基于效用函数的模糊数的比较与排序

对相同的模糊数进行比较,不同风险偏好的决策者,会得到不同的结论.效用函数是对风险偏好的度量,因此,模糊数的比较与排序的方法,一定要结合决策者的效用函数来构造.为此,根据效用函数定义了模糊效用函数,在此基础上定义了效用序.之后,证明效用序为全序,进一步利用结构元理论对效用序进行表述.根据效用函数反映风险偏好的程度,对效用序进行分类.这样,决策者对模糊数进行比较时,依据自身对风险偏好程度来选择效用序.

The Method of Comparison and Sequencing about Fuzzy Number Based on Utility Function

The decision-makers of different risk preferences will draw a different conclusion for the comparison of fuzzy numbers.Utility function is a measure of risk preference, therefore,the methods of fuzzy number comparison and sequencing must be made according to utility function of decision-maker so,the fuzzy utility function is defined according to utility function,on the basis of it the utility order is defined.and then,it is proved that the effective sequence is entire sequence,furthermore,utility sequence is expressed by using the theory of structured element,the utility sequence is classified according to the utility function how to reflect the risk preferences.In this way,when the fuzzy numbers are compared ,decision -maker choose the utility sequence according to the degree of risk preference.