Approximate realization of fuzzy mappings by regression models, neural networks and rule-based systems

We discuss the approximate realization of fuzzy mappings by fuzzy regression models, fuzzy neural networks, and fuzzy rule-based systems. These mathematical models are used as approximators of fuzzy mappings from fuzzy input vectors to fuzzy outputs (i.e., fuzzy numbers). First, we explain fuzzy regression models, which are extensions of linear regression models to the case of fuzzy inputs, fuzzy coefficients and fuzzy outputs. Next, we explain fuzzified neural networks where inputs, connection weights, biases and targets are fuzzy numbers. Then we explain the approximate realization of fuzzy mappings by fuzzy rule-based systems. We modify the simplified fuzzy reasoning method used in many fuzzy controllers in order to infer a fuzzy output (i.e., fuzzy number) from fuzzy if-then rules.