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A study of \((I_{O}, O)\)-fuzzy rough sets using overlap functions in complete lattices

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Abstract

Rough set theory provides a formal mathematical framework for handling knowledge uncertainty in data mining. Its core components, the upper and lower approximation operators, represent fundamental concepts within the theory. Their study within lattice theory frameworks marks an important mathematical advancement. Simultaneously, overlap functions, which are non-associative binary aggregation functions contrasting with conventional t-norms, play a pivotal role in formulating fuzzy rough approximation operators. In light of these two pivotal factors, this work introduces \((I_{O}, O)\)-fuzzy rough sets (\((I_{O}, O)\)-FRSs for short), which are based on overlap functions over complete lattices. More specifically, we first give the definition of two approximation operators and study some essential properties. Then, we consider the connection between \((I_{O}, O)\)-FRSs and L-fuzzy relations. Finally, we characterize the topological characteristics of \((I_{O}, O)\)-FRSs and highlight that, under some conditions, some established rough set models can be taken to be special instances of the \((I_{O}, O)\)-FRSs.

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Acknowledgements

This work was supported by grant from National Natural Science Foundation of China (Grant No. 12271319).

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  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 611756, People’s Republic of China

    Siyu Xu, Longyu He & Xiaodong Pan

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Xu, S., He, L. & Pan, X. A study of \((I_{O}, O)\)-fuzzy rough sets using overlap functions in complete lattices. Comp. Appl. Math. 45, 186 (2026). https://doi.org/10.1007/s40314-025-03424-3

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