Erzincan University Journal of Science and Technology 2149-4584 Erzincan Binali Yıldırım Üniversitesi 10.18185/erzifbed.1114721 Engineering Mühendislik On Neutrosophic Soft Multisets and Neutrosophic Soft Multi Topological Spaces https://orcid.org/0000-0002-4317-652X Yolcu Adem Kafkas Üniversitesi https://orcid.org/0000-0003-3654-1004 Aka Büşra KAFKAS ÜNİVERSİTESİ 03 31 2023 16 1 89 109 05 11 2022 03 13 2023 Copyright © 2008, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 2008 Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

Bu çalışma da, yeni bir hibrit sistem olan neutrosophic esnek çoklu kümeler tanıtılmaktadır. Ayrıca, alt küme, eşit küme, boş küme, mutlak küme, birleşim, kesişim, farklı gibi bazı temel özellikleri bu kavramlar üzerinde çalıştık. Dahası, neutrosophic esnek çoklu topolojik uzayları tanıttık. Bu topolojik uzaylar üzerinde açık küme, kapalı küme, iç, kapanış gibi bazı önemli kavramlar araştırılmıştır. İncelenen tüm kavramların önemli özellikleri araştırılmış, bazı önemli teoremler ispatlanmış ve konu ile ilgili çeşitli örnekler sunulmuştur.

 multisets neutrosophic soft multisets neutrosophic soft multi topology [1] Bakioglu, G., & Atahan, A. O. (2021). AHP integrated TOPSIS and VIKOR methods with Pythagorean fuzzy sets to prioritize risks in self-driving vehicles. Applied Soft Computing, 99, 106948. [2] Basumatary, B., Wary, N., Mwchahary, D. D., Brahma, A. K., Moshahary, J., Basumatary, U. R., & Basumatary, J. (2021). A Study on Some Properties of Neutrosophic Multi Topological Group. Symmetry, 13(9), 1689. [3] Bera T., Mahapatra N. K., Introduction to neutrosophic soft topological space, Opsearch, 54(4), (2017) 841–867. [4] Blizard,W. Multiset theory. Notre Dame J. Form. Logic 1989, 30, 36–66. [5] Boyacı, A. Ç., & Şişman, A. (2022). Pandemic hospital site selection: a GIS-based MCDM approach employing Pythagorean fuzzy sets. Environmental Science and Pollution Research, 29(2), 1985-1997. [6] Chang, C. L., Fuzzy topological spaces, J. Math. Anal. Appl. 24(1), (1968) 182–190. [7] Coker D., A note on intuitionistic sets and intuitionistic points, Tr. J. of Mathematics, 20, (1996) 343-351. [8] Das, R., & Tripathy, B. C. (2020). Neutrosophic multiset topological space. Neutrosophic sets and systems, 35, 142-152. [9] Deli I., Broumi S., Neutrosophic soft relations and some properties, Ann. Fuzzy Math. Inform. 9(1), (2015) 169–182. [10] Ejegwa, P. A. (2015). New operations on intuitionistic fuzzy multisets. J. of Mathematics and Informatics, 3, 17-23. [11] Garg, H. A new improved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method. Int. J. Uncertain. Quantif. 2017, 7, 463–474. [12] Ç Gunduz, T. Y. Ozturk, and S. Bayramov, “Separation axioms on neutrosophic soft topological spaces,” Turkish Journal of Mathematics, vol. 43, no. 1, pp. 498–510, 2019. [13] Kandil, A.; Nouth, A.A.; El-Sheikh, S.A. On fuzzy bitopological spaces. Fuzzy Sets Syst. 1995, 74, 353–363. [14] Kelly, J.C. Bitopological spaces. Proc. Lond. Math. Soc. 1963, 3, 71–89. [15] Lee, S.J.; Kim, J.T. Some Properties of Intuitionistic Fuzzy Bitopological Spaces. In Proceedings of the 6th International Conference on Soft Computing and Intelligent Systems, and The 13th IEEE International Symposium on Advanced Intelligence Systems, Kobe, Japan, 20–24 November 2012; pp. 20–24 [16] Lupianez, F.G. On neutrosophic topology. Int. J. Syst. Cybern. 2008, 37, 797–800. [17] Lupianez, F.G. Interval neutrosophic sets and topology. Int. J. Syst. Cybern. 2009, 38, 621–624. [18] Lupianez, F.G. On neutrosophic paraconsistent topology. Int. J. Syst. Cybern. 2010, 39, 598–601. [19] P. K. Maji, A. R. Roy, and R. Biswas, “An application of soft sets in a decision making problem,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1077–1083, 2002 [20] P. K. Maji, R. Biswas, and A. R. Roy, “Soft set theory,” Computers & Mathematics with Applications, vol. 45, no. 4-5, pp. 555–562, 2003 [21] Maji P. K., Neutrosophic soft set, Ann. Fuzzy Math. Inform. 5(1), (2013) 157–168. [22] Miyamoto, S. Fuzzy Multisets and Their Generalizations. In Multiset Processing; Springer: Berlin, Germany, 2001; pp. 225–235. [23] Miyamoto, S. (2000). Multisets and fuzzy multisets. In Soft computing and human-centered machines (pp. 9-33). Springer, Tokyo. [24] Molodtsov D., Soft Set Theory-First Results, Comput. Math. Appl.37 (1999) 19-31. [25] D. Molodtsov, V. Y. Leonov, and D. V. Kovkov, “Soft sets technique and its application,” Nechetkie Sistemy Myagkie Vychisleniya, vol. 1, pp. 8–39, 2006. [26] T. Y. Ozturk, “Some structures on neutrosophic topological spaces,” Applied Mathematics and Nonlinear Sciences, vol. 6, no. 1, pp. 467–478, 2021. [27] T. Y. Ozturk, C. G. Aras, and S. Bayramov, “A new approach to operations on neutrosophic soft sets and to neutrosophic soft topological spaces,” Communications in Mathematics and Applications, vol. 10, no. 3, pp. 481–493, 2019. [28] T. Y. Ozturk, E. Karatas, and A. Yolcu, “On neutrosophic soft continuous mappings,” Turkish Journal of Mathematics, vol. 45, no. 1, pp. 81–95, 2021. [29] Peng, X.; Liu, L. Information measures for q-rung orthopair fuzzy sets. Int. J. Intell. Syst. 2019, 34, 1795–1834. [30] Pinar, A.; Boran, F.E. A q-rung orthopair fuzzy multi-criteria group decision making method for supplier selection based on a novel distance measure. Int. J. Mach. Learn. Cybern. 2020, 11, 1749–1780. [31] Rajarajeswari, P., & Uma, N. (2014). Normalized hamming similarity measure for intuitionistic fuzzy multi sets and its application in medical diagnosis. International Journal of Mathematics Trends and Technology, 5(3), 219-225. [32] Riesgo, Á., Alonso, P., D az, I., & Montes, S. (2018). Basic operations for fuzzy multisets. International Journal of Approximate Reasoning, 101, 107-118. [33] Salama, A.A.; Smarandache, F.; Kroumov, V. Closed sets and Neutrosophic Continuous Functions. Neutrosophic Sets Syst. 2014, 4, 4–8. [34] Smarandache, F., Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math. 24, (2005) 287–297. [35] Smarandache, F. Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras and Applications; Pons Publishing House Brussels: Brussels, Belgium, 2017; p. 323. [36] Shinoj, T. K., & John, S. J. (2012). Intuitionistic fuzzy multisets and its application in medical diagnosis. World Academy of Science, Engineering and Technology, 6(1), 1418-1421. [37] Uluçay, V., & Şahin, M. (2019). Neutrosophic multigroups and applications. Mathematics, 7(1), 95. [38] Ullah, K., Mahmood, T., Ali, Z., & Jan, N. (2020). On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex & Intelligent Systems, 6(1), 15-27. [39] Yager, R.R. On the theory of bags. Int. J. Gen Syst. 1986, 13, 23-37. [40] Yager, R.R. Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 2017, 25, 1222–1230. [41] Yager, R.R.; Alajlan, N. Approximate reasoning with generalized orthopair fuzzy sets. Inf. Fusion 2017, 38, 65–73 [42] Ye, S., & Ye, J. (2014). Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis. Neutrosophic sets and systems, 6(1), 9. [43] A. Yolcu, E. Karatas, and T. Y. Ozturk, “A new approach to neutrosophic soft mappings and application in decision making,” in Neutrosophic Operational Research, F. Smarandache and M. Abdel-Basset, Eds., Springer, Cham, pp. 291–313, 2021. [44] Zadeh L. A., Fuzzy Sets, Inform. Control 8, (1965) 338-353. [45] Zhou, Q., Mo, H., & Deng, Y. (2020). A new divergence measure of pythagorean fuzzy sets based on belief function and its application in medical diagnosis. Mathematics, 8(1), 142.