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Properties of objects can be specified by a set of attributes which values can be symbolic. Defining a good measure of proximity (or remoteness) between objects is crucial importance in applied research like data mining or machine learning. Much attention has been devoted to continuous attributes while little attention to nominal attributes which seems to be much more difficult to handle. The proposed approach is based on the theory of multisets. In the paper we defined a group of objects with nominal description as a AT-tuple of multisets (i.e., an ordered collection of multisets). There are introduced the following definitions: perturbation of multisets’ for each attribute and a measure of groups’ perturbations. The measure of perturbation is assumed to return a value from [0, 1], where 1 is interpreted as the most level of perturbation, while 0 is the lowest level of perturbation. In general these two measures are different, asymmetrical, so they should not be considered as the distance between the groups.
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Projects co-financed by:
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.