Fuzzy inference neural networks with fuzzy parameters

This paper concerns fuzzy neural networks and fuzzy inference neural networks, which are two different approaches to neuro-fuzzy combinations. The former is a direct fuzzification of artificial neural networks by introducing fuzzy signals and fuzzy weights. The latter is a representation of fuzzy systems in the form of multi-layer connectionist networks, similar to neural networks. Parameters of membership functions (centers and widths) play the role of neural network weights. In this paper, fuzzy inference neural networks with fuzzy parameters are considered. Neuro-fuzzy systems of this kind utilize both approaches: fuzzy neural networks and fuzzy inference neural networks. They also pertain to fuzzy systems of type 2 since membership functions with fuzzy parameters characterize type 2 fuzzy sets. Various architectures of these networks have been obtained for fuzzy systems based on different fuzzy implications. By analogy with fuzzy inference neural networks with crisp parameters, methods of learning fuzzy parameters and rule generation can be derived for neuro-fuzzy systems with fuzzy parameters. Fuzzy inference neural networks are studied in the framework of fuzzy granulation. In particular, fuzzy clustering as fuzzy information granulation is proposed to be applied in order to generate fuzzy IF-THEN rules. Applications of fuzzy inference neural networks are also outlined.