Evaluating the Impact of Membership Functions and Defuzzification Methods in a Fuzzy System: Case of Air Quality Levels

Since the 1960s, fuzzy logic has contributed to developing control systems based on modeling nonlinear problems using linguistic terms and inference rules. In the air quality domain, fuzzy logic has allowed us to tackle inferential environmental systems that are tolerant of human uncertainty and aimed at decision support. These systems are composed of three processes: a function to define a membership degree of the system’s value concerning a human linguistic term; an inference engine for decision making; and defuzzification methods focused on transforming the aggregated fuzzy set into a real-world value. Over the years, multiple mathematical formulas have been proposed to enrich membership functions or defuzzification methods; however, their use is sometimes limited to classical functions, limiting the importance of other proposals. This paper aims to evaluate the impact of the transformation functions in an air quality fuzzy system. The results of this work prove that the defuzzification method has a more significant effect than the others. It should be noted that by considering these results or their evaluation method, the quality of future fuzzy systems can be improved in both industrial and academic domains.