基于扩散函数的内集-外集模型  

The Interior-outer-set Models Based on Diffusion Functions

作　　者：陈志芬[1] 黄崇福[1] 张俊香[1] 

机构地区：[1]北京师范大学资源学院

出　　处：《模糊系统与数学》2006年第1期42-48,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(40371002)

摘　　要：内集-外集模型用于计算小样本事件的可能性-概率分布(PPD),以表达概率估计的模糊性。基于分配函数的内集-外集模型存在三点不足:①论域步长的选取随意性太大;②PPD值在0.5到1之间无值;③信息过于集中,PPD值在很多区间值为0。本文从解决此三问题入手,对传统模型进行了改进。首先讨论了论域步长选取的合理性问题;其次引入扩散函数替换分配函数,同时解决了问题②和③;最后,仿真实验的结果显示,改进模型的估计比传统模型的估计更接近于真实分布。Interior-outer-set model can show the fuzziness of the probability by computing the possibility -probability distribution of small sample problems. However, it is not perfect, while based on distribution functions. Some deficiencies are arranged below： 1） the domain and the step length are chose arbitrarily; 2） an abrupt gradient descent in PPD from 0.5 to 1; 3） many PPDs are 0, because of the centralized information. In this paper, we first discussed how to choose the domain and the step length rationally. Then, we solved the last two deficiencies by building a model based on diffusion functions. Finally, from the simulation results, we proved that the improved model is more reasonable than the old one.

关 键 词：内集-外集模型 分配函数 扩散函数 

分 类 号：O158[理学—数学]