Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations

Sharifah Sakinah Syed; Nasreen; Murugan

doi:https://doi.org/10.54216/IJNS.250145

Full Length Article

Volume 25 • Issue 1 • PP: 505-517 • 2025

Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations

Sharifah Sakinah Syed ahmad ^1*

mail

,

Nasreen Kausar ²

mail

,

Murugan Palanikumar ³

mail

¹Department of Intelligent Computing & Analytics (ICA), Faculty of Information & Communication Technology, Universiti Teknikal Malaysia Melaka

²Faculty of Arts and Science, Yildiz Technical University, Esenler, 34220, Istanbul, Turkey

³Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.250145

format_quote Cite this article

Received: January 29, 2024 Revised: April 27, 2024 Accepted: July 19, 2024

View PDF open_in_new

Abstract

The Type-II Diophantine neutrosophic interval valued soft set (Type-II DioNSIVSS) and related similarity measure are presented in this study. An extension of the neutrosophic interval valued soft set (NSIVSS) and the Diophantine fuzzy soft set is the Type-II DioNSIVSS. The suggested measure for Type-II DioNSIVSS assessment. We support a method of solving the problem using the Type-II soft set model. To demonstrate how they can be applied to successfully handle uncertainty-related challenges, illustrative examples are given.

Keywords

Type-II DioNSIVS set PyNSIVS set decision making problem

References

[1] L. A. Zadeh, Fuzzy sets, Information and control 8(3),(1965), 338-353.

[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20(1), (1986), 87-96.

[3] R.R. Yager, Pythagorean membership grades in multi criteria decision making, IEEE Trans. Fuzzy Systems, 22, (2014), 958-965

[4] Bui Cong Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics, 30(4), (2014), 409- 420.

[5] B.C. Cuong and V. Kreinovich, Picture fuzzy sets a new concept for computational intelligence problems, in Proceedings of 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, (2013), 1-6.

[6] F. Smarandache, A unifying field in logics neutrosophy neutrosophic probability, set and logic, Rehoboth American Research Press (1999).

[7] R.Jansi, K.Mohana and F. Smarandache, Correlation measure for Pythagorean neutrosophic sets with T and F as dependent neutrosophic components, Neutrosophic Sets and Systems, 30,(2019), 202-212.

[8] S. Alkhazaleh, A.R. Salleh, and N. Hassan, possibility fuzzy soft set, Advances in Decision Sciences,

(2011), 1-18.

[9] SG Quek, H Garg, G Selvachandran,MPalanikumar, K Arulmozhi,VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set, Soft Computing, 1-27, 2023.

[10] M Palanikumar, K Arulmozhi, A Iampan, Multi criteria group decision making based on VIKOR and TOPSIS methods for Fermatean fuzzy soft with aggregation operators, ICIC Express Letters 16 (10), 1129–1138, 2022.

[11] M Palanikumar, K Arulmozhi, MCGDM based on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators, Neutrosophic Sets and Systems,, 538-555, 2022.

[12] M Palanikumar, S Broumi, Square root (ℏ, ε)phantine neutrosophic normal interval-valued sets and their aggregated operators in application to multiple attribute decision making, International Journal of Neutrosophic Science, 4, 2022.

[13] D. Molodtsov, Soft set theory first results, Computers and Mathematics with Applications, 37, (1999), 19-31.

[14] P.K. Maji, R. Biswas and A.R. Roy, On intuitionistic fuzzy soft set, Journal of Fuzzy Mathematics, 9(3), (2001), 677-692.

[15] P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft set, Journal of Fuzzy Mathematics, 9(3), (2001), 589-602.

[16] Yong Yang, Chencheng Liang, Shiwei Ji and Tingting Liu, Adjustable soft discernibility matrix based on picture fuzzy soft sets and its applications in decision making, Journal of Intelligent and Fuzzy Systems, 29, (2015), 1711-1722.

[17] X.D. Peng, Y. Yang, J.P. Song, Pythagorean fuzzy soft set and its application, Computer Engineering, 41(7), (2015), 224-229.

[18] P Majumdar, S.K. Samantab, Generalized fuzzy soft sets, Computers and Mathematics with Applications, 59, (2010), 1425-1432.

[19] Shawkat Alkhazaleh and Abdul Razak Salleh, Generalized interval valued fuzzy soft set, Journal of Applied Mathematics, (2012), 1-18.

[20] Faruk Karaaslan, Possibility neutrosophic soft sets and PNS-decision making method, Applied Soft Computing 54, (2017) 403-414.

[21] Souhail Dhouib, Said Broumi, M. Lathamaheswari, Single valued trapezoidal neutrosophic travelling salesman problem with novel greedy method, the dhouib matrix TSP1, International Journal of Neutrosophic Science, 17(2), 2021, 144-157.

[22] M. Lathamaheswari, Said Broumi, Florentin Smarandache, S. Sudha, Neutrosophic perspective of neutrosophic probability distributions and its application, International Journal of Neutrosophic Science, 17(2), 2021, 96-109.

Cite This Article

Choose your preferred format

format_quote

ahmad, Sharifah Sakinah Syed, Kausar, Nasreen, Palanikumar, Murugan. "Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 1, 2025, pp. 505-517. DOI: https://doi.org/10.54216/IJNS.250145

ahmad, S., Kausar, N., Palanikumar, M. (2025). Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations. International Journal of Neutrosophic Science, Volume 25(Issue 1), 505-517. DOI: https://doi.org/10.54216/IJNS.250145

ahmad, Sharifah Sakinah Syed, Kausar, Nasreen, Palanikumar, Murugan. "Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations." International Journal of Neutrosophic Science Volume 25, no. Issue 1 (2025): 505-517. DOI: https://doi.org/10.54216/IJNS.250145

ahmad, S., Kausar, N., Palanikumar, M. (2025) 'Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations', International Journal of Neutrosophic Science, Volume 25(Issue 1), pp. 505-517. DOI: https://doi.org/10.54216/IJNS.250145

ahmad S, Kausar N, Palanikumar M. Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 1):505-517. DOI: https://doi.org/10.54216/IJNS.250145

S. ahmad, N. Kausar, M. Palanikumar, "Finding new similarities measures for Type-II Diophantine neutrosophic interval valued soft sets and its basic operations," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 1, pp. 505-517, 2025. DOI: https://doi.org/10.54216/IJNS.250145

Digital Archive Ready