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On the category of rough sets

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Abstract

We consider the class of approximation spaces in the present paper. In this class we define the concept of lower natural transformations, upper natural transformations and natural transformations. We prove that the class of approximation spaces with the lower natural transformations, upper natural transformations and natural transformations form categories which are denoted by \(\underline{\mathbf{Apr }}{} \mathbf S \), \(\overline{\mathbf{Apr }}{} \mathbf S \) and \(\mathbf Apr {} \mathbf S \), respectively. We characterize a lower (upper) natural transformation through equivalence classes in an approximation space. We prove that two categories \(\mathbf Apr {} \mathbf S \) and \(\underline{\mathbf{Apr }}{} \mathbf S \) are the same. We characterize several kinds of epimorphisms and monomorphisms. In addition, we show that \(\underline{\mathbf{Apr }}{} \mathbf S \) is a (ExtrEpi, ExtrMono)-structured.

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Acknowledgments

The authors would like to express their sincere thanks to the referees for their valuable comments and suggestions which helped a lot to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran

    R. A. Borzooei & M. Mobini

  2. Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran

    A. A. Estaji

Authors
  1. R. A. Borzooei
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  2. A. A. Estaji
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  3. M. Mobini
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Correspondence to R. A. Borzooei.

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The authors declare that they have no conflict of interest.

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Communicated by A. Di Nola.

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Borzooei, R.A., Estaji, A.A. & Mobini, M. On the category of rough sets. Soft Comput 21, 2201–2214 (2017). https://doi.org/10.1007/s00500-016-2135-9

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