Similarity of histograms and circular histograms from interval and fuzzy data

In this paper, building on the general concepts of histograms and particularly focusing on histograms describing fuzzy data, we define various similarity measures that can be used to assess the similarity of histograms. Circular histograms are discussed as special case and the concept of modulo similarity in comparing circular histograms is extended to the case of fuzzy data. Additionally, we propose a bin-based similarity approach applicable to circular histograms. A numerical example is presented to illustrate the usefulness of the introduced measures.