Neither Concepts Nor Lotfi Zadeh are Fuzzy Sets

Abstract

In the 1960s and ’70s at the University of California, Berkeley, two people at opposite ends of the campus were doing work that challenged applications of classical set theory. In the Department of Computer Science, Lotfi Zadeh noticed that phenomena in the world do not necessarily come in the all-or-none packages required by classical sets (for example, a man may be tall to a degree), and he set out to devise a mathematical calculus by which matters of degree could be encompassed within a variant of classical logic. He gave it the name fuzzy logic. In the Department of Psychology, Eleanor Rosch (who happens to be myself) was doing empirical psychological research on the nature of concepts and categorization, matters that, from the time of the Greeks, had been assumed to have the basic form of classical sets. The prevailing belief was that humans categorized by identifying necessary and sufficient conditions for an item to belong to a category; once such criteria were met, all items that belonged to the category were equivalent with respect to membership; and the meaning of conceptual combinations could be explained by the operations of classical logic. My research indicated that nothing about this model was true either for the representation, processing or use of natural language concepts and categorizations. One of the ways in which people differ from the model is that they see category membership as a matter of degree (e.g. apple is judged a better fruit than plum, blueberry, etc.), a finding that is psychologically important because degree of membership predicts the other psychological operations on categories. It is also a finding that might, on the surface, appear to unite this research with fuzzy logic.