# Convexity properties of a problem for approximating pairwise comparison matrices by consistent matrices

Fülöp, János
(2006)
*Convexity properties of a problem for approximating pairwise comparison matrices by consistent matrices.*
-.
MTA SZTAKI, Budapest.

## Abstract

In several methods of multiattribute decision making pairwise comparison matrices are applied to derive implicit weights for the 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, this problem is nonconvex and is difficult to solve since it may have several local optima. In this 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. This technique can also be useful in branch and bound methods for solving the nonconvex problem.

Item Type: | Monograph (-) |
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Uncontrolled Keywords: | pairwise comparison, matrix, consistent matrix, global optimization, branch and bound method |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Depositing User: | Eszter Nagy |

Date Deposited: | 11 Dec 2012 15:26 |

Last Modified: | 11 Dec 2012 15:26 |

URI: | http://eprints.sztaki.hu/id/eprint/4556 |

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