A systematic approach to heterogeneous multiattribute group decision making

Heterogeneous multiattribute group decision making (MAGDM) problems which involve multi-granularity linguistic labels, fuzzy numbers, interval numbers and real numbers are very complex and important in practical applications of decision making theory. Hitherto, there exists no general theoretical inducement for solving such problems. The purpose of this paper is to develop a systematic methodology for solving the heterogeneous MAGDM problems by introducing the multiattribute ranking index based on the particular measure of closeness to the positive ideal solution (PIS) and using the weighted Minkowski distance to measure differences between each alternative and the PIS as well as the negative ideal solution (NIS). The proposed methodology is shown to have some advantages over the fuzzy TOPSIS. Validity and applicability of the methodology proposed in this paper is illustrated with a real example of the missile weapon system selection problem.