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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akram, M.: \(m\)-polar fuzzy graphs: theory, methods & applications. Studies in Fuzziness and Soft Computing, vol. 371, pp. 1–284. Springer (2019)
Akram, M.: Fuzzy Lie algebras. Studies in Fuzziness and Soft Computing, vol. 9, pp. 1–302. Springer (2018)
Akram, M., Luqman, A.: Intuitionistic single-valued neutrosophic hypergraphs. OPSEARCH 54(4), 799–815 (2017)
Akram, M., Luqman, A.: Bipolar neutrosophic hypergraphs with applications. J. Intell. Fuzzy Syst. 33(3), 1699–1713 (2017)
Akram, M., Sarwar, M.: Novel applications of \(m\)-polar fuzzy hypergraphs. J. Intell. Fuzzy Syst. 32(3), 2747–2762 (2016)
Akram, M., Sarwar, M.: Transversals of \(m\)-polar fuzzy hypergraphs with applications. J. Intell. Fuzzy Syst. 33(1), 351–364 (2017)
Akram, M., Shahzadi, G.: Hypergraphs in \(m\)-polar fuzzy environment. Mathematics 6(2), 28 (2018). https://doi.org/10.3390/math6020028
Akram, M., Shahzadi, G.: Directed hypergraphs under \(m\)-polar fuzzy environment. J. Intell. Fuzzy Syst. 34(6), 4127–4137 (2018)
Akram, M., Shahzadi, G., Shum, K.P.: Operations on \(m\)-polar fuzzy \(r\)-uniform hypergraphs. Southeast Asian Bull. Math. (2019)
Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)
Chen, G., Zhong, N., Yao, Y.: A hypergraph model of granular computing. In: IEEE International Conference on Granular Computing, pp. 130–135 (2008)
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/10.1155/2014/416530
Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, vol. 1. Masson, Paris (1977)
Lee, H.S.: An optimal algorithm for computing the maxmin transitive closure of a fuzzy similarity matrix. Fuzzy Sets Syst. 123, 129–136 (2001)
Lin, T.Y.: Granular computing. Announcement of the BISC Special Interest Group on Granular Computing (1997)
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)
Luqman, A., Akram, M., Koam, A.N.: Granulation of hypernetwork models under the \(q\)-rung picture fuzzy environment. Mathematics 7(6), 496 (2019)
Luqman, A., Akram, M., Koam, A.N.: An \(m\)-polar fuzzy hypergraph model of granular computing. Symmetry 11, 483 (2019)
Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)
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)
Wang, Q., Gong, Z.: An application of fuzzy hypergraphs and hypergraphs in granular computing. Inf. Sci. 429, 296–314 (2018)
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)
Yang, J., Wang, G., Zhang, Q.: Knowledge distance measure in multigranulation spaces of fuzzy equivalence relation. Inf. Sci. 448, 18–35 (2018)
Yao, Y.Y.: A partition model of granular computing. In: LNCS, vol. 3100, 232–253 (2004)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)
Zadeh, L.A.: The concept of a linguistic and application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)
Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) an outline. Inf. Sci. 172, 1–40 (2005)
Zhang, W.R., Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. Proc. IEEE Conf. 305–309 (1994)
Zhang, L., Zhang, B.: The structural analysis of fuzzy sets. J. Approx. Reason. 40, 92–108 (2005)
Zhang, L., Zhang, B.: The Theory and Applications of Problem Solving-Quotient Space Based Granular Computing. Tsinghua University Press, Beijing (2007)
Zhang, L., Zhang, B.: Hierarchy and Multi-granular Computing, Quotient Space Based Problem Solving, pp. 45–103. Tsinghua University Press, Beijing (2014)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Akram, M., Luqman, A. (2020). Granular Computing Based on m-Polar Fuzzy Hypergraphs. In: Fuzzy Hypergraphs and Related Extensions. Studies in Fuzziness and Soft Computing, vol 390. Springer, Singapore. https://doi.org/10.1007/978-981-15-2403-5_8
Download citation
DOI: https://doi.org/10.1007/978-981-15-2403-5_8
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2402-8
Online ISBN: 978-981-15-2403-5
eBook Packages: EngineeringEngineering (R0)