We investigate the family of concepts that an agent comes to know through a set of defining features, and examine the role played by these features in the process of categorization. In a qualitative framework, categorial membership is evaluated through an order relation among the objects at hand, which translates the fact that an object may fall more than another under a given concept. For concepts defined by their features, this global membership order depends on the degree with which each (...) feature applies to the objects of the universe. The passage from these individual membership degrees to a global membership order poses a problem analogous to vote aggregation in social choice theory. This similarity leads to an original solution that is particularly well-adapted to the framework of cognitive psychology. The resulting membership order extends to compound concepts, and provides a good description of the guppy paradox and the conjunction effect. (shrink)

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by (...) experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy. (shrink)