The q-Rung Simplified Neutrosophic Soft Set: Its Similarity Measure

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DOI: https://doi.org/10.28924/2291-8639-24-2026-143
Published: Apr 30, 2026
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Asma Hamad, Yousef Al-Qudah, Norazrizal Aswad bin Abdul Rahman, Faisal Al-Sharqi, The q-Rung Simplified Neutrosophic Soft Set: Its Similarity Measure, Int. J. Anal. Appl., 24 (2026), 143.

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Asma Hamad, Yousef Al-Qudah, Norazrizal Aswad bin Abdul Rahman, Faisal Al-Sharqi

Abstract

In this era, the literature has paid increasing attention to uncertainty measures, particularly among researchers and experts who work with imprecise, incomplete, or vague data, which is common in real-world contexts affected by ongoing environmental and economic fluctuations. Numerous mathematical tools have been proposed to address uncertainty, including the q-rung orthopair neutrosophic set (q-RONS). This model significantly extends the capabilities of earlier frameworks, such as the Intuitionistic Fuzzy Set, Pythagorean Set, and Fermatian Set, by overcoming limitations caused by their restriction to powers less than or equal to 3. In q-RONS, the sum of the q-th powers of the truth-membership (T) and falsity-membership degrees (F) is less than or equal to 1, allowing for a broader representation of uncertain information. Despite the enhanced flexibility and effectiveness of q-RONS in handling uncertain data, existing approaches fall short in efficiently dealing with nominal-valued parameters and standard evidence required for decision-making applications. In this paper, we propose a novel hybrid structure called the q-rung simplified neutrosophic soft set (q-RSNSS), which generalizes previous models. We introduce the formal definition of our proposed model, along with its foundational concepts and mathematical properties, including operations such as union, intersection, and complement, supported by rigorous proofs. We also define fundamental algebraic operations between two neutrosophic numbers. Furthermore, we develop an algorithmic approach to multi-criteria decision-making (MCDM) under a similarity measures environment.

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References

  1. L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  2. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3.
  3. D. Molodtsov, Soft Set Theory—First Results, Comput. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5.
  4. F. Smarandache, Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set, Int. J. Pure Appl. Math. 24 (2005), 287–297.
  5. R.R. Yager, Pythagorean Fuzzy Subsets, in: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), IEEE, Edmonton, AB, Canada, 2013: pp. 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375.
  6. Z. Ma, Z. Xu, Symmetric Pythagorean Fuzzy Weighted Geometric/Averaging Operators and Their Application in Multicriteria Decision-Making Problems, Int. J. Intell. Syst. 31 (2016), 1198–1219. https://doi.org/10.1002/int.21823.
  7. C. Huang, M. Lin, Z. Xu, Pythagorean Fuzzy MULTIMOORA Method Based on Distance Measure and Score Function: Its Application in Multicriteria Decision Making Process, Knowl. Inf. Syst. 62 (2020), 4373–4406. https://doi.org/10.1007/S10115-020-01491-Y.
  8. R.R. Yager, Generalized Orthopair Fuzzy Sets, IEEE Trans. Fuzzy Syst. 25 (2017), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005.
  9. X. Peng, J. Dai, H. Garg, Exponential Operation and Aggregation Operator for q-Rung Orthopair Fuzzy Set and Their Decision-Making Method with a New Score Function, Int. J. Intell. Syst. 33 (2018), 2255–2282. https://doi.org/10.1002/int.22028.
  10. X. Shu, Z. Ai, Z. Xu, J. Ye, Integrations of Q-Rung Orthopair Fuzzy Continuous Information, IEEE Trans. Fuzzy Syst. 27 (2019), 1974–1985. https://doi.org/10.1109/TFUZZ.2019.2893205.
  11. Z. Ai, Z. Xu, R.R. Yager, J. Ye, q-Rung Orthopair Fuzzy Integrals in the Frame of Continuous Archimedean T-Norms and T-Conorms and Their Application, IEEE Trans. Fuzzy Syst. 29 (2021), 996–1007. https://doi.org/10.1109/TFUZZ.2020.2965887.
  12. J. Gao, Z. Liang, J. Shang, Z. Xu, Continuities, Derivatives, and Differentials of q-Rung Orthopair Fuzzy Functions, IEEE Trans. Fuzzy Syst. 27 (2019), 1687–1699. https://doi.org/10.1109/TFUZZ.2018.2887187.
  13. A. Al-Quran, F. Al-Sharqi, A.M. Djaouti, q-Rung Simplified Neutrosophic Set: A Generalization of Intuitionistic, Pythagorean and Fermatean Neutrosophic Sets, AIMS Math. 10 (2025), 8615–8646. https://doi.org/10.3934/math.2025395.
  14. J. Ye, A Multicriteria Decision-Making Method Using Aggregation Operators for Simplified Neutrosophic Sets, J. Intell. Fuzzy Syst. 26 (2014), 2459–2466. https://doi.org/10.3233/IFS-130916.
  15. R. Jansi, K. Mohana, F. Smarandache, Correlation Measure for Pythagorean Neutrosophic Sets with T and F Are Dependent Neutrosophic Components, Neutrosophic Sets Syst. 30 (2019), 202–212. https://doi.org/10.5281/zenodo.3569786.
  16. C. Sweety, R. Jansi, Fermatean Neutrosophic Sets, Int. J. Adv. Res. Comput. Commun. Eng. 10 (2021), 23–27.
  17. M.G. Voskoglou, F. Smarandache, M. Mohamed, Q-Rung Neutrosophic Sets and Topological Spaces, Neutrosophic Syst. Appl. 15 (2024), 58–66. https://doi.org/10.61356/j.nswa.2024.1515356.
  18. P. Liu, M. Azeem, M. Sarfraz, S. Swaray, and B. Almohsen, A Parametric Similarity Measure for Neutrosophic Set and Its Applications in Energy Production, Heliyon, 10 (2024), e38272.
  19. A.H. Ganie, Y. Al-Qudah, Z. Salleh, A. Alhawarat, A Novel Picture Fuzzy Similarity Measure: Theory and Practical Applications, IEEE Access 13 (2025), 133426–133437. https://doi.org/10.1109/ACCESS.2025.3588325.
  20. Y. Al-Qudah, A.H. Ganie, Bidirectional Approximate Reasoning and Pattern Analysis Based on a Novel Fermatean Fuzzy Similarity Metric, Granul. Comput. 8 (2023), 1767–1782. https://doi.org/10.1007/s41066-023-00396-9.
  21. A.M. Jaradat, Y. Al-Qudah, A. Alsoboh, F. Al-Sharqi, A.A. Al-Maqbali, A New Approach of Possibility Single-Valued Neutrosophic Set and Its Application in Decision-Making Environment, Int. J. Anal. Appl. 23 (2025), 213. https://doi.org/10.28924/2291-8639-23-2025-213.
  22. P. Majumdar, S. Samanta, On Similarity Measures of Fuzzy Soft Sets, Int. J. Adv. Soft Comput. Appl. 3 (2011), 1–8.
  23. A. Kharal, Distance and Similarity Measures for Soft Sets, New Math. Nat. Comput. 06 (2010), 321–334. https://doi.org/10.1142/S1793005710001724.
  24. Y. Jiang, Y. Tang, H. Liu, Z. Chen, Entropy on Intuitionistic Fuzzy Soft Sets and on Interval-Valued Fuzzy Soft Sets, Inf. Sci. 240 (2013), 95–114. https://doi.org/10.1016/j.ins.2013.03.052.
  25. C. Wang, A. Qu, Entropy, Similarity Measure and Distance Measure of Vague Soft Sets and Their Relations, Inf. Sci. 244 (2013), 92–106. https://doi.org/10.1016/j.ins.2013.05.013.
  26. W.K. Min, Similarity in Soft Set Theory, Appl. Math. Lett. 25 (2012), 310–314. https://doi.org/10.1016/j.aml.2011.09.006.
  27. A. De Luca, S. Termini, A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory, Inf. Control. 20 (1972), 301–312. https://doi.org/10.1016/S0019-9958(72)90199-4.
  28. C.P. Pappis, N.I. Karacapilidis, A Comparative Assessment of Measures of Similarity of Fuzzy Values, Fuzzy Sets Syst. 56 (1993), 171–174. https://doi.org/10.1016/0165-0114(93)90141-4.
  29. C.P. Pappis, N.I. Karacapilidis, Application of a Similarity Measure of Fuzzy Sets to Fuzzy Relational Equations, Fuzzy Sets Syst. 75 (1995), 135–142. https://doi.org/10.1016/0165-0114(95)00023-E.
  30. Z. Liu, K. Qin, Z. Pei, Similarity Measure and Entropy of Fuzzy Soft Sets, Sci. World J. 2014 (2014), 161607. https://doi.org/10.1155/2014/161607.
  31. X. Yang, T.Y. Lin, J. Yang, Y. Li, D. Yu, Combination of Interval-Valued Fuzzy Set and Soft Set, Comput. Math. Appl. 58 (2009), 521–527. https://doi.org/10.1016/j.camwa.2009.04.019.
  32. F. Feng, Y.B. Jun, X. Liu, L. Li, An Adjustable Approach to Fuzzy Soft Set Based Decision Making, J. Comput. Appl. Math. 234 (2010), 10–20. https://doi.org/10.1016/j.cam.2009.11.055.
  33. Y. Al-Qudah, A.O. Hamadameen, N.A. Kh, F. Al-Sharqi, A New Generalization of Interval-Valued Q-Neutrosophic Soft Matrix and Its Applications, Int. J. Neutrosophic Sci. 25 (2025), 242–257. https://doi.org/10.54216/IJNS.250322.
  34. N. Hassan, Y. Al-Qudah, Fuzzy Parameterized Complex Multi-Fuzzy Soft Set, J. Phys.: Conf. Ser. 1212 (2019), 012016. https://doi.org/10.1088/1742-6596/1212/1/012016.
  35. A.A.R.M. Malkawi, A.M. Rabaiah, Fixed Point Theorems in Neutrosophic Mr-Metric Spaces with Measure-Theoretic Convergence, Int. J. Anal. Appl. 24 (2026), 61. https://doi.org/10.28924/2291-8639-24-2026-61.
  36. Z. Zhang, A Rough Set Approach to Intuitionistic Fuzzy Soft Set Based Decision Making, Appl. Math. Model. 36 (2012), 4605–4633. https://doi.org/10.1016/j.apm.2011.11.071.