ON THE VERY REAL DISTINCTION BETWEEN FUZZY AND STATISTICAL-METHODS - DISCUSSION

In this discussion we review the main remarks of Laviolette, Seaman, Barrett, and Woodall. First, we examine how the subjectivist view of probability faces the task of modeling human reasoning according to a cognitive viewpoint. We then investigate the nature of the fuzzy and probabilistic controllers analyzed by the authors, refuting the hypothesis of similarity We show that, due to the different theoretical basis, the representativeness of the fuzzy controller overcomes the probabilistic controller in resembling the expert's knowledge. We also review the authors' comparison between the fuzzy and probabilistic approaches to monitor multinomial processes, emphasizing biases and misconceptions in the authors' analysis.