Linear programming method for multiattribute group decision making using IF sets

The purpose of this paper is to develop a linear programming methodology for solving multiattribute group decision making problems using intuitionistic fuzzy (IF) sets. In this methodology, IF sets are constructed to capture fuzziness in decision information and decision making process. The group consistency and inconsistency indices are defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers. An IF positive ideal solution (IFPIS) and weights which are unknown a priori are estimated using a new auxiliary linear programming model, which minimizes the group inconsistency index under some constraints. The distances of alternatives from the IFPIS are calculated to determine their ranking order. Moreover, some properties of the auxiliary linear programming model and other generalizations or specializations are discussed in detail. Validity and applicability of the proposed methodology are illustrated with the extended air-fighter selection problem and the doctoral student selection problem.