Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Approaches to consistency adjustment
Journal of Optimization Theory and Applications
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
A common framework for deriving preference values from pairwise comparison matrices
Computers and Operations Research
An exact global optimization method for deriving weights from pairwise comparison matrices
Journal of Global Optimization
A different perspective on a scale for pairwise comparisons
Transactions on computational collective intelligence I
Remarks on pairwise comparison numerical and non-numerical rankings
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
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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 and difficult to solve, since it may have several local optima. In the paper the classic logarithmic transformation is applied and the problem is transcribed into the form of a separable programming problem based on a univariate function with special properties. We give sufficient conditions of the convexity of the objective function over the feasible set. If such a sufficient condition holds, the global optimum of the original problem can be obtained by local search, as well. For the general case, we propose a branch-and-bound method. Computational experiments are also presented.