Uncertainty measures for interval set information tables based on interval δ-similarity relation

Abstract The notion of uncertainty measure is one of the most important topics in rough set theory and has been studied in different kinds of information tables. However, few studies have focused on the interval set information table, which is regarded as one of the generalized models of single-valued information tables. This paper aims at studying the uncertainty measurements for interval set information tables. Firstly, an interval δ-similarity relation is induced based on the similarity degree. The similarity relation induces the granules, which form a covering in interval set information tables. Secondly, four types of granularity measures are defined to measure the granularity of a covering. Thirdly, the concepts of accuracy and roughness in rough set theory are respectively extended to δ-accuracy and δ-roughness for interval set information tables. Furthermore, four new combinations ofuncertainty measures by considering proposed granularity measures and δ-accuracy and δ-roughness are defined and analyzed. Theoretical analyses and experimental results illustrate that the proposed measures are effective and accurate for interval set information tables.

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