Volume 17 , Issue 2 , PP: 110 - 126, 2021 | Cite this article as | XML | Html | PDF | Full Length Article
Memet Sahin 1 *
Doi: https://doi.org/10.54216/IJNS.170203
In a way, the notion of neutrosophic multigroup is an application of neutrosophic multisets to the theory of group. The concept of neutrosophic multigroup is an algebraic structure of neutrosophic multiset that generalizes both the theories of classical group and neutrosophic group. Neutrosophic multigroup constitutes an application of neutrosophic multiset to the elementary theory of classical group. In this paper, we propose the concept of homomorphism on neutrosophic multigroup. We define homomorphism kerlf, automorphism, homomorphic image and homomorphic preimage of neutrosophic multigroup, respectively. Some homomorphic properties of neutrosophic multigroup are explicated. Some homomorphic properties of neutrosophic multigroup are also discussed. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, neutrosophic multiset theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroup homomorphism and give its applications to group theory
Neutrosophic multiset , Neutrosophic multi group , neutrosophic multigroup homomorphism.s
[1] Zadeh, L.A. “Fuzzy sets”. Inf. Control , 8, 338–353, 1965.
[2] Atanassov K.T. “Intuitionistic fuzzy set”. Fuzzy Sets Syst., 20, 87–96, 1986.
[3] Smarandache, F.A. “Unifying field in logics. Neutrosophy: neutrosophic probability, set and logic”, American Research Press, Rehoboth 1999.
[4] Singh, D.; Ibrahim, A. M.; Yohanna T.; Singh J. N, “An overview of the applications of multisets”, Novi Sad J. Math., 37 (2), 73-92, 2007.
[5] Syropoulos, A. “Mathematics of multisets”, Springer-Verlag Berlin Heidelberg 347-358, 2001.
[6] Wildberger, N. J. “A new look at multisets”, School of Mathematics, UNSW Sydney 2052, Australia 2003.
[7] Yager, R. R. “On the theory of bags”, Int. J. General Syst., 13, 23-37,1986.
[8] Sebastian, S.; Ramakrishnan, T.T. “Multi-Fuzzy Sets”. Int. Math. Forum, 5, 2471–2476, 2010.
[9] Shinoj, T.K.; John, S.S. “Intuitionistic fuzzy multisets and its application in medical diagnosis” World Acad. Sci.Eng. Technol., 6, 1418–1421, 2012.
[10] Eroǧlu, M. S. “The homomorphic image of a fuzzy subgroup is always a fuzzy subgroup”, Fuzzy sets and Systems, , 33(2), 255-256, 1989.
[11] Liu, H.; Wei, R.; Ge, Q. “Convex structures in a new kind of ordered fuzzy group”, Journal of Intelligent & Fuzzy Systems, (Preprint), 1-13. DOI: 10.3233/JIFS-200311, 2020.
[12] Rahmawati, M. S.; Kahar, M. S.; Amri, I.; Soekarta, R. “Level Subgroup Homomorphism in Fuzzy Subgroup”, In IOP Conference Series: Earth and Environmental Science, (Vol. 469, No. 1, p. 012120). IOP Publishing. 2020.
[13] Shinoj, T. K.; Baby, A.; Sunil, J. J. “On some algebraic structures of fuzzy multisets”, Annals of Fuzzy Mathematics and Informatics, 9(1), 77-90, 2015.
[14] Ejegwa, P. A. “Some Group Theoretic Notions in Fuzzy Multigroup Context” ,In Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures (pp. 34-62). IGI Global, 2020.
[15] Ejegwa, P. A. “Homomorphism of fuzzy multigroups and some of its properties”, Applications and Applied Mathematics, 13(1), 114-129, 2018.
[16] Onasanya, B. O.; Hoskova-Mayerova, S. “ Multi-fuzzy group induced by multisets”, Ital. J. Pure Appl. Math, 2019, 41, 597-604, 2019.
[17] Akin, C.” Multi-fuzzy soft groups”, Soft Computing, 25, 137–145. https://doi.org/10.1007/s00500-020-05471-w, 2021.
[18] Johnson, A. A.,; Ibrahim, M. A. “On homomorphism of fuzzy multigroups”, Ratio Mathematica, 39, 229, 2020.
[19] Adamu, I. M. “Homomorphism of intuitionistic fuzzy multigroups” Open J. Math. Sci, 4, 430-441, 2020.
[20] Adamu, I. M.;Tella, Y.; Alkali, A. J. “On normal Sub-intuitionistic fuzzy Multigroups” Annals of Pure and Applied Mathematics, 19(2), 127-139, 2019.
[21] Shuaib, U.; Alolaiyan, H.; Razaq, A., Dilbar, S.; Tahir, F, ” On some algebraic aspects of η-intuitionistic fuzzy subgroups” , Journal of Taibah University for Science, 14(1), 463-469, 2020.
[22] Dudek, W.A.; Davvaz,B.; Jun, Y.B. “On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups” Information Sciences, 170(2-4), 251-262, 2005.
[23] Dudek, W.A.; Zhan, J.; Davvaz, B. “Intuitionistic (S, T)-fuzzy hyperquasigroups” Soft Computing, 12(12), 1229-1238, 2008.
[24] Shinoj, T.K.; John, S.J ” Intuitionistic fuzzy multigroups” , Ann. Pure Appl. Math., 9, 131–143, 2015.
[25] Miyamoto S. “Fuzzy multisets and their generalizations”, Presented at Workshop on Multiset Processing, Romania, 21-25 August 2000.
[26] Ye S.; Ye J. “Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis”, Neutrosophic Sets and Systems, 6: 48–53, 2014.
[27] Smarandache F. “N-valued refined neutrosophic logic and its applications to physics”, Infinite Study, 4:143–146, 2013.
[28] WB, V.; Kandasamy, I.; Smarandache, F.”Neutrosophic components semigroups and multiset neutrosophic components semigroups” Symmetry, 12(5), 818, 2020.
[29] Şahin, M.; Kargın, A. “Neutrosophic triplet normed space” Open Physics, 15(1), 697-704, 2017.
[30] Smarandache, F.;Şahin, M ; Kargın, A. “Neutrosophic Triplet G-Module” Mathematics, 6(4), 53, 2018.
[31] Şahin, M.; Kargın, A. “Neutrosophic Triplet v-Generalized Metric Space” Axioms, 7(3), 67, 2018.
[32] Şahin, M.; Kargın, A.; Uz, M.S. “Neutrosophic Triplet Partial Bipolar Metric Spaces”, Neutrosophic Sets and Systems, 33, 297-312, 2020.
[33] Uluçay, V.; Şahin, M. “Neutrosophic multigroups and applications”, Mathematics, 7(1), 95, 2019.
[34] Uluçay, V. “Some concepts on interval-valued refined neutrosophic sets and their applications”, J Ambient Intell Human Comput. .1-16. https://doi.org/10.1007/s12652-020-02512-y, 2020.
[35] Ejegwa, P. A.; Ibrahim, A.M. “Some homomorphic properties of multigroups”, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, (1), 67-76, 2017.
[36] Wang H.; Smarandache F.;Zhang Y.; Sunderraman R. “Single valued neutrosophic sets”, Technical Sciences and Applied Mathematics, 6: 66-70, 2012.
[37] Ulucay, V., Deli, I., & Şahin, M. “Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making” Neural Computing and Applications, 29(3), 739-748, 2018.
[38] Bakbak, D., Uluçay, V., & Şahin, M. “ Neutrosophic soft expert multiset and their application to multiple criteria decision making”, Mathematics, 7(1), 50, 2019.
[39] Uluçay, V., Şahin, M., & Hassan, N. “ Generalized neutrosophic soft expert set for multiple-criteria decision-making”, Symmetry, 10(10), 437, 2018.
[40] Broumi, S., Bakali, A., Talea, M., Smarandache, F., Singh, P. K., Uluçay, V., & Khan, M.” Bipolar complex neutrosophic sets and its application in decision making problem”, In Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets (pp. 677-710). Springer, Cham. (2019).
[41] Uluçay, V., Deli, I., & Şahin, M. “Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems” , Complex & Intelligent Systems, 5(1), 65-78, 2019.
[42] Uluçay, V. “Q-neutrosophic soft graphs in operations management and communication network” , Soft Computing, 1-19, 2021.
[43] Hassan, N., Uluçay, V., & Şahin, M. “ Q-neutrosophic soft expert set and its application in decision making”, International Journal of Fuzzy System Applications (IJFSA), 7(4), 37-61, 2018.
[44] Şahin, M., Uluçay, V., & Menekşe, M. “Some New Operations of (α, β, γ) Interval Cut Set of Interval Valued Neutrosophic Sets” Journal of Mathematical & Fundamental Sciences, 50(2), 2018.
