• 论文 •

### 基于后件模糊集中心的Mamdani模糊系统的降维分解

1. 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
• 出版日期:2017-03-25 发布日期:2017-04-28

LI Xiaoping, ZHANG Deli. Lowering Dimension Decomposition of Mamdani Fuzzy System Based on Centers of Consequent Fuzzy Sets[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(3): 899-907.

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

LI Xiaoping1 ,ZHANG Deli2

1. 1. School of Management,Tianjin Normal University, Tianjin 300387; 2. Information Center, Jilin Provincial Institute of Education, Changchun 130022
• Online:2017-03-25 Published:2017-04-28

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.

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