A Tangent Similarity-Based Pentapartitioned Neutrosophic Soft Topological Framework for Cancer Diagnosis

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DOI: https://doi.org/10.28924/2291-8639-24-2026-270
Published: Aug 24, 2026
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Shoaib Arbab, Muhammad Idrees, Aqeedat Hussain, Walid Abdelfattah, Arif Mehmood, Cris L. Armada, A Tangent Similarity-Based Pentapartitioned Neutrosophic Soft Topological Framework for Cancer Diagnosis, Int. J. Anal. Appl., 24 (2026), 270.

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Shoaib Arbab, Muhammad Idrees, Aqeedat Hussain, Walid Abdelfattah, Arif Mehmood, Cris L. Armada

Abstract

This research paper introduces the concept of pentapartitioned neutrosophic soft topological spaces (PNSTS). In PNSTS, the indeterminacy is divided into three components: truth (ReT), hesitation (H), and falsehood (ReF). Fundamental topological concepts and tangent-based similarity measures have been discussed and applied to a cancer data set to ascertain the similarity between patients and potential treatments. To analyze results more effectively, we have employed Heatmaps, 3D surface plotting, PCA, t-SNE, and DBSCAN clustering. The experimental results demonstrated that the proposed framework was highly effective, as the maximum similarity value reached 0.7508. This indicates that the patient’s traits and the proposed diagnosis clearly aligned. This demonstrates that the proposed method can be effectively employed for intelligent medical decision-making.

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References

  1. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.
  2. I.B. Turksen, Interval Valued Fuzzy Sets Based on Normal Forms, Fuzzy Sets Syst. 20 (1986), 191-210. https://doi.org/10.1016/0165-0114(86)90077-1.
  3. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3.
  4. K. Atanassov, G. Gargov, Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 31 (1989), 343-349. https://doi.org/10.1016/0165-0114(89)90205-4.
  5. F. Smarandache, A Unifying Field in Logics: Neutrosophy, Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, 1998. https://doi.org/10.5281/zenodo.49174.
  6. F. Gallego Lupiáñez, On Neutrosophic Topology, Kybernetes 37 (2008), 797-800. https://doi.org/10.1108/03684920810876990.
  7. H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single Valued Neutrosophic Sets, Multispace Multistruct. 4 (2010), 410-413. https://fs.unm.edu/SingleValuedNeutrosophicSets.pdf.
  8. H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis, Phoenix, 2005. https://doi.org/10.5281/zenodo.8818.
  9. S. Broumi, F. Smarandache, Cosine Similarity Measure of Interval Valued Neutrosophic Sets, Neutrosophic Sets Syst. 5 (2014), 15-20. https://doi.org/10.6084/M9.FIGSHARE.1502645.
  10. S. Broumi, F. Smarandache, New Distance and Similarity Measures of Interval Neutrosophic Sets, in: 17th International Conference on Information Fusion, Salamanca, Spain, 2014, pp. 249-255. https://digitalrepository.unm.edu/math_fsp/487.
  11. J. Ye, Similarity Measures between Interval Neutrosophic Sets and Their Applications in Multicriteria Decision-Making, J. Intell. Fuzzy Syst. 26 (2014), 165-172. https://doi.org/10.3233/IFS-120724.
  12. S. Broumi, F. Smarandache, Correlation Coefficient of Interval Neutrosophic Set, in: Proceedings of the International Conference ICMERA, Bucharest, Romania, 2013. https://doi.org/10.5281/zenodo.48908.
  13. 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.
  14. S.-M. Chen, A New Approach to Handling Fuzzy Decision-Making Problems, IEEE Trans. Syst. Man Cybern. 18 (1988), 1012-1016. https://doi.org/10.1109/21.23100.
  15. S.-M. Chen, M.-S. Yeh, P.-Y. Hsiao, A Comparison of Similarity Measures of Fuzzy Values, Fuzzy Sets Syst. 72 (1995), 79-89. https://doi.org/10.1016/0165-0114(94)00284-E.
  16. D. Molodtsov, Soft Set Theory—First Results, Comput. Math. Appl. 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5.
  17. H. Aktaş, N. Çağman, Soft Sets and Soft Groups, Inf. Sci. 177 (2007), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008.
  18. K.V. Babitha, J.J. Sunil, Soft Set Relations and Functions, Comput. Math. Appl. 60 (2010), 1840-1849. https://doi.org/10.1016/j.camwa.2010.07.014.
  19. D. Chen, E.C.C. Tsang, D.S. Yeung, Some Notes on the Parameterization Reduction of Soft Sets, in: Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, IEEE, 2003, pp. 1442-1445. https://doi.org/10.1109/ICMLC.2003.1259720.
  20. D. Chen, E.C.C. Tsang, D.S. Yeung, X. Wang, The Parameterization Reduction of Soft Sets and Its Applications, Comput. Math. Appl. 49 (2005), 757-763. https://doi.org/10.1016/j.camwa.2004.10.036.
  21. N. Çağman, S. Enginoğlu, Soft Set Theory and Uni–Int Decision Making, Eur. J. Oper. Res. 207 (2010), 848-855. https://doi.org/10.1016/j.ejor.2010.05.004.
  22. 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.
  23. A.R. Roy, P.K. Maji, A Fuzzy Soft Set Theoretic Approach to Decision Making Problems, J. Comput. Appl. Math. 203 (2007), 412-418. https://doi.org/10.1016/j.cam.2006.04.008.
  24. K.N. Singh, J.K. Mantri, A Clinical Decision Support System Using Rough Set Theory and Machine Learning for Disease Prediction, Intell. Med. 4 (2024), 200-208. https://doi.org/10.1016/j.imed.2023.08.002.
  25. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Adv. Fuzzy Syst. 2009 (2009), 586507. https://doi.org/10.1155/2009/586507.
  26. B.K. Tripathy, R.K. Mohanty, T.R. Sooraj, On Intuitionistic Fuzzy Soft Set and Its Application in Group Decision Making, in: 2016 International Conference on Emerging Trends in Engineering, Technology and Science (ICETETS), IEEE, 2016, pp. 1-5. https://doi.org/10.1109/ICETETS.2016.7603002.
  27. P.K. Maji, R. Biswas, A.R. Roy, Soft Set Theory, Comput. Math. Appl. 45 (2003), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6.
  28. N. Çağman, I. Deli, Means of FP-Soft Sets and Their Applications, Hacet. J. Math. Stat. 41 (2012), 615-625. https://dergipark.org.tr/tr/download/article-file/86337.
  29. N. Çağman, I. Deli, Products of FP-Soft Sets and Their Applications, Hacet. J. Math. Stat. 41 (2012), 365-374. https://zbmath.org/6242318.
  30. I. Deli, Interval-Valued Neutrosophic Soft Sets and Its Decision Making, arXiv:1402.3130, 2014. https://doi.org/10.48550/arXiv.1402.3130.
  31. P. Majumdar, S.K. Samanta, Similarity Measure of Soft Sets, New Math. Nat. Comput. 4 (2008), 1-12. https://doi.org/10.1142/S1793005708000908.
  32. A. Kharal, Distance and Similarity Measures for Soft Sets, New Math. Nat. Comput. 6 (2010), 321-334. https://doi.org/10.1142/S1793005710001724.
  33. P. Grzegorzewski, Distances between Intuitionistic Fuzzy Sets and/or Interval-Valued Fuzzy Sets Based on the Hausdorff Metric, Fuzzy Sets Syst. 148 (2004), 319-328. https://doi.org/10.1016/j.fss.2003.08.005.
  34. M. Arora, R. Biswas, U.S. Pandey, Neutrosophic Relational Database Decomposition, Int. J. Adv. Comput. Sci. Appl. 2 (2011), 121-125. https://doi.org/10.14569/IJACSA.2011.020822.
  35. M. Arora, R. Biswas, Deployment of Neutrosophic Technology to Retrieve Answer for Queries Posed in Natural Language, in: 2010 3rd International Conference on Computer Science and Information Technology, IEEE, 2010, pp. 435-439. https://doi.org/10.1109/ICCSIT.2010.5564125.
  36. S. Aggarwal, R. Biswas, A.Q. Ansari, Neutrosophic Modeling and Control, in: 2010 International Conference on Computer and Communication Technology (ICCCT), IEEE, 2010, pp. 718-723. https://doi.org/10.1109/ICCCT.2010.5640435.
  37. H.D. Cheng, Y. Guo, A New Neutrosophic Approach to Image Thresholding, New Math. Nat. Comput. 4 (2008), 291-308. https://doi.org/10.1142/S1793005708001082.
  38. Y. Guo, H.D. Cheng, New Neutrosophic Approach to Image Segmentation, Pattern Recognit. 42 (2009), 587-595. https://doi.org/10.1016/j.patcog.2008.10.002.
  39. M. Zhang, L. Zhang, H.D. Cheng, A Neutrosophic Approach to Image Segmentation Based on Watershed Method, Signal Process. 90 (2010), 1510-1517. https://doi.org/10.1016/j.sigpro.2009.10.021.
  40. A.Q. Ansari, R. Biswas, S. Aggarwal, Proposal for Applicability of Neutrosophic Set Theory in Medical AI, Int. J. Comput. Appl. 27 (2011), 5-11. https://doi.org/10.5120/3299-4505.
  41. M.I. Ali, F. Feng, X. Liu, W.K. Min, M. Shabir, On Some New Operations in Soft Set Theory, Comput. Math. Appl. 57 (2009), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009.
  42. M.I. Ali, A Note on Soft Sets, Rough Soft Sets and Fuzzy Soft Sets, Appl. Soft Comput. 11 (2011), 3329-3332. https://doi.org/10.1016/j.asoc.2011.01.003.
  43. U. Acar, F. Koyuncu, B. Tanay, Soft Sets and Soft Rings, Comput. Math. Appl. 59 (2010), 3458-3463. https://doi.org/10.1016/j.camwa.2010.03.034.
  44. Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tang, Interval-Valued Intuitionistic Fuzzy Soft Sets and Their Properties, Comput. Math. Appl. 60 (2010), 906-918. https://doi.org/10.1016/j.camwa.2010.05.036.
  45. N. Çağman, I. Deli, Similarity Measures of Intuitionistic Fuzzy Soft Sets and Their Decision Making, arXiv:1301.0456, 2013. https://doi.org/10.48550/arXiv.1301.0456.
  46. S. Broumi, Generalized Neutrosophic Soft Set, Int. J. Comput. Sci. Eng. Inf. Technol. 3 (2013), 17-30. https://doi.org/10.5121/ijcseit.2013.3202.
  47. S. Broumi, F. Smarandache, Several Similarity Measures of Neutrosophic Sets, Neutrosophic Sets Syst. 1 (2013), 54-62. https://digitalrepository.unm.edu/nss_journal/vol1/iss1/10.
  48. T. Bera, N.K. Mahapatra, Introduction to Neutrosophic Soft Topological Space, OPSEARCH 54 (2017), 841-867. https://doi.org/10.1007/s12597-017-0308-7.
  49. P.K. Maji, Neutrosophic Soft Set, Ann. Fuzzy Math. Inform. 5 (2013), 157-168.
  50. I. Deli, S. Broumi, Neutrosophic Soft Relations and Some Properties, Ann. Fuzzy Math. Inform. 9 (2015), 169-182. https://doi.org/10.5281/zenodo.23153.
  51. F. Smarandache, Neutrosophic Set – a Generalization of the Intuitionistic Fuzzy Set, in: 2006 IEEE International Conference on Granular Computing, IEEE, 2006, pp. 38-42. https://doi.org/10.1109/GRC.2006.1635754.
  52. C.D. Manning, P. Raghavan, H. Schütze, Introduction to Information Retrieval, Cambridge University Press, 2008. https://doi.org/10.1017/CBO9780511809071.
  53. L. Wilkinson, The Grammar of Graphics, Springer-Verlag, 2005. https://doi.org/10.1007/0-387-28695-0.
  54. J. Han, M. Kamber, J. Pei, Data Mining: Concepts and Techniques, 3rd ed., Elsevier, 2011. https://doi.org/10.1016/C2009-0-61819-5.
  55. E.R. Tufte, The Visual Display of Quantitative Information, Graphics Press, 2001.
  56. K. Pearson, On Lines and Planes of Closest Fit to Systems of Points in Space, Philos. Mag. J. Sci. 2 (1901), 559-572. https://doi.org/10.1080/14786440109462720.
  57. C. de Boor, A Practical Guide to Splines, Springer New York, 1978. https://doi.org/10.1007/978-1-4612-6333-3.
  58. MathWorks, MATLAB Documentation, The MathWorks Inc., Natick, 2026. https://www.mathworks.com/help/matlab/.
  59. S. Lloyd, Least Squares Quantization in PCM, IEEE Trans. Inf. Theory 28 (1982), 129-137. https://doi.org/10.1109/TIT.1982.1056489.
  60. R.A. Fisher, The Use of Multiple Measurements in Taxonomic Problems, Ann. Eugen. 7 (1936), 179-188. https://doi.org/10.1111/j.1469-1809.1936.tb02137.x.
  61. M.M. Saeed, R. Hatamleh, A.M. AbdEl-latif, A. Al-Husban, H.M. Attaalfadeel, T. Fujita, K.A. Aldwoah, A.M. Khattak, A Breakthrough Approach to Quadri-Partitioned Neutrosophic Soft Topological Spaces, Eur. J. Pure Appl. Math. 18 (2025), 5845. https://doi.org/10.29020/nybg.ejpam.v18i2.5845.
  62. A.A. Abubaker, R. Hatamleh, K. Matarneh, A. Al-Husban, On the Numerical Solutions for Some Neutrosophic Singular Boundary Value Problems by Using (LPM) Polynomials, Int. J. Neutrosophic Sci. 25 (2025), 197-205. https://doi.org/10.54216/IJNS.250217.
  63. A.A. Abubaker, R. Hatamleh, K. Matarneh, A. Al-Husban, On the Irreversible k-Threshold Conversion Number for Some Graph Products and Neutrosophic Graphs, Int. J. Neutrosophic Sci. 25 (2025), 183-196. https://doi.org/10.54216/IJNS.250216.
  64. R. Hatamleh, A. Al-Husban, K. Sundareswari, G. Balaj, M. Palanikumar, Complex Tangent Trigonometric Approach Applied to (γ, τ)-Rung Fuzzy Set Using Weighted Averaging, Geometric Operators and Its Extension, Commun. Appl. Nonlinear Anal. 32 (2025), 133-144. https://doi.org/10.52783/cana.v32.2978.
  65. R. Hatamleh, 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.
  66. H. Qawaqneh, Fractional Analytic Solutions and Fixed Point Results with Some Applications, Adv. Fixed Point Theory 14 (2024), 1. https://doi.org/10.28919/afpt/8279.
  67. H. Qawaqneh, M.S.M. Noorani, H. Aydi, A. Zraiqat, A.H. Ansari, On Fixed Point Results in Partial b-Metric Spaces, J. Funct. Spaces 2021 (2021), 1-9. https://doi.org/10.1155/2021/8769190.
  68. H. Qawaqneh, M.S.M. Noorani, H. Aydi, Some New Characterizations and Results for Fuzzy Contractions in Fuzzy b-Metric Spaces and Applications, AIMS Math. 8 (2023), 6682-6696. https://doi.org/10.3934/math.2023338.
  69. H. Qawaqneh, J. Manafian, M. Alharthi, Y. Alrashedi, Stability Analysis, Modulation Instability, and Beta-Time Fractional Exact Soliton Solutions to the van der Waals Equation, Mathematics 12 (2024), 2257. https://doi.org/10.3390/math12142257.
  70. R. Hatamleh, On the Form of Correlation Function for a Class of Nonstationary Field with a Zero Spectrum, Rocky Mt. J. Math. 33 (2003), 159-173. https://doi.org/10.1216/rmjm/1181069991.
  71. R. Hatamleh, V.A. Zolotarev, On Two-Dimensional Model Representations of One Class of Commuting Operators, Ukr. Math. J. 66 (2014), 122-144. https://doi.org/10.1007/s11253-014-0916-9.
  72. R. Hatamleh, V.A. Zolotarev, On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component, Zh. Mat. Fiz. Anal. Geom. 11 (2015), 174-186. https://doi.org/10.15407/mag11.02.174.
  73. R. Hatamleh, V.A. Zolotarev, Triangular Models of Commutative Systems of Linear Operators Close to Unitary Operators, Ukr. Math. J. 68 (2016), 791-811. https://doi.org/10.1007/s11253-016-1258-6.
  74. A.S. Heilat, H. Zureigat, R. Hatamleh, B. Batiha, New Spline Method for Solving Linear Two-Point Boundary Value Problems, Eur. J. Pure Appl. Math. 14 (2021), 1283-1294. https://doi.org/10.29020/nybg.ejpam.v14i4.4124.
  75. A. Qazza, I. Bendib, R. Hatamleh, R. Saadeh, A. Ouannas, Dynamics of the Gierer–Meinhardt Reaction–Diffusion System: Insights into Finite-Time Stability and Control Strategies, Partial Differ. Equ. Appl. Math. 14 (2025), 101142. https://doi.org/10.1016/j.padiff.2025.101142.
  76. T. Qawasmeh, A. Qazza, R. Hatamleh, M.W. Alomari, R. Saadeh, Further Accurate Numerical Radius Inequalities, Axioms 12 (2023), 801. https://doi.org/10.3390/axioms12080801.
  77. A. Shihadeh, K.A.M. Matarneh, R. Hatamleh, M.O. Al-Qadri, A. Al-Husban, On the Two-Fold Fuzzy n-Refined Neutrosophic Rings for 2≤n≤3, Neutrosophic Sets Syst. 68 (2024), 8-25. https://doi.org/10.5281/zenodo.11406449.
  78. T.Y. Ozturk, C.G. Aras, S. Bayramov, A New Approach to Operations on Neutrosophic Soft Sets and to Neutrosophic Soft Topological Spaces, Commun. Math. Appl. 10 (2019), 481-493. https://doi.org/10.26713/cma.v10i3.1068.