Proposing two defuzzification methods based on output fuzzy set weights

Abstract

Defuzzification converts the final fuzzy output set of fuzzy controller and fuzzy inference systems to a significant crisp value. However, there are various mathematical methods for defuzzification, but there is not any certain systematic method for choosing the best strategy. In this paper, first we explain the structure of a fuzzy inference system and then after a short review of defuzzification criteria and properties, the main classification groups of most widely used defuzzification methods are presented. In the following after discussing some existing techniques, two new defuzzification methods are proposed by presenting their general performance and computational formulas. However, the principle of these two methods is using weights associated with output fuzzy set like WFM or QM, but unlike the existing approaches, they consider the final aggregated consequent and implicated functions simultaneously to calculate the weights. To show how the proposed methods act, two numerical examples are solved using the presented methods and the results are compared with some of common defuzzification techniques.