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Defining a good measure of proximity or similarity (or remoteness or dissimilarity) between objects is crucial importance in theories of knowledge. Usually each object is represented as a point in some coordinate space so the metric distance between points reflects similarities between the respective objects. In general, the space is assumed to be Euclidean. A metric distance is a function which assigns a nonnegative number, called their distance to every pair of objects. The assumption of symmetry underlies essentially all theoretical treatments of similarity. Tversky (1977) provides empirical evidence of asymmetric similarities and argues that similarity should not be treated as a symmetric relation. Tversky considered objects as sets of features instead of geometric points in a metric space. In this paper we propose the measure of remoteness between sets of nominal values based on Tversky’s similarity measures. Instead of considering distance between two sets, we introduce a definition of measure of perturbation of one set by another set, the consideration is based on set-theoretic operations. The measure describes changes of the first set after adding the second set. The measure of sets’ perturbation returns a value from [0, 1], where I is interpreted as highest level of perturbation, while 0 denotes the lowest level of perturbation. It is interesting that this measure is not symmetric.
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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.