Preliminaries

Abstract

(1) Fuzzy logic is popular. The number of papers dealing, in some sense, with fuzzy logic and its applications is immense, and the success in applications is evident, in particular in fuzzy control. From numerous books written on this subject we mention at least [224], [68], [134]. As is stated in the introduction to [134], in 1991 there were about 1400 papers dealing with fuzzy systems. Naturally, in this immense literature the quality varies; a mathematician (logician) browsing in it is sometimes bothered by papers that are mathematically poor (and he/she may easily overlook those that are mathematically excellent). This should not lead to a quick rejection of the domain. Let us quote Zadeh, the inventor of fuzzy sets ([134], Preface): “Although some of the earlier controversies regarding the applicability of fuzzy logic have abated, there are still influential voices which are critical and/or skeptical. Some take the position that anything that can be done with fuzzy logic can be done equally well without it. Some are trying to prove that fuzzy logic is wrong. And some are bothered by what they perceive to be exaggerated expectations. That may well be the case but, as Jules Verne had noted at the turn of the century, scientific progress is driven by exaggerated expectations.”