A Multiple Attribute Decision-Making Approach for Integrating Subjective and Objective Information

The fuzzy multiple attribute decision-making (MADM) problem with fuzzy preference information is investigated.An integrated eigenvector method is proposed to combine the subjective preference information with the objective information.The subjective preference information is expressed by a fuzzy preference complementary matrix of the decision alternatives and a pairwise comparison reciprocal matrix of the weights of attributes,and the objective information is expressed by a objective decision matrix.A least-square deviation estimation method is proposed to solve the multiple attribute decision-making problems.The quadratic programming model is constructed to determine the weight vector of the attributes and to rank the alternatives.Finally,a numerical example is presented to illustrate the usefulness of the proposed method.