Fuzzy system modeling

While constructing a system model to find out input/ output relation, fuzzy functions (FF) method use Fuzzy c- means (FCM) algorithm to determine membership values. Instead of determining fuzzy rule bases (FRB) for each cluster, by using FF method each cluster is explained by functions. Proposed FF approach says that membership values and their user defined transformations should be add into the input matrices as independent variable with the real inputs. This suggestion is heuristic. In this study, we defined Fuzzy Normal Equations (FNE). Our proposed fuzzy normal equations explain the detail of how to add various transformations of membership values into the input matrices in fuzzy functions approach. We have modelled two real life data sets. One of them is Concrete Compressive Strength and the other one is Apple's Closing Stock Price data set. Fuzzy model performances compared with two benchmark strategies: Artificial neural networks (ANN) and adaptive neuro fuzzy systems (ANFIS).