Bidirectional Comparison of Nominal Sets: Asymmetry of Proximity

The authors propose a novel measure of proximity between two sets of nominal elements. This measure describes the changes in the first set after adding the second set or changes in the second set after adding the first set. It is crucial to note that this measure is not symmetric, it means that the perturbation of the first set on the second set can be different than the perturbation of the opposition direction. The introduced set impact measure allows for the direct treatment of objects described by nominal-valued attributes. The ordinary sets, multisets, fuzzy sets, and the intuitionistic fuzzy sets are considered. The book is intended for data science professionals, philosophers as well as cognitive psychologists, who struggle with practical problems in which asymmetry of proximity of objects cannot be neglected. The use of the proposed measures of perturbation between compared objects can be very important in data mining or in exploration of Internetresources.