Mathematics of Fuzzy logic

In 1965 Lotfi Zadeh introduced Fuzzy Sets, in 1973 he introduced Fuzzy Logic. The former refers to an extension of classical Set Theory in such a way that, given a set A, an element can belong only partially to A. The latter is a kind of many-valued logic. The phrase fuzzy logic has nowadays, however, several meanings. Usually one distinguishes between fuzzy logic in broad sense and fuzzy logic in narrow sense. A pleasantry way is to say that former is more fuzzy than logic while the latter is more logic than fuzzy. Seriously speaking, fuzzy logic in broad sense has a multitude of industrial application, in particular in control. A  comprehensive description on what is going on in Fuzzy Logic in broad sense can be found e.g. here, while the main entrance to fuzzy logic in narrow sense is here.