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Transformation Semigroups for Rough Sets

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Rough Sets (IJCRS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11103))

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Abstract

In this article we define transformation semigroups for rough sets. Basic constructions such as closures, products, coverings and partitions for transformation semigroups are defined. A decomposition theorem for reset transformation semigroups is given. A connection with automata is also presented by defining a semiautomaton for rough sets.

This work has been supported by the Council of Scientific and Industrial Research (CSIR) India, Research Grant No. 09/092(0875)/2013-EMR-I.

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References

  1. Arbib, M.A., Krohn, K., Rhodes, J.L.: Algebraic Theory of Machines, Languages, and Semigroups. Academic Press, London (1968)

    Google Scholar 

  2. Basu, S.: Rough finite-state automata. Cybern. Syst. 36(2), 107–124 (2005). https://doi.org/10.1080/01969720590887324

    Article  MATH  Google Scholar 

  3. Bavel, Z.: The source as a tool in automata. Inf. Control 18(2), 140–155 (1971). https://doi.org/10.1016/S0019-9958(71)90324-X

    Article  MathSciNet  MATH  Google Scholar 

  4. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups. Volume II. American Mathematical Society (1961)

    Google Scholar 

  5. Eilenberg, S., Tilson, B.: Automata, Languages, and Machines. Volume B. Pure & Applied Mathematics, vol. B. Academic Press, New York (1976)

    Google Scholar 

  6. Ginsburg, S.: Some remarks on abstract machines. Trans. Am. Math. Soc. 96(3), 400–444 (1960). https://doi.org/10.1090/S0002-9947-60-99988-8

    Article  MATH  Google Scholar 

  7. Holcombe, W.M.L.: Algebraic Automata Theory. Cambridge University Press, New York (1982)

    Book  Google Scholar 

  8. Iwiński, T.B.: Algebraic approach to rough sets. Bull. Polish Acad. Sci. Math. 35, 673–683 (1987)

    MathSciNet  MATH  Google Scholar 

  9. Li, X.S., Yuan, X.H.: The category \({RSC}\) of \({I}\)-rough sets. In: Fifth International Conference on Fuzzy Systems and Knowledge Discovery, vol. 1, pp. 448–452, October 2008. https://doi.org/10.1109/FSKD.2008.106

  10. Linton, S.A., Pfeiffer, G., Robertson, E.F., Ruškuc, N.: Groups and actions in transformation semigroups. Math. Z. 228(3), 435–450 (1998). https://doi.org/10.1007/PL00004628

    Article  MathSciNet  MATH  Google Scholar 

  11. Mikolajczak, B.: Algebraic and Structural Automata Theory. Annals of Discrete Mathematics. North-Holland, Amsterdam (1991)

    Google Scholar 

  12. More, A.K., Banerjee, M.: Categories and algebras from rough sets: new facets. Fundam. Inf. 148(1–2), 173–190 (2016). https://doi.org/10.3233/FI-2016-1429

    Article  MathSciNet  MATH  Google Scholar 

  13. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982). https://doi.org/10.1007/BF01001956

    Article  MATH  Google Scholar 

  14. Sharan, S., Srivastava, A.K., Tiwari, S.P.: Characterizations of rough finite state automata. Int. J. Mach. Learn. Cybernet. 8(3), 721–730 (2017). https://doi.org/10.1007/s13042-015-0372-3

    Article  Google Scholar 

  15. Tiwari, S.P., Sharan, S., Singh, A.K.: On coverings of products of rough transformation semigroups. Int. J. Found. Comput. Sci. 24(03), 375–391 (2013). https://doi.org/10.1142/S0129054113500093

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

We are grateful to the anonymous referees for their suggestions and valuable remarks.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Kanpur, 208016, India

    Anuj Kumar More & Mohua Banerjee

Authors
  1. Anuj Kumar More
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  2. Mohua Banerjee
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Correspondence to Anuj Kumar More .

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Editors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Hung Son Nguyen

  2. Faculty of Information Technology, Vietnam National University, Hanoi, Vietnam

    Quang-Thuy Ha

  3. School of Information Science, Southwest Jiaotong University, Chengdu, China

    Tianrui Li

  4. Institute of Computer Science, University of Silesia, Sosnowiec, Poland

    Małgorzata Przybyła-Kasperek

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More, A.K., Banerjee, M. (2018). Transformation Semigroups for Rough Sets. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_46

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  • DOI: https://doi.org/10.1007/978-3-319-99368-3_46

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99367-6

  • Online ISBN: 978-3-319-99368-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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