A New Approach of Possibility Single-Valued Neutrosophic Set and Its Application in Decision-Making Environment

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DOI: https://doi.org/10.28924/2291-8639-23-2025-213
Published: Sep 8, 2025
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Abeer M.M. Jaradat, Yousef Al-Qudah, Abdullah Alsoboh, Faisal Al-Sharqi, Abdullrahman 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.

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Abeer M.M. Jaradat, Yousef Al-Qudah, Abdullah Alsoboh, Faisal Al-Sharqi, Abdullrahman A. Al-Maqbali

Abstract

The single-valued neutrosophic set (SVNS) is a widely known model for dealing with uncertain, conflicting, and indeterminate information. In practice, the SVNSs are very useful tools to be used in solving multi-criteria decision-making (MCDM), but in the process of processing by the three functions of SVNS the evaluation process for this handling disappears. To overcome this deficiency, we present in this work a new approach called possibility single-valued neutrosophic set (PSVNS) that differs from previous approaches. The implementation of this proposed approach in this work is based on giving each of the three functions in SVNS a fuzzy degree ranging between 0 and 1. As a result, firstly, the elementary notion of possibility single neutrosophic set is proposed, and some of its primary properties, i.e., subset, null set, absolute set, and complement are explored, as well as some numerical examples that explain the mechanism of the obtained results. Secondly, the basic set-theoretic operations i.e., such as extended union, the intersection of two PSVNSs, and the complement operation of PSVNS, as well as some relevant properties, are investigated, and numerical examples are provided to illustrate the mechanism behind these results. Lastly, the similarity measure between two PSVNSs is characterized with the help of an example. This technique of similarity measure is successfully used in decision-making to choose the appropriate college.

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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. F. Smarandache, Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set, Int. J. Pure Appl. Math. 24 (2005), 287–297.
  4. H. Yang, Z. Guo, Y. She, X. Liao, On Single Valued Neutrosophic Relations, J. Intell. Fuzzy Syst. 30 (2015), 1045–1056. https://doi.org/10.3233/ifs-151827.
  5. J.S. Chai, G. Selvachandran, F. Smarandache, V.C. Gerogiannis, L.H. Son, Q. Bui, B. Vo, New Similarity Measures for Single-Valued Neutrosophic Sets with Applications in Pattern Recognition and Medical Diagnosis Problems, Complex Intell. Syst. 7 (2020), 703–723. https://doi.org/10.1007/s40747-020-00220-w.
  6. P. Majumdar, S.K. Samanta, On Similarity and Entropy of Neutrosophic Sets, J. Intell. Fuzzy Syst. 26 (2014), 1245–1252. https://doi.org/10.3233/ifs-130810.
  7. E. Bolturk, C. Kahraman, A Novel Interval-Valued Neutrosophic Ahp with Cosine Similarity Measure, Soft Comput. 22 (2018), 4941–4958. https://doi.org/10.1007/s00500-018-3140-y.
  8. 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.
  9. A. Al-Quran, F. Al-Sharqi, A.U. Rahman, Z.M. Rodzi, The Q-Rung Orthopair Fuzzy-Valued Neutrosophic Sets: Axiomatic Properties, Aggregation Operators and Applications, AIMS Math. 9 (2024), 5038–5070. https://doi.org/10.3934/math.2024245.
  10. A. admin, A. Hazaymeh, On the Topological Spaces of Neutrosophic Real Intervals, Int. J. Neutrosophic Sci. 25 (2025), 130–136. https://doi.org/10.54216/ijns.250111.
  11. R. Raed, A. Hazaymeh, On Some Topological Spaces Based on Symbolic N-Plithogenic Intervals, Int. J. Neutrosophic Sci. 25 (2025), 23–37. https://doi.org/10.54216/ijns.250102.
  12. P.K. Maji, A Neutrosophic Soft Set Approach to a Decision Making Problem, Ann. Fuzzy Math. Inform. 3 (2012), 313–319.
  13. I. Deli, S. Broumi, Neutrosophic soft relations and some properties, Ann. Fuzzy Math. Inform. 9 (2015), 169–182.
  14. M. Ali, L.H. Son, I. Deli, N.D. Tien, Bipolar Neutrosophic Soft Sets and Applications in Decision Making, J. Intell. Fuzzy Syst. 33 (2017), 4077–4087. https://doi.org/10.3233/jifs-17999.
  15. E. Hussein, Y. Al-Qudah, H.M. Jaradat, F. Al-Sharqi, S. Elnajar, A. Jaradat, Similarity Measure and Sine Exponential Measure of Possibility Interval-Valued Neutrosophic Hypersoft Sets and Their Applications, Neutrosophic Sets Syst. 81 (2025), 41–61.https://doi.org/10.5281/zenodo.14810922.
  16. Y. Yousef, A.O. Hamadameen, N.A. Kh, F.A. 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.
  17. M.U. Romdhini, A.A. Al-Quran, F.A. Al-Sharqi, M.K. Tahat, A. Lutfi, Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields, Int. J. Neutrosophic Sci. 22 (2023), 93–105. https://doi.org/10.54216/ijns.220408.
  18. Y.A. Al-Qudah, A Robust Framework for the Decision-Making Based on Single-Valued Neutrosophic Fuzzy Soft Expert Setting, Int. J. Neutrosophic Sci. 23 (2024), 195–210. https://doi.org/10.54216/ijns.230216.
  19. Y. Al-Qudah, A. Jaradat, S.K. Sharma, V.K. Bhat, Mathematical Analysis of the Structure of One-Heptagonal Carbon Nanocone in Terms of Its Basis and Dimension, Phys. Scr. 99 (2024), 055252. https://doi.org/10.1088/1402-4896/ad3add.
  20. A.H. Ganie, N.E.M. Gheith, Y. Al-Qudah, A.H. Ganie, S.K. Sharma, A.M. Aqlan, M.M. Khalaf, An Innovative Fermatean Fuzzy Distance Metric with Its Application in Classification and Bidirectional Approximate Reasoning, IEEE Access 12 (2024), 4780–4791. https://doi.org/10.1109/access.2023.3348780.
  21. H. Fathi, M. Myvizhi, A. Abdelhafeez, M.R. Abdellah, M. Eassa, M.S. Sawah, H. Elbehiery, Single-Valued Neutrosophic Graph with Heptapartitioend Structure, Neutrosophic Sets Syst. 80 (2025), 728–748. https://doi.org/10.5281/zenodo.14825936.
  22. S. Alkhazaleh, A.R. Salleh, N. Hassan, Possibility Fuzzy Soft Set, Adv. Decis. Sci. 2011 (2011), 479756. https://doi.org/10.1155/2011/479756.
  23. G. Selvachandran, A.R. Salleh, Possibility Intuitionistic Fuzzy Soft Expert Set Theory and Its Application in Decision Making, Int. J. Math. Math. Sci. 2015 (2015), 314285. https://doi.org/10.1155/2015/314285.
  24. F. Karaaslan, Possibility Neutrosophic Soft Sets and Pns-Decision Making Method, Appl. Soft Comput. 54 (2017), 403–414. https://doi.org/10.1016/j.asoc.2016.07.013.
  25. F. Al-Sharqi, A. Al-Quran, M.U. Romdhini, Decision-making Techniques Based on Similarity Measures of Possibility Interval Fuzzy Soft Environment, Iraqi J. Comput. Sci. Math. 4 (2023), 18–29. https://doi.org/10.52866/ijcsm.2023.04.04.003.
  26. S. Al-Hijjawi, S. Alkhazaleh, Possibility Neutrosophic Hypersoft Set (PNHSS), Neutrosophic Sets Syst. 53 (2023), 117–129. https://doi.org/10.5281/zenodo.7535981.
  27. N.M. Hammad, F. Al-Sharqi, Z.M. Rodzi, Similarity Measures of Bipolar Interval Valued-Fuzzy Soft Sets and Their Application in Multi-Criteria Decision-Making Method, J. Appl. Math. Inform. 43 (2025), 821–837. https://doi.org/10.14317/JAMI.2025.821.
  28. Y. Al-qudah, M. Alaroud, H. Qoqazeh, A. Jaradat, S.E. Alhazmi, S. Al-Omari, Approximate Analytic–numeric Fuzzy Solutions of Fuzzy Fractional Equations Using a Residual Power Series Approach, Symmetry 14 (2022), 804. https://doi.org/10.3390/sym14040804.
  29. Y.A. Al-Qudah, F.A. Al-Sharqi, Algorithm for Decision-Making Based on Similarity Measures of Possibility Interval-Valued Neutrosophic Soft Setting Settings, Int. J. Neutrosophic Sci. 22 (2023), 69–83. https://doi.org/10.54216/ijns.220305.
  30. S.Y. Musa, B.A. Asaad, Bipolar M-Parametrized N-Soft Sets: A Gateway to Informed Decision-Making, J. Math. Comput. Sci. 36 (2024), 121–141. https://doi.org/10.22436/jmcs.036.01.08.
  31. M.M. Abed, F.G. Al-Sharqi, A.A. Mhassin, Study Fractional Ideals Over Some Domains, AIP Conf. Proc. 2138 (2019), 030001. https://doi.org/10.1063/1.5121038.
  32. M.M. Abed, F.G. Al-Sharqi, Classical Artinian Module and Related Topics, J. Phys.: Conf. Ser. 1003 (2018), 012065. https://doi.org/10.1088/1742-6596/1003/1/012065.
  33. Y. Al-qudah, M. Alaroud, H. Qoqazeh, A. Jaradat, S.E. Alhazmi, S. Al-Omari, Approximate Analytic–numeric Fuzzy Solutions of Fuzzy Fractional Equations Using a Residual Power Series Approach, Symmetry 14 (2022), 804. https://doi.org/10.3390/sym14040804.