正态模糊数型多属性决策模型及其应用  

Multi-Attribute Decision Making Model of Normal Fuzzy Number and Its Application

作　　者：桑广[1] 吴涛[1,2] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230601 [2]安徽大学计算智能与信号处理教育部重点实验室,安徽合肥230039

出　　处：《山西大学学报（自然科学版）》2013年第1期34-39,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家973计划(2007BC311003);国家自然科学基金(61073117);安徽大学创新团队(KJTD001B)

摘　　要：针对属性权重未知(完全未知或部分未知)且方案属性值、主观偏好值为正态模糊数型的多属性决策问题,基于规范化理想解和相似度提出一种决策方法.该方法首先给出模糊数的相似度、期望、方差等概念,基于相似度最大化建立并求解优化模型,得到各属性的最佳权重.然后从期望和方差的综合角度考虑求出决策方案的规范化理想解,进而求出各方案与规范化理想解之间的相似度大小,并据此对各方案进行排序.最后通过算例分析说明了该方法的可行性和实效性.Based on the standardized ideal solution and the similarity,it proposes a method for some multi- attribute decision making problems,where the information on the attribute weights is unknown （complete- ly or partly unknown）, and the attribute values and the subjective preference values are expressed in the form of normal fuzzy numbers. At first, the similarity between fuzzy numbers, the expected values and vari- ance of fuzzy numbers and other concepts are given, and an optimization model based on the maximization of the similarity is established and solved, from which the optimal weights are obtained. Then the standard- ized ideal solution is acquired. Based on the similarity between each scheme and the ideal solution, all schemes are ranked. Finally, an example analysis shows that the method is feasible and effective.

关 键 词：多属性决策 正态模糊数 相似度 期望 规范化理想解 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]