ASPG Menu
search

American Scientific Publishing Group

verified Journal

International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

Publication Model

Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 23Issue 3PP: 29-43 • 2024

Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers

Ligin P. Mathew 1* ,
Lovelymol Sebastian 1 ,
Baiju Thankachan 2
1Department of Mathematics, St Thomas College, Palai,Kerala, India
2Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal-576104, Karnataka,India
* Corresponding Author.
Received: August 02, 2023 Revised: November 18, 2023 Accepted: January 18, 2024

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.

Cite This Article

Choose your preferred format

format_quote
Mathew, Ligin P., Sebastian, Lovelymol, Thankachan, Baiju. "Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, 2024, pp. 29-43. DOI: https://doi.org/10.54216/IJNS.230303
Mathew, L., Sebastian, L., Thankachan, B. (2024). Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers. International Journal of Neutrosophic Science, Volume 23(Issue 3), 29-43. DOI: https://doi.org/10.54216/IJNS.230303
Mathew, Ligin P., Sebastian, Lovelymol, Thankachan, Baiju. "Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers." International Journal of Neutrosophic Science Volume 23, no. Issue 3 (2024): 29-43. DOI: https://doi.org/10.54216/IJNS.230303
Mathew, L., Sebastian, L., Thankachan, B. (2024) 'Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers', International Journal of Neutrosophic Science, Volume 23(Issue 3), pp. 29-43. DOI: https://doi.org/10.54216/IJNS.230303
Mathew L, Sebastian L, Thankachan B. Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 3):29-43. DOI: https://doi.org/10.54216/IJNS.230303
L. Mathew, L. Sebastian, B. Thankachan, "Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, pp. 29-43, 2024. DOI: https://doi.org/10.54216/IJNS.230303
Digital Archive Ready