Triple-I FMP algorithm for double hierarchical fuzzy system based on manifold learning

As is well known, Zadeh presented the compositional rule of inference to discuss complex inference modes. After that other researchers also investigated this problem. However, the classic fuzzy control systems in the application often encounter the curse of dimensionality. To overcome these difficulties in the classic fuzzy control systems with high-dimensional input variables, the entire triple-I algorithm for double fuzzy control systems and manifold learning of dimensionality reduction will be discussed in this paper. Specifically, triple-I FMP algorithm is presented for double hierarchical fuzzy control system based on Guojun Wang's implication operator and its reversibility is proved. Using manifold learning, dimension reduction SNE algorithm is given for double-layer hierarchical fuzzy control systems to keep the distribution of peak possibly point, so as to minimize the control stability impact due to reducing dimension. Since any type of multi-layer fuzzy control system is regarded as multiple fusion of double-layer hierarchical fuzzy system, the proposed algorithms and their reversibility are universal.