基于概率统计的模糊隶属函数计算研究

数学理论与应用 ›› 2016, Vol. 36 ›› Issue (3): 93-100.

基于概率统计的模糊隶属函数计算研究

马万元，耿秀丽

上海理工大学管理学院,上海,200093

出版日期:2016-09-30 发布日期:2020-09-28
基金资助:
国家自然科学基金项目(71301104);

高等学校博士学科点专项科研基金资助课题(20133120120002);

上海市教育委员会科研创新项目(14YZ088);

上海市一流学科项目(S1201YLXK);

沪江基金(A14006)

Research on the Fuzzy Membership Function Determination Based on Probability Statistics

Ma Wanyuan， Geng Xiuli

Business School,University of Shanghai for Science and Technology,Shanghai 200093,China

Online:2016-09-30 Published:2020-09-28

摘要/Abstract

摘要： 应用模糊数学方法解决实际问题的关键在于建立符合实际情况的隶属函数.常用计算模糊隶属函数的模糊统计法建立在大量调查数据和函数图形分析法的基础上,巨大的运算量和复杂的过程限制了模糊技术的实际应用.本文从统计学的角度提出了一种基于概率统计的模糊隶属函数计算方法,该方法相对简单并且能适应多种情况的隶属函数计算.最后通过实际算例对两种算法得到的隶属函数曲线进行了比对,验证了本文的方法具有较好的精度.

关键词: 模糊集, 隶属函数, 概率统计

Abstract: The key of using fuzzy mathematics to solve practical problems is to establish realistic membership function.The commonly used method to compute the fuzzy membership function is fuzzy statistic method, which relies on a large number of survey data and analysis on the function graph,and the calculation with heavy workload and complex process limits the practical application of fuzzy technology.A method for determining the fuzzy membership function based on probability statistics is proposed from the view of statistics.The proposed method is relatively simple and can adapt to much more cases of fuzzy membership function determination. Finally,a real world case is given and membership function curves derived from two methods are compared to verify the proposed method having higher accuracy.

Key words: Fuzzy set, Membership function, Probability statistics

马万元, 耿秀丽. 基于概率统计的模糊隶属函数计算研究[J]. 数学理论与应用, 2016, 36(3): 93-100.

Ma Wanyuan, Geng Xiuli. Research on the Fuzzy Membership Function Determination Based on Probability Statistics[J]. Mathematical Theory and Applications, 2016, 36(3): 93-100.