Axiomatic Characterizations of Quadripartitioned Single Valued Neutrosophic Rough Sets

Abstract

In this paper, axiomatic characterizations of quadripartitioned single-valued neutrosophic rough sets have been studied and also studied some properties of quadripartitioned single-valued neutrosophic rough sets. A numerical example in medical diagnosis is given, which is based on the similarity measure of quadripartitioned single-valued neutrosophic rough sets.

Keywords

• Quadripartitioned single valued neutrosophic rough sets,similarity measure,axiomatic characterization,quadripartitioned single-valued neutrosophic number

References

1. L. Zadeh, Fuzzy Sets, Information and Control 8(3) (1965) 87-96.
2. K. Atanasov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986) 87-96.
3. F. Smarandache, Neutrosophy, Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, (1998) p 105.
4. F. Smarandache, A Unifying Field in Logics, Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, (1999) Rehoboth.
5. Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences 11(5) (1982) 341-356.
6. S. Broumi, F. Smarandache, Rough Neutrosophic Sets. Italian Journal of Pure and Applied Mathematics 32 (2014) 493-502. [7] F. Smarandache, n-Valued Refined Neutrosophic Logic and Its Applications in Physics, Progress in Physics, 4 (2013) 143-146.
7. H. Wang, F. Smarandache, Y. Q. Zhang, R. Sunderraman, Single Valued Neutrosophic Sets, Multispace Multistruct 4 (2010) 410-413.
8. S Broumi, A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari, R. Kumar, Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment, Complex and Intelligent Systems, (2019) 1-8.

9. S. Broumi, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari, M. Parimala, Shortest Path Problem in Fuzzy, Intuitionistic Fuzzy and Neutrosophic Environment: An Overview, Complex and Intelligent Systems 5 (2019) 371–378.
10. S. Broumi, D. Nagarajan, A. Bakali, M. Talea, F. Smarandache, M. Lathamaheswari, The Shortest Path Problem in Interval Valued Trapezoidal and Triangular Neutrosophic Environment, Complex and Intelligent Systems 5 (2019) 391–402.
11. H. L. Yang, A Hybrid Model of Single-Valued Neutrosophic Sets and Rough Sets: Single-Valued Neutrosophic Rough Set Model, Soft Computing 21 (2017) 6253-6267.
12. N. D. Belnap, A Useful Four-Valued Logic, Modern Uses of Multiple-Valued Logic, (1977) 5-37.
13. K. Mohana, M. Mohanasundari, Quadripartitioned Single Valued Neutrosophic Rough Sets, Nirmala Annual Research Congress (NARC-2018), ISBN-978-93-5321-859-1, 3 (2018) p. 165.
14. R. Chatterjee, P. Majumdar, S. K. Samanta, On Some Similarity Measures and Entropy on Quadripartitioned Single-Valued Neutrosophic Sets, Journal of Intelligent and Fuzzy Systems 30 (2016) 2475-2485.