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 1.80 m” 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 1.80 m 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 that “if one wishes to write a program or the individual. formalism for reasoning about uncertainty. build a machine that will perform inference Overall, I am wary of the enterprise of Moreover, most of the references given in the same way as human beings, then one even making an attempt to classify the actually support this claim. must build the basic equations of probabil- types of uncertainty. A complete and con- Before I discuss these references one by ity theory into it, or face the inevitable out- sistent analysis of all the many varieties of one, it is worth emphasizing that I use the come that it will not perform as required’ uncertainty involved in human thinking term “expert system” to designate a reason-Neither humans nor machines always re- and revealed in human language is a philo- ing system that applies a large base of exquire formal rigor to act successfully in the sophical goal that we should not expect to plicit knowledge to perform a task requiring world, nor is success always guaranteed by achieve soon. Moreover, this aspiration is a complex inference, such as diagnosis, rigor. Successful controllers and expert variant of the quest for formal rigor criti- scheduling, or design. A fuzzy controller is a systems can use heuristic, shallow knowl- cized above as neither necessary nor suffi- knowledge-based system of a different naedge and therefore they can use arbitrary cient for engineering success. As Freksa ture. If a fuzzy controller is called an expert reasoning formalisms such as certainty points out, it is always the case that “the system, this blurs some important distincfactors or fuzzy logic. I also do not agree represented real world and its representa- tions. As Zadeh writes,“what differentiates that “Proponents of fuzzy logic appear to tion are formally incommensurable.” applications to control from applications to be unaware of Cox’s work and that of Therefore, however ideal the logics that[general] knowledge-based systems is that Jaynes and Tribus”; for evidence see the one has at hand, knowledge engineering is in control the main problem which has to be …