An extended LINMAP method for MAGDM under linguistic hesitant fuzzy environment

The linear programming technique for multidimensional analysis of preference (LINMAP) is a representative decision making method with respect to preference information for given alternatives. In the classical LINMAP method, all of the decision data is known precisely or is given as crisp values. It cannot be used to solve the MAGDM problems under the linguistic hesitant fuzzy environment. In this paper, an extended LINMAP method is proposed to solve the MAGDM problems in which all the attribute values of alternatives and the truth degrees of all pair-wise alternatives' comparisons are in the form of linguistic hesitant fuzzy sets (LHFSs). In this method, a formula is first presented to calculate the similarity coefficient for the LHFS. On the basis of this, the weight of each expert with respect to each attribute is determined using the support function of the power average (PA) operator. Meanwhile, the collective consistency and inconsistency measurements are introduced to depict the incomplete pair-wise comparison preference relations on alternatives provided by the experts. Then, a linear programming model is constructed to determine the optimal weights of attributes. Furthermore, by calculating the comprehensive ranking values, the ranking of alternatives can be determined. Finally, a numerical example is used to illustrate the use of the proposed method.