Indicators of Similarity and Dissimilarity of Multi-Attribute Objects in the Metric Spaces of Sets and Multisets

Abstract

The concepts of the similarity and dissimilarity (difference) of analyzed objects play an important role in many theoretical and practical problems of decision making, artificial intelligence, pattern recognition, processing of heterogeneous information, etc. The similarity or dissimilarity of objects is usually estimated by their proximity in the attribute space. This paper considers new classes of metric spaces of finite, bounded, and measurable sets and multisets. The possibilities are shown for using new types of metrics to evaluate the similarity or dissimilarity of multi-attribute objects that are present in several instances with differing values of attributes and are represented by multisets of attributes.