中文摘要：

针对现有文献对区间粗糙数的数据分布形式处理欠缺以及排序方法存在不足的问题,首先结合实际对区间数的分布情况进行了更为切合实际的假设,提出了一种带参数的新型区间粗糙数;在此基础上研究了区间粗糙数的相关数学性质,并给出了区间粗糙数的期望、方差等度量指标,决策者可依据期望―方差对区间粗糙数进行排序和比较.然后对区间粗糙数的两两比较问题提出了基于随机变量分布的可能度面积法计算公式,并结合优势关系给出了基于区间粗糙数的多属性决策方法.最后通过实例验证了排序方法的可行性与有效性.

英文摘要：

Against existing literature having deficiencies in data distributed form of interval rough numbers and lacking of in sorting method,a more realistic assumption about the data distribution is given,that is the two stage of uniform distribution,and a new kind of parameterized interval rough numbers is proposed,this parameter can be used as probability measurement of data values in a given range.A range of related mathematical properties of interval rough numbers are studied based on it.The new calculation methods of expectation and variance are given as the measure metrics of interval rough numbers,decision-makers can compare and sort the interval rough numbers based on expectations-variance.Then against the pairwise comparison question,a formula of the area method for calculation possibility degree based on the distribution of the random variable is raised,through the plane coordinate to calculate two interval rough numbers＇ area is divided by linear y=x.The multiple attribute decision making sorting method based on interval rough numbers is given combining the dominance relation.Finally,an example about the location of logistics center is used to verify the feasibility and effectiveness of the proposed sorting method,then compared and analyzed with the existing interval rough number ranking method,the results are basically the same.This method has certain reference significance to the actual decision problems.