A method of defuzzification based on the approach of areas' ratio

Abstract

The new method of defuzzification of output parameters from the base of fuzzy rules for a Mamdani fuzzy controller is given in the paper. The peculiarity of the method is the usage of the universal equation for the area computation of the geometric shapes. During the realization of fuzzy inference linguistic terms, the structure changes from the triangular into a trapezoidal shape. That is why the universal equation is used. The method is limited and can be used only for the triangular and trapezoidal membership functions. Gaussian functions can also be used while modifying the proposed method. Traditional defuzzification models such as Middle of Maxima − MoM, First of Maxima − FoM, Last of Maxima − LoM, First of Suppport − FoS, Last of Support − LoS, Middle of Support − MoS, Center of Sums − CoS, Model of Height − MoH have a number of systematic errors: curse of dimensionality, partition of unity condition and absence of additivity. The above-mentioned methods can be seen as Center of Gravity − CoG, which has the same errors. These errors lead to the fact that accuracy of fuzzy systems decreases, because during the training root mean square error increases. One of the reasons that provokes the errors is that some of the activated fuzzy rules are excluded from the fuzzy inference. It is also possible to increase the accuracy of the fuzzy system through properties of continuity. The proposed method guarantees fulfilling of the property of continuity, as the intersection point of the adjustment linguistic terms equals 0.5 when a parametrized membership function is used. The causes of errors and a way to delete them are reviewed in the paper. The proposed method excludes errors which are inherent to the traditional and non- traditional models of defuzzification. Comparative analysis of the proposed method of defuzzification with traditional and non-traditional models shows its effectiveness.