%0 Journal Article
%T Deriving Weights of Criteria from Inconsistent Fuzzy Comparison Matrices by Using the Nearest Weighted Interval Approximation
%A Mohammad Izadikhah
%J Advances in Operations Research
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/574710
%X Deriving the weights of criteria from the pairwise comparison matrix with fuzzy elements is investigated. In the proposed method we first convert each element of the fuzzy comparison matrix into the nearest weighted interval approximation one. Then by using the goal programming method we derive the weights of criteria. The presented method is able to find weights of fuzzy pairwise comparison matrices in any form. We compare the results of the presented method with some of the existing methods. The approach is illustrated by some numerical examples. 1. Introduction Weight estimation technique in multiple criteria decision making (MADM) problem has been extensively applied in many areas such as selection, evaluation, planning and development, decision making, and forecasting [1]. The conventional MADM requires exact judgments. In the process of multiple criteria decision making, a decision maker sometimes uses a fuzzy preference relation to express his/her uncertain preference information due to the complexity and uncertainty of real-life decision making problem and the time pressure, lack of knowledge, and the decision maker¡¯s limited expertise about problem domain. The priority weights derived from a fuzzy preference relation can also be used as the weights of criteria or used to rank the given alternatives. Xu and Da [2] utilized the fuzzy preference relation to rank a collection of interval numbers. Fan et al. [3] studied the multiple attribute decision-making problem in which the decision maker provides his/her preference information over alternatives with fuzzy preference relation. They first established an optimization model to derive the attribute weights and then to select the most desirable alternative(s). Xu and Da [4] developed an approach to improving consistency of fuzzy preference relation and gave a practical iterative algorithm to derive a modified fuzzy preference relation with acceptable consistency. Xu and Da [5] proposed a least deviation method to obtain a priority vector from a fuzzy preference relation. Determining criteria weights is a central problem in MCDM. Weights are used to express the relative importance of criteria in MCDM. When the decision maker is unable to rank the alternatives holistically and directly with respect to a criterion, pairwise comparisons are often used as intermediate decision support. In the other words, in evaluating competing alternatives under a given criterion, it is natural to use the framework of pairwise comparisons represented by a square matrix from which a set of preference values for the
%U http://www.hindawi.com/journals/aor/2012/574710/