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Mapper-based fuzzy rough sets
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DOI：10.1016/j.ijar.2026.109745.png)
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Abstract
En 中文
Many generalizations of rough set theory have been proposed to suit different use case scenarios. In this paper we focus on covering-based rough set theory (CBRS) where the partition of the universe, used in the classical rough set approximations, is generalized to a covering. In previous work we used the Mapper algorithm, from topological data analysis, to construct meaningful coverings of datasets. Under certain conditions, these coverings form a granular structure, in the sense that adjusting certain parameters of Mapper, changes the accuracy of the resulting CBRS approximations monotonically. We show that this granular structure naturally suggests an interesting way to obtain fuzzy approximations of a set, which leads to the definition of Mapper-based fuzzy rough sets (MBFRS). Compared to classical fuzzy rough sets, the membership of an object x to MBFRS approximations is determined only by its topological neighborhood, canceling out the undesirable influence of objects residing at medium instance to x. On the other hand, the new approximations also have promising properties that closely mimic the properties of classical fuzzy rough sets, and covering-based rough set approximations.
Keywords:
Fuzzy rough sets
Covering-based rough sets
Mapper algorithm
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