Generalized Fuzzy Similarity Indexes

Features Contrast Model (FCM) and Fuzzy Features Contrast Model (FFCM) are usually used to evaluate the similarity between objects. The universe of discourse is defined by two sets: A, the set of objects; and E, the set of features. A matrix is defined, which elements represent the degree in which an object verifies a feature, namely, the membership values in fuzzy terms. A classical generalization of crisp similarity indexes is well known but using some crisp properties before make the generalization, for this reason it can be said weak generalization. Y. A. Tolias et al, made a strong generalization but it does not include all the usual indexes, as simple matching or Rao's coefficients. This generalization is the goal of this paper. Some reliable conditions are proved and conditions to define a proximity relation in A are found.