利用凸包和SVD技术降低模糊系统复杂性  

Complexity reduction of fuzzy system using SVD and convex hull

作　　者：刘斌[1,2] 曹卉宇[1] 何建敏[1] 

机构地区：[1]东南大学经济管理学院,江苏南京210096 [2]南京工业大学信息科学与工程学院,江苏南京210009

出　　处：《控制理论与应用》2008年第5期887-890,897,共5页Control Theory & Applications

基　　金：国家自然科学基金资助项目(70371035).

摘　　要：对模糊规则库后件矩阵Ω进行奇异值分解,根据给定的阈值适当舍弃奇异值,得到矩阵Ω的近似表示U(k)Σ(k)(V(k))T,对U(k)和V(k)进行标准和(SN)处理,并利用凸包技术进行非负性(NN)和正态性(NO)处理,利用处理后的U(k),Σ(k)和V(k)生成新规则库的前件隶属函数和后件矩阵,重新构造规则库,新规则库的功能与原规则库近似,但规则总数显著减少.仿真结果表明该方法能够有效降低模糊系统的复杂性.The singular value decomposition of the matrix Ω composed by the consequence rule is addressed. An approximate expression U^（k）∑^（k）（V（k））^T of Ω is derived by discarding some singular values based on the given threshold. By applying the technology of convex hull to U^（k） and V^（k） for processing the sum normalization （SN）, the non-negativeness （NN） and the normality （NO）, we rebuild the rule set from the changed singular-value matrix and the corresponding eigenvectors, producing the consequence matrix and the antecedent membership functions for the new rule set. Generally, the function of the new rule set is similar to that of the old one, but the total number of rules is reduced. Finally, the simulation result indicates that the presented method can reduce the complexity of fuzzy system effectively.

关 键 词：模糊规则库 奇异值分解(SVD) 凸包 约简 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]