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Granular Computing Based on m-Polar Fuzzy Hypergraphs

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Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 390)

Abstract

An m-polar fuzzy model, as an extension of fuzzy and bipolar fuzzy models, plays a vital role in modeling of real-world problems that involve multi-attribute, multipolar information, and uncertainty. The m-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models.

References

  1. 1.
    Akram, M.: \(m\)-polar fuzzy graphs: theory, methods & applications. Studies in Fuzziness and Soft Computing, vol. 371, pp. 1–284. Springer (2019)Google Scholar
  2. 2.
    Akram, M.: Fuzzy Lie algebras. Studies in Fuzziness and Soft Computing, vol. 9, pp. 1–302. Springer (2018)Google Scholar
  3. 3.
    Akram, M., Luqman, A.: Intuitionistic single-valued neutrosophic hypergraphs. OPSEARCH 54(4), 799–815 (2017)CrossRefGoogle Scholar
  4. 4.
    Akram, M., Luqman, A.: Bipolar neutrosophic hypergraphs with applications. J. Intell. Fuzzy Syst. 33(3), 1699–1713 (2017)CrossRefGoogle Scholar
  5. 5.
    Akram, M., Sarwar, M.: Novel applications of \(m\)-polar fuzzy hypergraphs. J. Intell. Fuzzy Syst. 32(3), 2747–2762 (2016)CrossRefGoogle Scholar
  6. 6.
    Akram, M., Sarwar, M.: Transversals of \(m\)-polar fuzzy hypergraphs with applications. J. Intell. Fuzzy Syst. 33(1), 351–364 (2017)CrossRefGoogle Scholar
  7. 7.
    Akram, M., Shahzadi, G.: Hypergraphs in \(m\)-polar fuzzy environment. Mathematics 6(2), 28 (2018).  https://doi.org/10.3390/math6020028MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Akram, M., Shahzadi, G.: Directed hypergraphs under \(m\)-polar fuzzy environment. J. Intell. Fuzzy Syst. 34(6), 4127–4137 (2018)CrossRefGoogle Scholar
  9. 9.
    Akram, M., Shahzadi, G., Shum, K.P.: Operations on \(m\)-polar fuzzy \(r\)-uniform hypergraphs. Southeast Asian Bull. Math. (2019)Google Scholar
  10. 10.
    Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)zbMATHGoogle Scholar
  11. 11.
    Chen, G., Zhong, N., Yao, Y.: A hypergraph model of granular computing. In: IEEE International Conference on Granular Computing, pp. 130–135 (2008)Google Scholar
  12. 12.
    Chen, J., Li, S., Ma, S., Wang, X.: \(m\)-polar fuzzy sets: an extension of bipolar fuzzy sets. Sci. World J. 8 (2014).  https://doi.org/10.1155/2014/416530Google Scholar
  13. 13.
    Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, vol. 1. Masson, Paris (1977)Google Scholar
  14. 14.
    Lee, H.S.: An optimal algorithm for computing the maxmin transitive closure of a fuzzy similarity matrix. Fuzzy Sets Syst. 123, 129–136 (2001)CrossRefGoogle Scholar
  15. 15.
    Lin, T.Y.: Granular computing. Announcement of the BISC Special Interest Group on Granular Computing (1997)Google Scholar
  16. 16.
    Liu, Q., Jin, W.B., Wu, S.Y., Zhou, Y.H.: Clustering research using dynamic modeling based on granular computing. In: Proceeding of IEEE International Conference on Granular Computing, pp. 539–543 (2005)Google Scholar
  17. 17.
    Luqman, A., Akram, M., Koam, A.N.: Granulation of hypernetwork models under the \(q\)-rung picture fuzzy environment. Mathematics 7(6), 496 (2019)CrossRefGoogle Scholar
  18. 18.
    Luqman, A., Akram, M., Koam, A.N.: An \(m\)-polar fuzzy hypergraph model of granular computing. Symmetry 11, 483 (2019)CrossRefGoogle Scholar
  19. 19.
    Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)zbMATHGoogle Scholar
  20. 20.
    Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and Their Applications, pp. 77–95. Academic Press, New York (1975)Google Scholar
  21. 21.
    Wang, Q., Gong, Z.: An application of fuzzy hypergraphs and hypergraphs in granular computing. Inf. Sci. 429, 296–314 (2018)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Wong, S.K.M., Wu, D.: Automated mining of granular database scheme. In: Proceeding of IEEE International Conference on Fuzzy Systems, pp. 690–694 (2002)Google Scholar
  23. 23.
    Yang, J., Wang, G., Zhang, Q.: Knowledge distance measure in multigranulation spaces of fuzzy equivalence relation. Inf. Sci. 448, 18–35 (2018)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Yao, Y.Y.: A partition model of granular computing. In: LNCS, vol. 3100, 232–253 (2004)Google Scholar
  25. 25.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  26. 26.
    Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Zadeh, L.A.: The concept of a linguistic and application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) an outline. Inf. Sci. 172, 1–40 (2005)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Zhang, W.R., Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. Proc. IEEE Conf. 305–309 (1994)Google Scholar
  30. 30.
    Zhang, L., Zhang, B.: The structural analysis of fuzzy sets. J. Approx. Reason. 40, 92–108 (2005)CrossRefGoogle Scholar
  31. 31.
    Zhang, L., Zhang, B.: The Theory and Applications of Problem Solving-Quotient Space Based Granular Computing. Tsinghua University Press, Beijing (2007)Google Scholar
  32. 32.
    Zhang, L., Zhang, B.: Hierarchy and Multi-granular Computing, Quotient Space Based Problem Solving, pp. 45–103. Tsinghua University Press, Beijing (2014)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan
  2. 2.Department of MathematicsUniversity of the PunjabLahorePakistan

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