A Summary and Update of “Fuzzy Logic”

What is fuzzy logic and what does it have to offer? There are many misconceptions about fuzzy logic. To begin with, fuzzy logic is not fuzzy. Fuzzy logic is precise. Basically, fuzzy logic is a precise logic of imprecision. More concretely, fuzzy logic is a system of reasoning and computation in which the objects of reasoning and computation are classes with unsharp boundaries. Fundamentally, unsharpness of class boundaries may be equated to fuzziness. Fuzziness of human concepts is a pervasive facet of human cognition. Everyday examples are the concepts of red, small, near, fast, heavy, similar, etc. Fuzzy logic may be viewed as a wide-ranging generalization of the classical, Aristotelian, bivalent logic. In bivalent logic, no degrees of truth are allowed. In multivalued logic, degrees of truth are allowed. Fuzzy logic goes far beyond. In fuzzy logic everything is or is allowed to be a matter of degree. Furthermore, the degrees are allowed to be fuzzy.