An information-based discussion of vagueness

The issue of understanding and modeling vagueness has been addressed by many authors, especially in the second half of the XXieth century. They are mainly philosophers, logicians, psychologists, and computer scientists. Often these authors have privileged one type or one view of vagueness and tried to provide some representation scheme for this view using some formalism on hand. In this paper, we try to 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 representations frameworks are proposed for each case. However they have in common to lead 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 thus gives birth to a different type of fuzzy set-based construction in each case.