Method for hybrid multiple attribute decision making based on the maximum deviation

With respect to the problem of hybrid multiple attribute decision-making with incomplete information on attribute weights to which the attribute values are given in terms of precision number, interval number and fuzzy numbers, a new method is proposed. Firstly, the three different forms of numbers are unified into the form of interval number. The operational laws of interval numbers and a formula of possibility degree for the comparison between interval numbers, and then define the concept of deviation degree between interval numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined is established. The uncertain weighting average (UWA) operator is utilized to aggregate the interval numbers decosion making information corresponding to each alternative, and the formula of possibility degree is utilized to construct a possibility degree matrix (or called complementary judgement matrix), and then the priority formula of complementary judgement matrix is utilized to rank the alternatives and select the most desirable one(s). Finally, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.