基于可能度的区间粗糙数排序方法

Method for Ranking Interval Rough Numbers Based on Possibility Degree

针对属性权重信息未知或属性权重信息不完全且属性值为区间粗糙数的多属性决策问题,给出一种基于可能度的区间粗糙数排序方法。首先引进和补充了区间粗糙数的一些运算法则及集成算子。然后首次给出了区间粗糙数的可能度定义公式,并研究了该公式所具有的一些良好性质,随后,建立了基于投影思想的极小-极大优化模型来确定各属性权重,同时给出基于可能度矩阵的区间粗糙数排序算法。最后通过实例说明该方法的有效性和可行性。

For multiple attribute decision making problems, in which the information on the attribute weights is unknown or incomplete and attribute values are interval rough numbers, a method of ranking interval rough numbers based on possibility degree is proposed. Firstly, some operational rules and aggregation operators are adduced and complemented for interval rough numbers. Secondly, a possibility degree formula for comparing two interval rough numbers is proposed, and some desirable properties for this formula are studied. Then, a minimax optimization model based on projection idea is established, and the attribute weights are derived by solving this model. Simultaneously, an algorithm to rank interval rough numbers based on the possibility degree matrix is presented. Finally, a numerical example is given to show the effectiveness and feasibility of the method.