Evolving a linear programming technique for MAGDM problems with interval valued intuitionistic fuzzy information

It is believed that multi attribute decision making problem is an ill-defined and unstructured problem. This difficulty intensifies while considering the uncertainty of decision makers' information about the problem. In recent years, interval valued intuitionistic fuzzy sets (hereafter IVIFs) as a generalization of ordinal fuzzy sets, became a well-known and widely applied framework for dealing with uncertainty of decision making problems. However, the mathematical programming aspects of interval valued intuitionistic fuzzy sets besides their applications in decision making problems are neglected. To reinforce the mathematical programming approach in IVIF environment, an IVIF multi attribute group decision making problem is formulated as a linear programming model. Using a variable transformation and the notion of aggregation operators, the proposed model is transformed into an equivalent linear programming model solvable by common approaches. Application of the proposed method is represented in a group decision making problem and the results are compared with similar methods, proving the compatibility of the proposed method with previous ones. The solid and understandable logic with computational easiness are the main advantages of the proposed method. Solving interval valued intuitionistic fuzzy linear programming problems can be applied lucratively in other problems being formulated in this context.