1
Department of Mathematics, St Thomas College, Palai,Kerala, India
(liginpmathew@stthomascollege.info)
2
Department of Mathematics, St Thomas College, Palai,Kerala, India
(lovelymaths95@gmail.com)
3
Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal-576104, Karnataka,India
(baiju.t@manipal.edu)
Abstract :
Almost all situations that arise in applied mathematics involve uncertainty, inconsistency, and indeterminacy. This can be simultaneously handled by the use of single valued neutrosophic fuzzy sets and single valued neutrosophic fuzzy numbers. In this paper, we propose the operations of addition, subtraction, and scalar multiplication on trapezoidal single valued neutrosophic fuzzy numbers. We introduce some component-wise interval operations on the union of closed bounded intervals. Then we show how this can be used to perform the proposed operations on trapezoidal single valued neutrosophic fuzzy numbers with the help of finite α− cuts, finite β− cuts, finite γ− cuts, and finite δ− cuts, which we define in this paper itself.
Keywords :
Single valued neutrosophic fuzzy number; Trapezoidal single valued neutrosophic fuzzy number; Operations on Trapezoidal single valued neutrosophic fuzzy number.
References :
[1] L. A. Zadeh, ”Fuzzy sets,” Information and control, vol.8, no.3,pp. 338–353, 1965.
[2] S. Das, B. K. Roy, M. B. Kar, S. Kar, and D. Pamuˇcar, “Neutrosophic fuzzy set and its application in decision making,” Journal of Ambient Intelligence and Humanized Computing, vol. 11, no. 11, pp. 5017– 5029, 2020.
[3] H.Wang, F. Smarandache, Y. Zhang, and R. Sunderraman, Single valued neutrosophic sets, Infinite study, 2010.
[4] L. P. Mathew and L. Sebastian, “An introduction to single valued neutrosophic fuzzy numbers, trapezoidal single valued neutrosophic fuzzy numbers and triangular single valued neutrosophic fuzzy numbers,” AIP Conference Proceedings, vol. 2875, AIP Publishing, 2023.
[5] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986.
[6] F. Smarandache, ”Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & SyntheticAnalysis,” Rehoboth, NM: American Research Press, 1998.
[7] D. Dubois and H. Prade, ”Fuzzy sets and systems: theory and applications,” Mathematics in Science and Engineering, Vol. 144, pp 1-393, 1980.
| Style | # |
|---|---|
| MLA | Ligin P. Mathew, Lovelymol Sebastian, Baiju Thankachan. "Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers." International Journal of Neutrosophic Science, Vol. 23, No. 3, 2024 ,PP. 29-43 (Doi : https://doi.org/10.54216/IJNS.230303) |
| APA | Ligin P. Mathew, Lovelymol Sebastian, Baiju Thankachan. (2024). Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 29-43 (Doi : https://doi.org/10.54216/IJNS.230303) |
| Chicago | Ligin P. Mathew, Lovelymol Sebastian, Baiju Thankachan. "Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers." Journal of International Journal of Neutrosophic Science, 23 no. 3 (2024): 29-43 (Doi : https://doi.org/10.54216/IJNS.230303) |
| Harvard | Ligin P. Mathew, Lovelymol Sebastian, Baiju Thankachan. (2024). Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 29-43 (Doi : https://doi.org/10.54216/IJNS.230303) |
| Vancouver | Ligin P. Mathew, Lovelymol Sebastian, Baiju Thankachan. Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 3 ): 29-43 (Doi : https://doi.org/10.54216/IJNS.230303) |
| IEEE | Ligin P. Mathew, Lovelymol Sebastian, Baiju Thankachan, Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 3 , (2024) : 29-43 (Doi : https://doi.org/10.54216/IJNS.230303) |