Modified Concept of Indiscernibility and a Formal Base of Classification
Hiroshi Watanabe
Abstract:
Establishing the notion of equivalence, or indiscernibility, with the concept of attribute, precedes every measurement practice. The present paper proposes a formal theory of classification, and sheds a new light upon the notion of equivalence underlying nominal level of measurement. Assuming that each object is characterized by a set of predicates as a binary vector, whose components are 1 or 0 according as the object affirms a predicate or not, we first examine the relationship among objects in reference to the choice of predicates, or classifier, and formulate a formal theory of classification of objects by predicates. The formalization is perfectly symmetrical between the objects and the predicates, and allows us to consider a classification of predicates by objects. Based on this reciprocal view of classification we introduce a modified concept of equality between two groups of objects, propose a new approach to clustering, and discuss its merits by showing example.
