基于正态分布区间数的概率测度及多属性决策

针对决策中采用均匀分布区间数描述模糊评价值的局限性,提出了应用正态分布区间数进行多属性决策的方法。分析了模糊数的可能性测度,通过概率分布特征量生成正态分布区间数,给出了基于正态分布区间数与一般模糊区间数的互换关系。由正态分布特性确定了正态分布区间数两个模糊算子,采用简化方法对模糊综合评判向量进行模糊集结。采用模糊随机仿真方法生成综合评估值,对统计结果采用模糊均值和方差的排序方法进行决策。实例计算表明了两种方法的有效性。

Probability measure of interval-number based on normal distribution and multi-attribute decision making

The uniform interval-number is limited for modeling the fuzzy evaluation values and weight coefficient,and the interval-number which obeys normal distribution is used in multi-attribute decision making.The probability measure of the fuzzy interval is analyzed,and the normal distribution interval-number is produced by distribution characters.The transform relationship between the intervalnumber of normal distribution and the normal interval-number is given.According to the normal distribution law,two fuzzy operators are designed,which are used to aggregate the fuzzy integrate evaluation vector.The integrate evaluation is also produced by fuzzy random simulation,so the average and variance of the samples are utilized to rank.The example's results show the two methods' validity.