基于后件模糊集中心的Mamdani模糊系统的降维分解

李晓萍,张德利

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (3) : 899-907.

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系统科学与数学 ›› 2017, Vol. 37 ›› Issue (3) : 899-907. DOI: 10.12341/jssms13112
论文

基于后件模糊集中心的Mamdani模糊系统的降维分解

    李晓萍1,张德利2
作者信息 +

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

    LI Xiaoping1 ,ZHANG Deli2
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文章历史 +

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.

Abstract

A fuzzy system is a kind of important tool to deal with uncertain informations 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 example is given to illustrate the decomposition formula not only can reduce the space's dimensions 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.

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李晓萍 , 张德利. 基于后件模糊集中心的Mamdani模糊系统的降维分解. 系统科学与数学, 2017, 37(3): 899-907. https://doi.org/10.12341/jssms13112
LI Xiaoping , ZHANG Deli. Lowering Dimension Decomposition of Mamdani Fuzzy System Based on Centers of Consequent Fuzzy Sets. Journal of Systems Science and Mathematical Sciences, 2017, 37(3): 899-907 https://doi.org/10.12341/jssms13112
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