Compensation for the Error of Narrowing the Defuzzification Range by the Areas’ Ratio Method

The purpose of research is to examine the hypothesis that the area ratio method can be used to compensate for the defuzzification interval narrowing error inherent in traditional models, such as center of gravity sums, height models, first maxima, mean maxima, and last maxima.

Methods. A fuzzy model consisting of two input variables and one output variable was used to analyze the properties of the area ratio method. The input variables had two triangular membership functions each, and the output variable had three triangular membership functions. The knowledge base consisted of four fuzzy rules. Zadeh's compositional rule was used as an implication model. Two models of classical center of gravity and a model based on the area ratio method were used in the defuzzification process.

Results. In the course of experimental studies, it was found that the proposed defuzzifier based on the area ratio method compensates the error of narrowing the defuzzification interval. It was also found during the experimental studies that when using the center-of-gravity model, a resultant surface that only 50% overlaps with the caliper of the output variable is formed at the output, which forms the error of defuzzification interval narrowing. When the area ratio method is used, the resulting surface overlaps 100% with the output variable caliper, suggesting that the area ratio method eliminates the error associated with defuzzification interval narrowing.

Conclusion. This article presents a fuzzy MISO model that is used to analyze the properties of the area ratio method. A distinctive feature of the proposed model is the use of the area ratio method in defuzzification. Analysis of its simulation process has shown that this method allows to compensate the error of defuzzification interval narrowing. 

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