模糊数学存在的问题及解决方法  

A problem in fuzzy mathematics and its solution method

作　　者：刘开第[1] 庞彦军[1] 周少玲[1] 

机构地区：[1]河北工程大学不确定信息研究所,河北邯郸056038

出　　处：《河北工程大学学报（自然科学版）》2011年第4期106-112,共7页Journal of Hebei University of Engineering:Natural Science Edition

基　　金：国家自然科学基金资助项目(60940036;60874116)

摘　　要：指出模糊数学的问题是没有计算,因为支撑模糊集合转换的不是数学计算而是基于"取大取小"和"If…then"型模糊逻辑的专家系统。解决模糊数学问题的途径是,不借用"取大取小"和"模糊逻辑"等辅助性支撑条件来实现模糊集合转换,而是直接研究基于隶属函数的"不确定性转换"。做法是,用构造隶属函数的方法确定目标在单指标下具有某种状态程度的不确定性,进而用隶属度向量表征目标在单指标下的不确定性状态,并把确定目标在多指标下的不确定状态具体化为实现"指标隶属度到目标隶属度转换"。从分析指标隶属度中包含对目标分类的冗余值入手,通过建立一系列定理、推论揭示隶属度转换的非线性转换机理,由此构建实现隶属度转换的非线性计算方法。A vital problem pointed out is that there is no computation in fuzzy mathematics. Fuzyy set transformation is based on ＂ max - rain＂ algorithm and ＂ if ... then＂ fuzzy logical expert system. In this paper, fuzzy set transformation is realized by membership function. First, membership function is proposed to determne the subject uncertainty under the condition of only one index. Then membership function is used to illusrate this uncertainty. Finally the transformation from index membership to object membership is used to determine uncertainty. By discussing reduntant value. It is show that membership transformation is nonlinear. Thus nonlinear algorithm is given.

关 键 词：模糊数学 隶属函数 隶属度转换 非线性 区分权滤波 

分 类 号：O159[理学—数学]