Bidirectional comparison of multi-attribute qualitative objects

In the paper, the multi-attribute objects with repeating qualitative values of attributes are considered. Each object is represented by a collection of multisets drawn from sets of values of the attributes. Formalism of the theory of multisets allows taking into account simultaneously all the combinations of attribute values and various versions of the objects. The effective procedure for comparing such objects as well as groups of such objects is developed. The proposed concept of the perturbation of one object by another is considered as the difference of the multisets representing the objects. The measure of perturbation describes remoteness between the considered objects, and, in general, is asymmetrical. Next, we consider the measure of the perturbation of one group of objects by another group of objects. Then, we generate the description of each group in the form of the classification rules. A practical illustration of the proposed approach is carried out for the task of classification of text documents.