Generalization of Jaccard index for interval data analysis

The article is devoted to the analysis of data samples with interval uncertainty. We propose to use the Jaccard measure (index), which is widely used when comparing sets in various problem areas, as a measure (functional) of the compatibility of interval values and their samples. Information about interval analysis, classical and complete (Kaucher) interval arithmetic is presented. For interval quantities, the necessary concepts and definitions of operations are introduced, in particular, generalizations of the concepts of intersection and union of sets. The Jaccard measure is generalized to the case of data with interval uncertainty and samples of interval data. Various variants of interval relations are described in detail – from their coincidence to incompatible cases. Various definitions of the Jaccard measure, both symmetric and non-symmetric with respect to operands, are considered. The question of the connection of the proposed measure with the interval mode and for estimating the results of calculations with twins is discussed. A practical example of finding the information set of an interval problem using a new measure is given.

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