Preference degree of triangular fuzzy numbers and its application to multi-attribute group decision making

Triangular fuzzy number (TFN) reflects the membership by the function, which can express decision maker's (DM's) information more accurately in the complex decision making problem. In complex multi-attribute group decision making (MAGDM), how to rank TFNs and get the best alternative from MAGDM are two important issues. Existing ranking methods of TFNs only consider the minimum value, the maximum value and the most likely value, which ignores the other possible values. To avoid the limitation, the preference degree of TFNs is defined combining the probability with possibility of TFN, which considers all the possible values in TFN. Then a preference degree based algorithm is designed to rank TFNs. Furthermore, the triangular fuzzy MAGDM is investigated. Considering the group consensus of DMs, the attitude-based individual consensus index of DM is defined and applied to determine DMs' weights. The attribute weights are obtained by the comprehensive utility ratings of alternatives with a control parameter. Thus, a new method is proposed to solve triangular fuzzy MAGDM problem. Finally, a public experience evaluation in new smart city is applied to illustrate the effectiveness of the proposed MAGDM method.