The Inevitability of Vagueness in Fuzzy Logic

Abstract

Fuzzy Logic, in its fuzzy control incarnation, can be as well seen as an answer to the belated question on how can an algorithm take in account the subtle variations in a complex system -- be it the simple and paradigmatic thermostat, the description of a traffic jam or the inner workings of a spaceship. Contrary to the best whodunit, the answer is given at the very start, and the history of the following years of fuzziness is a long demonstration of how, thanks to its explanatory power, a simple idea can be implemented in countless devices, and become the manifest for a technological society in which the logic discourse is based more on the human approach and on embracing the permanent state of flux and uncertainty that is the human experience than on the futile search for absolute truths and endless precision. If the control answer is somehow a given, so many other answers that concern foundations of Fuzzy Logic still beget proper questions. In this paper some of such foundational questions pertaining vagueness, its role in the definition of fuzziness and its many incarnations are set in their historical perspective, and some of the dots outlining the path from a rigid search for truth typical of the end of the nineteenth century to the more nuanced approach that has swept the twentieth century are connected.