Abstract: A multi-attribute decision-making method based on cross-entropy and score function is presented for information environment is normal distribution interval number. The transformation approach between classical interval number and normal distribution interval number is introduced by [3σ]criterion, and concepts are proposed such as cross-entropy and entropy and relevant propositions. Based on the principle of minimizing the total discrimination information between every object and the positive ideal object, the formula of attribute weights is proposed by constructing non-linear programming model. This paper also studies the aggregating method and comparison method of normal distribution interval number, and proposes a new multi-attribute decision-making approach. The method is applied in multi-attribute decision-making and pattern recognition respectively, and the feasibility and facility of the proposed method are verified.

Key words: normal distribution interval number, multi-attribute decision-making, cross-entropy, score function, aggregating

摘要： 针对以正态分布区间数为信息环境的多属性决策问题，提出了一种基于交叉熵和得分函数的决策方法。给出利用[3σ]原则将一般区间数转化为正态分布区间数的方法，提出正态分布区间数的交叉熵，熵等概念及相关性质。基于各对象与正理想对象的总区别信息最小化准则，通过建立非线性规划模型求解出了属性权重的公式，研究了正态分布区间数的集结方法和比较方法，给出了一种新的多属性决策途径。分别将所提方法应用于多属性决策和模式识别中，验证了该方法的可行性和简易性。

关键词: 正态分布区间数, 多属性决策, 交叉熵, 得分函数, 集结