ABSTRACT
Vague categories are those that are not clearly defined, so that, at least for some individuals, full belonging to the category cannot be absolutely determined. Vagueness is due to some form of imprecision in the characterization of the category or set. One of the most recurrent examples of vagueness is the category of “tall people,” for which a single height (expressed, for example, in centimeters) delimiting membership cannot be clearly determined. Vagueness has been recognized by cognitive psychology as an inherent characteristic of many human categorization processes. One of the most prominent theories of categorization was that developed by Rosch (1988), in which categories are considered not to have clear-cut boundaries, and belonging to a category is described as a matter of distance to “prototypical instances,” i.e. to those individuals that have the clearest cases of membership, and share a larger number of properties with other individuals in the class. Rosch considered that the functional purpose of classes was to provide maximum information with the least cognitive effort, so that human categories cannot be considered as arbitrary or the product of historical accident. These principles are consistent with the branch of research in mathematics commonly known as “fuzzy set theory,” and its related “fuzzy logic.” The theory of fuzzy sets, initiated in the seminal work of Zadeh (1965), provides a mathematical framework for the numerical representation of vague categories, emphasizing the role of vagueness in linguistic labels. Fuzzy sets representing vague categories are characterized by membership functions in the form (x): X →[0, 1] (X being the universe of discourse), and the logical connectives of classical logics are generalized to deal with the partial membership values of individuals. Fuzzy modeling techniques have been applied to many aspects of engineering and problem solving, including ergonomics (Karwowski et al. 1984) and the narrower field of usability evaluation (Garcia et al. 2003; Sicilia et al. 2003; Wong et al. 2003).
