On Robustness And Learning Algorithm Of Fuzzy Neural Networks

Uncertainty exists widely in the subjective and objective world. In all kinds of uncertainty, fuzziness is one of the most important and fundamental kinds. Studying the uncertainty problem has been a hot research topic and an important leading problem. As the important tools of dealing with uncertain problem, fuzzy neural networks which have merits of artificial neural networks and fuzzy logic systems can simulate the biological structures and some functions of human brains and the characteristic of information processing. When constructing fuzzy neural network systems, pattern pairs of systems usually have uncertainty, But such perturbation of given pattern pairs probably makes various negative to follow processing and causes the fuzzy neural network systems which is established based on this uncertain pattern pairs to produce meaningless even destructive output. When the topology structure of the network is set, the learning algorithm of fuzzy neural network is the key to guarantee that it has good fault-tolerant, the sensitivity or robustness. So, it studies the following two sides in the paper.(1) Studied the influences and control of perturbations of training pattern pairs on FBAM, among it, firstly proposed a new concept for the robustness of fuzzy neural networks to perturbations of training pattern pairs and analyzed this kind of robustness of FBAM as a typical instance. The theoretical studies in the paper show that the FBAM using the Hebbian learning algorithm has good robustness, however the FBAM using another learning algorithm presented recently has poor robustness. So a method to control perturbations of pattern pairs is proposed to make such robustness of FBAM be good when the latter learning algorithm is employed. Finally, some theoretical results are also confirmed by the experiment on image processing. The work in the paper is of some benefit to the performance analyses, the choice of learning algorithm, and the guidance to pattern pair for FBAM.(2) Proposed an efficient general learning algorithm for a class of fuzzy Hopfield networks (Max-T FUZZY HNs) based on T-norms, among it, it takes fully advantages of the concomitant implication operator of T-norms and the convergence of fuzzy power matrix series in the paper, theoretical analyses obtains that for any given set of patterns, the leaning algorithm always can find the maximum of all connection weight matrices that can make the set become a set of the equilibrium points of the max-T FHOP when T is a left-continuous T-norm. This maximum matrix is idempotent matrix in sense of Max-T composition , with which the max-T FHOP...