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Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

A connection between fuzzy Γ-hypergroups and Γ -groups

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pp. 207–214Vol. 26Issue 1February 2021DOI: 10.1080/09720529.2021.1930651 Crossmark XML
Received:
31 Oct 2020
Accepted:
30 Mar 2021
Published Online:
15 Nov 2021
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1351
Pages:
207–214

Abstract

By applying the notion of fuzzy Γ -hypergroups, we demonstrate that the defined equivalence relation ϵ is the smallest fuzzy strongly regular relation and the quotient H / ϵ* is a Γ / β* -group. Especially, the homomorphism of fuzzy Γ-hypergroups is introduced to obtain some related conclusions. Also, the functor from the category of fuzzy Γ-hypergroups is assigned to the category of fundamental Γ / β* -groups in order to show that the functor is covariant.

Keywords

Fuzzy Γ-hypergroupΓ-groupFundamental relationFundamental functor

Subject Classifications

(2010) 03E7220N2016Y80

References

  1. Sen, M.K., Ameri, R. and Chowdhury, G., 2008. Fuzzy hypersemigroups. Soft Computing, 12(9), pp.891-900. doi: https://doi.org/10.1007/s00500-007-0257-9 [Crossref], [Web of Science ®], [Google Scholar]
  2. Leoreanu-Fotea, V. and Davvaz, B., 2009. Fuzzy hyperrings. Fuzzy sets and systems, 160(16), pp.2366-2378. doi: https://doi.org/10.1016/j.fss.2008.11.007 [Crossref], [Web of Science ®], [Google Scholar]
  3. Fotea, V.L., 2009. Fuzzy hypermodules. Computers and Mathematics with Applications, 57(3), pp.466-475. doi: https://doi.org/10.1016/j.camwa.2008.11.004 [Crossref], [Web of Science ®], [Google Scholar]
  4. Sen, M.K. and Saha, N. K., 1986. On-semigroup. I, Bulletin of the Calcutta Mathematical Society, vol. 78, no. 3, pp. 180-186. [Google Scholar]
  5. Nobusawa, N., 1964. On a generalization of the ring theory. Osaka Journal of Mathematics, 1(1), pp.81-89. [Google Scholar]
  6. Ameri, R. and Sadeghi, R., 2013. On fuzzy gamma hypermodules. Ratio Mathematica, 24(1), pp.11-30. [Google Scholar]
  7. Leoreanu-Fotea, V., Zhan, J. and Leoreanu, L., 2013. Fuzzy Γ-hyperrings and fuzzy Γ-hypermodules. Journal of Intelligent and Fuzzy Systems, 24(3), pp.647-655. doi: https://doi.org/10.3233/IFS-2012-0584 [Crossref], [Web of Science ®], [Google Scholar]
  8. Davvaz, B. and Firouzkouhi, N., 2019. Fundamental relation on fuzzy hypermodules. Soft Computing, 23(24), pp.13025-13033. doi: https://doi.org/10.1007/s00500-019-04299-3 [Crossref], [Web of Science ®], [Google Scholar]
  9. Davvaz, B. and Firouzkouhi, N., 2020. Commutative Rings Derived From Fuzzy Hyperrings. Honam Mathematical Journal, 42(2), pp.219–234. [Web of Science ®], [Google Scholar]
  10. Firouzkouhi, N. and Davvaz, B., 2020. New fundamental relation and complete part of fuzzy hypermodules. Journal of Discrete Mathematical Sciences and Cryptography, pp.1-14. doi: https://doi.org/10.1080/09720529.2020.1740496 [Taylor & Francis Online], [Google Scholar]
  11. Talee, A.F., Abbasi, M.Y., Khan, S.A. and Hila, K., 2019. Fuzzy set approach to hyperideal theory of po-ternary semihypergroups. Journal of Discrete Mathematical Sciences and Cryptography, 22(3), pp.411-431. doi: https://doi.org/10.1080/09720529.2019.1600846 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
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