基于理想解和熵的不确定语言多属性决策方法

In this paper, we study the multiple attribute decision making problems, in which the information about attribute weights is completely unknown and the attribute values and preference information on alternatives take the form of uncertain linguistic variables. We introduce the operational laws of uncertain linguistic variables and a formula of possibility degree for the comparison between uncertain linguistic variables, and then define the concept of deviation degree between uncertain linguistic variables. A new method of uncertain linguistic multiple attribute decision-making is presented. Applying the deviation of decision alternatives and ideal decision alternatives and the randomicity of attribute weight coefficients, a new mathematical programming model is established. The objective is to minimize the deviation of decision alternatives and ideal decision alternatives and to maximize the entropy of weights of each attribute. The optimal solution is the best attribute weight coefficients, which is solved by the Lagrange multiple method. And the exact and reliable decision results combining the subjectivity and the facts are obtained. Then we utilize the uncertain linguistic weighting average (ULWA) operator to aggregate the uncertain linguistic variables corresponding to each alternative, and utilize the formula of possibility degree to construct a possibility degree matrix (or called complementary judgement matrix), and then utilize the priority formula of complementary judgement matrix to rank the alternatives and select the most desirable one(s). Finally, an illustrative example is shown to highlight the procedure of the proposed algorithm at the end of this paper.