Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to two-valued logic. Moreover, there are few if any published reports of expert systems in real-world use that reason about uncertainty using fuzzy logic. It appears that the limitations of fuzzy logic have not been detrimental in control applications because current fuzzy controllers are far simpler than other knowledge-based systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledge-based systems. 1

The responses to my article provide an that I have is whether the distinction is re- knowledge becomes implicit background exceptionally wide range of perspectives ally well defined. On the one hand, there knowledge that must be used tacitly in tunon the current state of research on fuzzy may be multiple types of imprecision and ing the allowed interactions between the logic and its applications. Overall, I find vagueness. Is the domain-independent im- items of explicit shallow knowledge. To that with most commentators I agree more precision involved in “around 1.80m ” the quote Garcia, “The dogma of generality than I disagree. I shall try here to steer a same as the human-specific imprecision versus efficiency strikes again, and knowlmiddle course between simply repeating involved in “tall”? On the other hand, it edge engineering and machine learning are points of agreement and narrowly counter- may be possible to model some types of not exempted.” ing points of disagreement. imprecision probabilistically. For example, the degree of truth of the assertion “ 1.SOm Fuzzy logic in expert systems. Only three The foundations of fuzzy logic. Some is tall ” might be modeled as the probability of the responses give references in an atcommentators take a more extreme posi- that an individual with height 1.80m would tempt to dispute the claim that there are tion than I do concerning the coherence of be labeled as tall given incomplete knowl- very few deployed expert systems that acfuzzy logic. I do not agree with Attikiouzel edge, that is, given no other information on tually use fuzzy logic as their principal