Results On Sb-Bipolar Interval Neutrosophic Set

Abstract

The neutrosophic set is mathematical tool for dealing with uncertain.  In this paper, we extend it further by introducing the definition of a SB-bipolar interval neutrosophic set. Mathematical operations such as complement, union, and intersection are developed for these sets. Theorems related to SB-bipolar interval neutrosophic set are also proved.

Keywords: Bipolar neutrosophic sets, fuzzy set, interval neutrosophic sets, interval fuzzy set, neutrosophic sets

المستخلص:
 دالة  النتروفزك  Neutrosophicمن الدوال الرياضية  التي تستخدم في دراسة البيانات المتعددة  والغير دقيقة  واستنادا علي هذه الدالة الرياضية   تم تعريف  دالة  جديدة وهي اس بي النتروفزك ذات الفترة ثنائية القطب  في هذه الورقة البحثية لتكون اوسع وأكثر شمولا في التعامل مع البيانات. كما تم دراسة الخصائص الرياضية لهذه الدالة واثبات العديد من النظريات المتعلقة بها.

الكلمات المفتاحية: الدالة نتروفزك ثنائية القطب، الدالة الضبابية، الدالة نترو فزك، الدالة الضبابية ذات الفترة، الدالة نتروفزك ذات الفترة

References

Abdulkadhim, M. M., Imran, Q. H., Al-Obaidi, A. H., & Broumi, S. (2022). On neutrosophic crisp generalized alpha generalized closed sets. International Journal of Neutrosophic Science, 19(1), 107–115. https://doi.org/10.54216/IJNS.190108

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3

Das, R., Smarandache, F., & Tripathy, B. C. (2020). Neutrosophic fuzzy matrices and some algebraic operations. Neutrosophic Sets and Systems, 32, 1–15.

Deli, I., Ali, M., & Smarandache, F. (2015). Bipolar neutrosophic sets and their application based on multi-criteria decision-making problems. Proceedings of the International Conference on Advanced Mechatronic Systems, 22–24. https://doi.org/10.1109/ICAMechS.2015.7287068

Gulistan, M., Yaqoob, N., Elmoasry, A., & Alebraheem, J. (2021). Complex bipolar fuzzy sets: An application in a transport company. Journal of Intelligent & Fuzzy Systems, 40(3), 3981–3997. https://doi.org/10.3233/JIFS-200234

Hamad, F. A., & Algamudi, B. M. (2023). N-cylindrical fuzzy interval neutrosophic set. Al-Satil, 17(35).

Lee, K. M. (2000). Bipolar-valued fuzzy sets and their operations. In Proceedings of the International Conference on Intelligent Technologies (pp. 307–312). Bangkok, Thailand.

Satya Narayana, B., & Devanandam. (2023). SB-neutrosophic structures in BCK/BCI-algebras. Journal of Hyperstructures, 12(1), 51–77.

Smarandache, F. (1999). Unifying field in logics: Neutrosophic logic, neutrosophy, neutrosophic set, neutrosophic probability. American Research Press.

Turksen, I. B. (1986). Interval-valued fuzzy sets based on normal forms. Fuzzy Sets and Systems, 20(2), 191–210. https://doi.org/10.1016/0165-0114(86)90077-1

Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2005). Interval neutrosophic sets and logic: Theory and applications in computing. Hexis. (Neutrosophic Book Series, No. 5).

Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace and Multistructure, 4, 410–413.

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X