区间数决策矩阵规范化方法的性质分析  

Character Analysis of Standardization Methods of Decision Matrix with Intervals

作　　者：胡明礼[1,2] 范成贤[3] 史开泉[4] 

机构地区：[1]南京航空航天大学经济与管理学院,南京211106 [2]南京航空航天大学科学发展研究中心,南京211106 [3]山东大学电气工程学院,济南250061 [4]山东大学数学与系统科学学院,济南250100

出　　处：《计算机科学》2013年第10期203-207,共5页Computer Science

基　　金：国家自然科学基金(90924022;71171112);教育部人文社科基金项目(10YJC630084);中国博士后科学基金项目(2013M531356);中央高校基本科研业务费专项科研项目(NS2011018;NN2012016;NJ20130020)资助

摘　　要：区间数决策矩阵的规范化是区间数多属性决策的基础,规范化使得不同类型的属性值之间可以进行比较和计算。分析了现有规范化公式的优缺点,提出了区间数决策矩阵规范化函数应满足的性质;鉴于现有区间数决策矩阵规范化方法的局限性,采用极差变换的思想,给出区间数属性值的规范化公式,经过规范化之后,属性值均在区间[0,1]中,且不同方案在同一属性值下的序关系保持不变。从理论上证明了新的规范化公式具有单调性、平移不变性、差异比不变性、缩放不变性和区间稳定性等性质。最后,算例的结果验证了方法的可行性和有效性。Standardization of the decision matrix with interval numbers is the basis for interval multi-attribute decision-making. Standardization makes the different types of attribute values can be compared and calculated. The advantages and disadvantages of the existing standardization formula were analyzed. This paper presented several characters that standardization function should satisfy. According to limits of the existing method, a new formula was given based on the range transformation idea. After a standardized, the attribute values are in the range of [0,1], and the relation of dif-ferent projects under the same attribute remainis unchanged. It is proven that the new formula satisfies characters of monotone, translation invariance, difference ratio invariance, scaling invariance and stability properties of interval. Final- ly, an example was given to verify the feasibility and effectiveness of new method.

关 键 词：区间数 决策矩阵 规范化 性质 

分 类 号：N94[自然科学总论—系统科学]