Multiple attribute group decision making (MAGDM) is a very active research field in management sciences. Many practical MAGDM problems are often characterized by ambiguity and uncertainty. The aim of this paper is to develop an integrated MAGDM method with unknown weight information under trapezoidal interval type-2 fuzzy environment based on the grey relational projection (GRP) method. Firstly, to determine the comprehensive weights of attributes, a novel method is proposed by combining the analytic hierarchy process (AHP) technique under trapezoidal interval type-2 fuzzy environment and inter-attribute coefficient method. Secondly, the traditional GRP method is extended to solve MAGDM problems under trapezoidal interval type-2 fuzzy environment, i.e., the optimial alternative should have the largest grey relational projection on the trapezoidal interval type-2 fuzzy positive ideal solution (TIT2-FPIS) and smallest grey relational projection on the trapezoidal interval type-2 fuzzy negative ideal solution (TIT2-FNIS) simultaneously. Finally, an emergency medical department selection problem is taken as an illustrative example to demonstrate the calculation process of the proposed method.
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