基于可信性理论的模糊离差MADM模型研究

A Study on MADM Model of Fuzzy Deviation Based on Credibility Theory

针对属性值以模糊变量形式给出的特点,运用2004年基础数学领域完成的研究模糊现象数量规律的一个新的数学分支——可信性理论的原理,我们做了以下三点研究:(i)结合模糊变量之间的距离,定义模糊离差,构造了模糊属性值之间离差最大化的算子;(ii)得到了计算属性权重值的模糊规划期望值模型(EVM);(iii)考虑到属性的重要性程度不同,利用信息熵最大化原理,构造了具有平衡能力的权重计算模型,从而得到基于可信性理论的模糊离差多属性决策(FD-MADM)模型.最后结合实例进行分析和计算,显示该模型的可行性和有效性.

In view of the fuzzy variable attribute,three tasks were accomplished based on Credibility Theory,a new branch of basic mathematics founded in 2004 about fuzzy variable：（i） A fuzzy deviation maximum operator of fuzzy attribute was constructed by defining fuzzy deviation with distance between fuzzy variables;（ii） A fuzzy programming expected value model（EVM） of attribute weight was worked out;（iii） Considering the difference in the importance of attributes,the weight calculation model with balance was built by using maximum information entropy principle,and then the last fuzzy deviation multi-attribute decision making（FD-MADM） model was made.Finally,the feasibility and validity of the model was proved by analyzing and calculating example.