratio matrices. We note that the Cook and Kress formulation has the shortcoming that alternative optimal solutions may occur, which would lead to an infinite set of possible weights. This paper proposes to resolve the problem by formulating a Phase II optimizat...
متن کاملOn 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 کاملDeriving Weights from Pairwise Comparison Matrices: the Additive Case
The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the ar...
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ژورنال
عنوان ژورنال: Journal of Intelligent & Fuzzy Systems
سال: 2014
ISSN: 1064-1246
DOI: 10.3233/ifs-141164