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Fuzzy covering-based rough set on two different universes and its application

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Abstract

In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy \(\beta\)-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy \(\beta\)-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of the fuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not only enrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

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Acknowledgements

The authors are extremely grateful to the editor and anonymous referees for their valuable comments and helpful suggestions which helped to improve the presentation of this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 12101500) and the Chinese Universities Scientific Fund (Grant No. 2452018054).

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  1. College of Science, Northwest A & F University, Yangling, 712100, People’s Republic of China

    Bin Yang

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Yang, B. Fuzzy covering-based rough set on two different universes and its application. Artif Intell Rev 55, 4717–4753 (2022). https://doi.org/10.1007/s10462-021-10115-y

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