The Prototype View of Concepts

Concepts are important and basic elements in human’s cognition process. The formal concept gives a mathematical format of the classical view of concepts in which all instances of a concept share common properties. But in some situation this view is not consistent with human’s understanding of concepts. The prototype view of concepts is more appropriate in our daily life. This view characters some analog categories as internally structured into a prototype (clearest cases, best examples of the category) and non-prototype members, with non-prototype members tending toward an order from better to poorer examples. The objective of this paper is to give a mathematical description of prototype view of concepts. Firstly, we give a similarity measurement of an object to another object in a formal context. Then based on this similarity measurement, the mathematical format of prototype view of concepts, named k-cutting concept, induced by one typical object is obtained. Finally, the properties of k-cutting concepts are studied. In addition to presenting theorems to summarize our results, we use some examples to illustrate the main ideas.