Volume 22 • Issue 2 • PP: 78-94 • 2023
Characterization of fuzzy algebraic structure based on diophantine Q-neutrosophic subbisemiring of bisemiring
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We propose the concept of diophantine Q-neutrosophic subbisemiring(DioQNSBS), level sets of DioQNSBS of a bisemiring. The idea of DioQNSBS is an extension of fuzzy subbisemiring over bisemiring. Exploring the concept for DioQNSBS over bisemiring. Let H be the diophantine Q-neutrosophic subset in D, prove H = ⟨(Γ_H^T,Γ_H^I,Γ_H^F ), (ΛH, ΞH, ΦH )⟩ is a DioQNSBS of D if and only if all non empty level set H(t,s) is a subbisemiring of D for t, s ∈ [0, 1]. Let H be the DioQNSBS of a bisemiring D and M be the strongest diophantine Q-neutrosophic relation (SDioQNSR)of D, we notice H is a DioQNSBS of D if and only if M is a DioQNSBS of D × D. Let H1, H2, ..., Hn be the family of DioQNSBSs of D1, D2, ..., Dn respectively, prove H1 × H2 × ... × Hn is a DioQNSBS of D1 × D2 × ... × Dn. The homomorphic image of DioQNSBS is a DioQNSBS. The homomorphic preimage of DioQNSBS is a DioQNSBS. Illustrations are presented to demonstrate results.
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References
[1] Ahsan.J, Saifullah.K, Khan.F, Fuzzy semirings, Fuzzy Sets and systems,60,(1993),309-320.
[2] Atanassov. K, Intuitionistic fuzzy sets, Fuzzy Sets and Systems,20(1),(1986),87-96.
[3] Faward Hussian,Raja Muhammad Hashism, Ajab Khan,Muhammad Naeem, Generalization of bisemirings, International Journal of Computer Science and Information Security,14(9),(2016), 275-289. London.
[4] Golan.S.J, Semirings and their Applications, Kluwer Academic Publishers, 1999;
[5] Iseki.K, Ideal theory of semiring, 1956; Proceedings of the Japan Academy, Vol. 32. pp. 554-559.
[6] Iseki.K, Ideals in semirings, Proceedings of the Japan Academy, 34,(1958),29-31.
[7] Iseki.K, Quasi-ideals in semirings without zero, Proceedings of the Japan Academy,34(2),(1958),79-81.
[8] Palanikumar.M, Arulmozhi.K, (α, β)-neutrosophic subbisemiring of bisemiring, Neutrosophic Sets and Systems,48,(2022),368-385.
[9] Palanikumar.M, Arulmozhi.K, On intuitionistic fuzzy normal subbisemiring of bisemiring, Nonlinear Studies, 28(3),(2021),717-721.
[10] Palanikumar.M, Arulmozhi.K, Jana.C, Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued aggregation operators, Comp. Appl. Math. 41(90), (2022), 1-27.
[11] Palanikumar.M, Arulmozhi.K, On Pythagorean normal subbisemiring of bisemiring, Annals of Communications in Mathematics,4,(2021), 63-72
[12] Palanikumar.M, Arulmozhi.K, On new approach towards cubic vague subbisemirings in bisemirings, Annals of Communications in Mathematics,4,(2021), 237-248
[13] Palanikumar.M, Iampan.A, Spherical fermatean interval valued fuzzy soft set based on multi criteria group decision making, International Journal of Innovative Computing, Information and Control,18(2),(2022),607-619.
[14] Palanikumar.M, Arulmozhi.K, Iampan.A, Interval valued Neutrosophic Subbisemiring of Bisemiring, International Journal of Neutrosophic Science,19(1),(2022), 116-131.
[15] Palanikumar.M, Iampan.A, Novel approach to decision making based on type-II generalized fermatean bipolar fuzzy soft sets, International Journal of Innovative Computing, Information and Control,18(3),(2022), 769-781.
[16] Palanikumar.M, Arulmozhi.K, Iampan.A, Interval valued Neutrosophic Subbisemiring of Bisemiring, International Journal of Neutrosophic Science,19(1),(2022), 116-131.
[17] Palanikumar.M, Arulmozhi.K, Iampan.A, Said Broumi,New algebraic extension of interval valued Q-neutrosophic normal subbisemirings of bisemirings, International Journal of Neutrosophic Science,20(1),(2023), 106-118.
[18] Palanikumar.M, Iampan.A, Arulmozhi.K, Iranian.D, Seethalakshmy, Raghavendran.R, New approach to- wards (ς1, ς2)-interval valued Q1 neutrosophic subbisemirings of bisemirings and its extension, International Journal of Neutrosophic Science,20(1),(2023), 49-58.
[19] Riaz.M, Hashmi,M.R, Linear diophantine fuzzy set and its applications towards multi attribute decision making problems, Journal of Intelligent and Fuzzy Systems,37(4),(2019),5417-5439.
[20] Sen.M.K, Ghosh.S, An introduction to bisemirings, Southeast Asian Bulletin of Mathematics,28(3),(2001), 547-559.
[21] Smarandache.F, A unifying field in logics Neutrosophy Neutrosophic Probability,Set and Logic, Rehoboth American Research Press,(1999).
[22] Vandiver, H. S, Note on a simple type of algebra in which the cancellation law of addition does not hold, Yulletin of the American Mathematical Society, 40(12), (1934), 914-920.
[23] Zadeh.L.A, Fuzzy sets, Information and Control, 8,(1965),38-353.
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