A Modified TOPSIS Method for Obtaining the Associated Weights of the OWA-Type Operators

AbstractThe ordered weighted averaging OWA operator proposed by Yager and its some extensions have been extensively utilized to perform the mean-type aggregation of individual preference relations in group decision making. An important issue in the theory of the OWA-type operators is the determination of the associated weights. In the present paper, the technique for order preference by similarity to ideal solution is modified to propose a new method for generating the associated weights under the environment of a group of additive reciprocal matrices. First, a consistent additive reciprocal matrix is obtained from each additive reciprocal matrix. It is further used to generate an ideal additive reciprocal matrix by using the arithmetic averaging operator. Then, a similarity degree between every additive reciprocal matrix and the ideal one is defined. Based on the similarity degree, the associated weights are determined by making use of an exponential function and they show that more importance is given to that with more similarity degree. Finally, a numerical example is carried out to illustrate the given method.