The Research On Weights Of Interval Reciprocal Comparison Matrices

Since Analytic Hierarchy Process (AHP) was considered as a decision-making tool, it has been applied extensively in many areas, such as in decision-making, evaluation planning selection and so on. Due to the complexity involved in decision problems and the inherent subjective nature of human judgments. It is more natural and easier to express their strength of preference with interval number in some particular situations, as a result interval comparison matrices are generated. How to derive the weights from interval reciprocal comparison matrices is always an important research. This thesis mainly discusses the problems as follows:(1) The correct of reciprocal comparison matrices is researched. A method of revising reciprocal comparison matrices is proposed, based on the existing logical relation. The inconsistent reciprocal comparison matrices are not only adjusted by this method, but also retain the informations of the original reciprocal comparison matrices.(2) Obtaining weights from interval reciprocal comparison matrices is researched. Two logical relations with parameter between the elements and weights of the real reciprocal comparison matrices are extended to the interval reciprocal comparison matrices. Two methods for obtaining weights from consistent interval reciprocal comparison matrices and inconsistent interval reciprocal comparison matrices are proposed separately. The advantages and disadvantages are also analyed.(3) A simple and effective algorithm to obtain informations from the interval reciprocal comparison matrices is proposed in this thesis. From the algorithm every columns obtain all the infomations of the interval reciprocal comparison matrices, and the equivalent theorems are also proved theoretically. Based on the proposed algorithm, interval weights are obtained from the interval reciprocal comparison matrices, no matter whether the interval reciprocal comparison matrices are consistent or not.