区间概率条件下属性值为不确定语言变量的风险型多属性决策研究

针对区间概率条件下属性值为不确定语言信息且属性权重未知的风险型多属性决策问题,提出了一种基于概率理论和不确定语言变量的TOPSIS决策方法。首先建立了区间概率转化为点概率的数学模型,通过期望值将风险型决策矩阵转化为确定型矩阵;然后利用方案与理想解越近方案越优,与负理想解越远方案越优的原则建立属性权重确定模型,并利用TOPSIS方法的相对优属度大小确定方案的排序;最后通过应用案例说明了本方法的决策步骤。

A Study on Risk Multi-attribute Decision-making with Uncertain Linguistic Variables under the Condition of Interval Probability

An extended TOPSIS method based on the probability theory and uncertain linguistic variables is presented to solve the risk multiple attribute decision making problems with unknown weight and the attribute values take the form of uncertain linguistic variables under the interval probability.To begin with,the mathematical model is constructed by which interval probability can be transformed into the point probability,and the risk decision making matrix can be transformed into the certainty decision making matrix by expected value;then according to the rules that the closer the distance between the alternative and the positive ideal solution,the better the alternative is,and the further the distance between the alternative and the negative ideal solution,the better the alternative is,the model of the certain attribute weight is constructed;furthermore,according to the relative optimal membership degree of TOPSIS,the ranking order of alternatives is determined.Finally,an illustrate example is given to show the decision-making steps and the effectiveness of this method.