Reply to Comments on The Paradoxical Success of Fuzzy Logic

The fifteen responses to my paper provide an exceptionally wide range of perspectives on the current state of research on fuzzy logic and its applications. Overall, I find that with most commentators I agree more than I disagree. In this response, I shall try to steer a middle course between simply repeating points of agreement and narrowly countering points of disagreement. My comments are divided into four sections. The first section below discusses the extent to which we can reasonably expect any type of logic to capture the many varieties of uncertainty. Then, the next section reviews the applications of fuzzy logic suggested by some commentators as counter-examples to my claim that fuzzy logic has in fact shown little usefulness for expert systems as opposed to controllers. The third section responds to the mathematical criticisms of my theorem on the potential (but not necessary) collapse of fuzzy logic to binary logic. Finally, the last section returns to the issue of which aspects of fuzzy logic are essential to the indisputable practical usefulness of fuzzy controllers.