基于对称K-L距离及决策者主观偏好的混合属性决策方案客观权重确定方法

A Determination Method of Objective Weights for Mixed Attribute Decisions Based on Symmetric K-L Distances and Decision Makers'Subjective Preferences

为直接获得含有不确定信息的混合属性决策方案指标属性的客观权重,提出对称Kullback-Leibler(K-L)距离并考虑决策者对不确定数的确定项和不确定项设定偏好比例的方法.将混合型数据指标值统一转化为二元联系数,进而转化为二元组数,并进行规范化处理以使其在各属性下具有可比性.计算各个属性下各个方案指标之间的两两对称K-L距离.汇总各属性下的两两对称指标K-L距离的值作为其初始客观权重,并经归一化后得到各属性的客观权重.算例分析表明,该客观属性权重确定方法能够最大程度上减少信息的失真,且处理方法统一,原理简单,能够较好地解决含有不确定信息的客观属性权重的确定问题,同时也验证了决策者的主观偏好对客观权重的确定具有较大的影响.

The symmetric Kullback-Leibler(K-L)distance is adopted considering the preference ratios of decision makers(DM)for deterministic and uncertain terms of a uncertain number to directly determine the objective weights of mixed attribute decisions involving uncertain information.This approach first converts the indicators of mixed data into binary connection numbers and further divides them into two-tuple numbers.These converted numbers are normalized for comparison of various attributes.Then the symmetric K-L distances among indicators of each attribute are calculated.Moreover,the symmetric K-L distances of each attribute are summarized as the initial objective weight.It is normalized to obtain the final objective weight of each attribute.The numerical example shows that the proposed determination method of objective weights can minimize the information loss with unified processing and simple principles.Besides,it can effectively solve the problem of determining objective attribute weights containing uncertain information,which also verifies that the subjective preferences of DMs have a significant effect on the determination of objective weights.