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

中文关键词  模糊规则库  奇异值分解(SVD)  凸包  约简

英文关键词  fuzzy rule set  SVD(singular value decomposition)  convex hull  reduction

中文摘要

      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.

英文摘要

      The singular value decomposition of the matrix Ω composed by the consequence rule is addressed. An approximate expression U^(k) Σ^(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 e ectively.