Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part I

Although there are some papers on using neural networks to solve fuzzy relation equations, they have some widespread problems. For example, the best learning rate cannot be decided easily and strict theoretic analyses on convergence of algorithms are not given due to the complexity in a given system. To overcome these problems, we present some novel neural algorithms in this paper. We first describe such algorithms for max-min operator networks, then we demonstrate these algorithms can also be extended to max-times operator network. Important results include some improved fuzzy δ rules, a convergence theorem and an equivalence theorem which reflects fuzzy theory and neural networks can reach the same goal by different routes. The fuzzy bidirectional associative memory network and its training algorithms are also discussed. All important theorems are well-proved and a simulation and a comparison result with Blanco and Pedrycz are reported.