On the capability of fuzzy set theory to represent concepts

Abstract

The aim of this paper is to examine the conclusions drawn by Osherson and Smith ["On the adequacy of prototype theory as a theory of concepts", Cognition 9 (1981), pp. 35-58] concerning the inadequacy of the apparatus of fuzzy set theory to represent concepts. Since Osherson and Smith derive their conclusions from specific examples, we show for each of these examples that the respective conclusion they arrive at is not warranted. That is, we demonstrate that fuzzy set theory is sufficiently expressive to represent the various strong intuitions and experimental evidence regarding the relation between simple and combined concepts that are described by Osherson and Smith. To pursue our arguments, we introduce a few relevant notions of fuzzy set theory.