An Extended LINMAP Method for Multi-Attribute Group Decision Making under Interval-Valued Intuitionistic Fuzzy Environment

The linear programming technique for multidimensional analysis of preference (LINMAP) is one of the well-known methods for multiple attribute group decision making (MAGDM). In this paper, we extend the LINMAP method to solve MAGDM problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision- makers is presented as interval-valued intuitionistic fuzzy decision matrices and the preference information about the alterna- tives is completely unknown. We introduce two definitions of distances between interval-valued intuitionistic fuzzy sets. To calculate the weights of attributes we develop a new linear programming model based on the group consistency and incon- sistency index defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers, the weighted distance of each alternative to the interval-valued intuitionistic fuzzy positive ideal solution can be calculated to determine the ranking order of all alternatives for the decision makers, and the ranking order of alternatives and the best alternative(s) for the group are generated by using the Borda's function.