Probabilistic hyperrough set and covering hyperrough set

Authors

  • Takaaki Fujita * Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan.

https://doi.org/10.48313/uda.v2i2.70

Abstract

Rough set theory provides a mathematical framework for approximating subsets using lower and upper bounds defined by equivalence relations, effectively capturing uncertainty in classification and data analysis. Building on these foundational ideas, further generalizations such as Hyperrough Sets and Superhyperrough Sets have been developed. Probabilistic Rough Sets provide a framework for estimating uncertainty by utilizing membership probabilities, allowing for the definition of lower and upper approximations based on specified threshold values. Covering rough sets approximate information via overlapping covers, providing lower definite and upper possible boundaries when true partitions are unavailable.
In this paper, we introduce newly defined concepts of the Probabilistic HyperRough Set and Covering HyperRough Set, as well as the Probabilistic SuperHyperRough Set and Covering SuperHyperRough Set. These models extend the existing frameworks of the Probabilistic Rough Set and Covering Rough Set, respectively.

Keywords:

Rough set, Hyperrough set, Covering rough set, Superhyperrough set, Probabilistic rough set

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Published

2025-06-15

Issue

Vol. 2 No. 2 (2025): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Fujita, T. (2025). Probabilistic hyperrough set and covering hyperrough set. Uncertainty Discourse and Applications, 2(2), 124-138. https://doi.org/10.48313/uda.v2i2.70

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