摘要
以GM(1,1)模型为代表的灰色预测模型是以精确数序列为基础,难以满足实际需要.为了使灰色模型适应于模糊数序列,具体给出了一种基于三角模糊数序列的建模方法,这种方法也可以实现对二元区间模糊数和梯形模糊数序列的建模.首先由三角模糊数序列得出三个含有等量信息的精确数序列:重心序列、隶属函数的覆盖面积序列和中界点序列,对这三个序列分别建模后,再导出原始三角模糊数序列的三个界点的预测模型.这种建模方法既保持了模糊数的整体性又提高了建模序列的光滑度,提高了预测精度.最后进行了多组随机三角模糊数序列的数据模拟,验证了模型的有效性.
Grey prediction models have been established based on real numbers. In order to generalize them to be suitable for fuzzy numbers, an approach for the building of grey prediction model based on triangular fuzzy numbers is studied in the paper. This approach can be generalized to build grey models based on other interval fuzzy numbers. Three real number series are derived from the triangular fuzzy number series. They contain the equivalent information as the triangular fuzzy number series and keep the integrity of fuzzy numbers. Grey models （GM （1, 1）） are built based on the three series firstly. From the results of them, the prediction model of the triangular fuzzy number series is deduced. Three numerical examples are presented to show the effectiveness of the proposed model.
出处
《数学的实践与认识》
CSCD
北大核心
2012年第19期107-112,共6页
Mathematics in Practice and Theory
基金
国家自然科学基金(11071178
11162004)
教育部人文社会科学规划基金(11YJAZH131)
关键词
三角模糊数
GM(1
1)
重心
隶属函数
中界点
triangular fuzzy numbers
GM （1, 1）, gravity center
cover area of membership function
mid boundary point
