基于后件模糊集中心的Mamdani模糊系统的降维分解  

Lowering Dimension Decomposition of Mamdani Fuzzy System Based on Centers of Consequent Fuzzy Sets

作　　者：李晓萍[1] 张德利[2] 

机构地区：[1]天津师范大学管理学院,天津300387 [2]吉林省教育学院信息中心,长春130022

出　　处：《系统科学与数学》2017年第3期899-907,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61374009);吉林省自然科学基金(201215190)资助课题

摘　　要：模糊系统是通过模糊规则来处理不确定信息的一种重要工具,而Mamdani模糊系统则是最简单的一类高维系统模型.文章首先从理论上指出Mamdani模糊系统的传统分解存在错误,并分别针对二维和三维Mamdani模糊系统的实际分解公式进行了分析.其次,基于后件(输出)模糊集中心指标重新获得了n维Mamdani模糊系统的降维分解公式.最后,通过实例分析说明该分解公式不仅可以降低高维Mamdani模糊系统的空间维数,而且也可减少系统内部的模糊规则总数.A fuzzy system is a kind of important tool to deal with uncertain infor- mations through some fuzzy rules, Mamdani fuzzy system is one of the most simple high-dimensional system models. Firstly, this article points out that the traditional decomposition of Mamdani fuzzy system exists errors in theory, the actual dimension formulas of 2-dimensional and 3-dimensional Mamdani fuzzy systems are analyzed. And then, the lowering dimension decomposition formulas of n-dimensional systems based on the center indexs of the consequent fuzzy sets are obtained. Finally, an ex- ample is given to illustrate the decomposition formula not only can reduce the space＇sdimensions of a high-dimensional Mamdani fuzzy system, but also can reduce the total number of fuzzy rules within the fuzzy system.

关 键 词：后件模糊集中心 Mamdani模糊系统 降维分解 规则数 一致完备正规模糊集 

分 类 号：N941[自然科学总论—系统科学]