An information-based discussion of vagueness

The issue of understanding and modelling vagueness has been addressed by many authors, especially in the second half of the 20th Century. They were mainly philosophers, logicians, psychologists and computer scientists. Often, these authors have preferred one type or one view of vagueness, and have tried to provide some representation scheme for this view using some formalism at hand. In this paper, we provide an organized discussion of different categories of vagueness, pointing out in what circumstances they appear, with a unified view of the formalisms which can be used. Basic representation frameworks are proposed for each case. However, what they have in common leads to a trichotomy of the universe of discourse, which seems to be the common feature of the different forms of vagueness. In each situation, we examine how a fuzzy set-based representation can take place, which gives birth to a different type of fuzzy set-based construction in each case.