Interval valued (α, β)-fuzzy hyperideals in Krasner (m, n)-hyperrings

Document Type : Original Article

Author

Imam Khomeini International University

Abstract

In this paper, the notion of quasicoincidence of a fuzzy interval valued with an interval valued fuzzy set, which generalizes the concept of quasicoincidence of a fuzzy point in a fuzzy set is concentrated. Based on the idea, we study the concept of interval valued (α, β)-fuzzy hyperideals in Krasner (m, n)-hyperrings. In particular, some fundamental aspects of interval valued  (E, EVq)-fuzzy hyperideals will be considered. Moreover, we examine the notion of implication-based interval valued fuzzy hyperideals in a Krasner (m, n)-hyperring. 

Keywords

References

[1] R. Ameri, M. Norouzi, Prime and primary hyperideals in Krasner (m, n)-hyperrings, European Journal Of Combinatorics, (2013), 379–390.
[2] M. Anbarloei, n-ary 2-absorbing and 2-absorbing primary hyperideals in Krasner (m, n)- hyperrings, Matematicki Vesnik, 71(3) (2019), 250–262.
[3] M. Anbarloei, Unifing the prime and primary hyperideals under one frame in a Krasner (m, n)-hyperring, Communications in Algebra, 49 (2021), 3432–3446.
[4] A. Asadi, R. Ameri, Direct limit of Krasner (m,n)-hyperrings, Journal of Sciences, 31(1) (2020), 75–83.
[5] S. Corsini, Prolegomena of hypergroup theory, Italy: Second edition, Aviani editor, 1993.
[6] P. Corsini, V. Leoreanu, Join spaces associated with fuzzy sets, Journal of Combinatorics, Information System Sciences, 20(1-4) (1995), 293–303.
[7] S. Corsini, V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics, Kluwer Academic Publishers, Springer New York, NY, 5 (2003). DOI: 10.1007/978-1-4757- 3714-1.
[8] B. Davvaz, Fuzzy Krasner (m, n)-hyperrings, Computers and Mathematics with Applications, 59 (2010), 3879–3891.
[9] B. Davvaz, V. Leoreanu-Fotea, Hyperring theory and applications, USA: International Academic Press, Palm Harbor, 2007.
[10] B. Davvaz, T. Vougiouklis, n-ary hypergroups, Iranian Journal of Science and Technology, 30(A2) (2006), 165–174.
[11] T.M. Dutta, S. Kar, S. Purkait, Interval-valued fuzzy prime and semiprime ideals of a hypersemiring, Annals of Fuzzy Mathematics and Informatics, 9(2) (2015), 261–278.
[12] M. Farshi, B. Davvaz, Krasner F (m,n) -hyperrings, Iranian Journal of Fuzzy Systems, 11(6) (2014), 67–88.
[13] K. Hila, K. Naka, B. Davvaz, On (k, n)-absorbing hyperideals in Krasner (m, n)-hyperrings, Quarterly Journal of Mathematics, 69 (2018), 1035–1046.
[14] M. Krasner, A class of hyperrings and hyperfields, International Journal of Mathematics and Mathematical Sciences, 2 (1983), 307–312.
[15] V. Leoreanu-Fotea, Canonical n-ary hypergroups, Italian Journal of Pure and Applied Mathematics, 24(2008). https://www.researchgate.net/publication/281572515 Canonical n-ary hypergroups.
[16] V. Leoreanu-Fotea, B. Davvaz, n-hypergroups and binary relations, European Journal of Combinatorics, 29 (2008), 1027–1218.
[17] V. Leoreanu-Fotea, B. Davvaz, Roughness in n-ary hypergroups, Information Sciences, 178 (2008), 4114–4124.
[18] V. Leoreanu-Fotea, B. Davvaz, Fuzzy hyperrings, Fuzzy Sets and Systems, 160 (2009), 2366– 2378.
[19] F. Marty, Sur une generalization de la notion de groupe, 8 th Congress Math. Scandenaves, Stockholm, (1934), 45–49.
[20] S. Mirvakili, B. Davvaz, Relations on Krasner (m, n)-hyperrings, European Journal of Combinatorics, 31 (2010), 790–802.
[21] M. Norouzi, R. Ameri, V. Leoreanu-Fotea, Normal hyperideals in Krasner (m, n)-hyperrings, Analele stiintifice ale Universitatii Ovidius Constanta, 26(3) (2018), 197–211.
[22] S. Ostadhadi-Dehkordi, B. Davvaz, A note on isomorphism theorems of Krasner (m, n)- hyperrings, Arabian Journal of Mathematics, 5 (2016), 103–115.
[23] T. Vougiouklis, Hyperstructures and their representations, Florida: Hadronic Press Inc., 1994.
[24] A. Yassine, M.J. Nikmehr, R. Nikandish, n-Ary k-absorbing hyperideals in krasner (m, n)- hyperrings, Afrika Matematika, (2022), 19–33. DOI:10.1007/s13370-022-00961-6.
[25] Y. Yin, B. Davvaz, J. Zhan, A fuzzy view of Γ-hyperrings, Neural Computing and Applications, 21(5) (2012), 979–992.
[26] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.
[27] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reason, Information and Control, 18 (1975), 199–249.
[28] M.M. Zahedi, A. Hasankhani, F-polygroups I, The Journal of Fuzzy Mathematics, 4(3) (1996), 533–548.
[29] M.M. Zahedi, A. Hasankhani, F-polygroups II, Information Sciences, 89(3-4) (1996), 225–243.
[30] J. Zhan, B. Davvaz, Y. Jun, Generalized fuzzy algebraic hypersystems, Italian Journal of Pure and Applied Mathematics, (30) (2013), 43–58.
[31] J. Zhan, B. Davvaz, K.P. Shum, Generalized fuzzy hyperideals of hyperrings, Computers and Mathematics with Applications, 56 (2008), 1732–1740.
[32] J. Zhan, B. Davvaz, K.P. Shum, A new view of fuzzy hypernear-rings, Information Sciences. An International Journal, 178(2) (2008), 425–438.
Journal of Algebraic Hyperstructures and Logical Algebras
Volume 4, Issue 1
May 2023
Pages 13-25

Files

Share

How to cite

Statistics