Partitions and fuzziness
This paper presents properties of classical or generalized partitions. First of all, fuzzy binary relations are defined on a finite set, satisfying an extension of the transitivity property and associated with a distance. Characterizations of such relations by matricial properties are given. Partitions are then constructed by means of cliques and spheres associated with the corresponding distance. The case of fuzzy partitions is specially investigated, quasi-partitions are connected with ultrametricity properties. The gain of information resulting from the replacement of a given fuzzy partition by another one is presented, with respect to a given threshold, and it provides a good tool to choose a fuzzy partition in a family or to improve a given classification of the studied population, for example.
scientific article; zbMATH DE number 3959295