An exact global optimization method for deriving weights from pairwise comparison matrices
نویسندگان
چکیده
منابع مشابه
Deriving 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...
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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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We study properties of weight extraction methods for pairwise comparison matrices that minimize suitable measures of inconsistency, average error gravitymeasures, including one that leads to the geometric row means. The measures share essential global properties with the AHP inconsistency measure. By embedding the geometric mean in a larger class of methods we shed light on the choice between...
متن کاملDeriving fuzzy weights of criteria from inconsistent fuzzy comparison matrices by using goal programming method
In this paper, deriving the fuzzy weights of criteria from the fuzzy pair-wise comparison matrix with triangular fuzzy elements is investigated. In the proposed method we first use the ranking function to convert the triangular fuzzy data into crisp one. Then by using the goal programming method we derive the fuzzy weights of criteria. We propose two new methods, and it is shown that these meth...
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ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 2006
ISSN: 0925-5001,1573-2916
DOI: 10.1007/s10898-006-9073-5