Similarity Measures Based on a Fuzzy Set Model and Application to Hierarchical Clustering

A fuzzy set model for generalizing similarity measures of binary characters for numerical classification is proposed. A set-theoretical model representation is given for well-known similarities of binary characters in mathematical taxonomy. Then a fuzzy extension of the set-theoretical model leads to generalizations of these similarities. Moreover an algorithm of hierarchical agglomerative clustering is developed in which similarity between a pair of clusters is calculated by referring to the model. An example based on psychological association is shown.