Volume 18 • Issue 2 • PP: 227-242 • 2022
Introduction to Restricted Neutrosophic Set and Its Application
View PDF Abstract
This paper is devoted to introduce a novel concept known as restricted neutrosophic set (RNS) as another subclass of neutrosophic set (NS). The purpose of introducing the notion of RNS is to give a new mathematical theory that is more promising and purposeful than the existing fuzzy-centric theories to solve the uncertainty based real-world problems in a lucid manner. From decision-makers point of view, the new mathematical tool can be viewed as a direct extension of Pythagorean neutrosophic set (PNS). The PNS has its own inherent limitation for which the decision-makers can’t answer a certain type of problem. For example, in a certain problem, if we consider the degree of truth-membership =0.8, degree of indeterminate-membership , and the degree of falsity-membership =0.8, then it gives an absurd result under PNS. To remove such kind of absurdity, there is a demand to introduce another superior set-theoretical concept that provides more information for the decision-makers. This gives rise to the introduction of RNS. In RNS, we choose any value belongs to for the three membership degrees so that their product always limited to 1. So, the beauty of RNS is that it can accommodate more information within small range with relaxed membership values i.e under RNS we can consider the maximum membership triplet as . Undoubtedly the RNS gives more compact set-theoretical model to describe imprecise knowledge with ease. Finally, a decision-making approach based algorithm is introduced and applied to solve medical diagnosis problem.
Keywords
References
[1] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. doi:10.1016/s0019-9958(65)90241-x
[2] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96. doi:10.1016/s0165-0114(86)80034-3
[3] Yager, R. (2013). Pythagorean fuzzy subsets. IEEE 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS, 57-61. doi:10.1109/ifsa-nafips.2013.6608375
[4] Cuong, B. C. (2014). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30, 409-420.
[5] Ashraf, S., Abdullah, S., Aslam, M., Qiyas, M., & Kutbi, M. A. (2019). Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms. Journal of Intelligent & Fuzzy Systems, 36, 6089-6102.
[6] Yager, R. R. (2016). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222-1230.
[7] Senapati, T., & Yager, R. R. (2020). Fermatean fuzzy sets. Journal of Ambient Intelligence and Humanized Computing, 11, 663-674.
[8] Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics, 24, 287-297.
[9] Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Review of the Air Force Academy, 1, 10-14.
[10] Jansi, R., Mohana, K., & Smarandache, F. (2019). Correlation measure for Pythagorean neutrosophic sets with T and F as dependent neutrosophic components. Neutrosophic Sets and Systems, 30, 202-212.
[11] Ajay, D., & Chellamani, P. (2020). Pythagorean neutrosophic fuzzy graphs. International Journal of Neutrosophic Science, 11, 108-114. doi: https://doi.org/10.54216/IJNS.0110205.
[12] Veerappan, C., & Arulselvam, A. (2021). Pythagorean neutrosophic ideals in semigroups. Neutrosophic Sets and Systems, 41, 258-269.
[13] Rajan, J., & Krishnaswamy, M. (2020). Similarity measures of Pythagorean neutrosophic sets with dependent neutrosophic components between T and F. Journal of New Theory, 33, 85-94.
[14] Jansi, R., & Mohana, K. (2021). Pairwise Pythagorean neutrosophic P-spaces (with dependent neutrosophic components between T and F). Neutrosophic Sets and Systems, 246-257.
Cite This Article
Choose your preferred format