Abstract

Decision-making theory serves as an effective framework to guide decision-makers in solving problems. One notable application of this theory is in the medical field, where it aids doctors in analyzing patient data to determine whether a patient is infected. To enhance this theory with more adaptable mathematical methods, we propose an expanded approach based on previously introduced matrixes of Q-neutrosophic soft under an Interval-valued setting (IV-Q-NSM). This represents a new finding of existing mathematical tools to address the two-dimensional uncertainty prevalent in various life domains. This work explores several algebraic properties and matrix operations associated with IV-Q-NSM. Subsequently, we introduce a new methodology for decision-making (DM) in medical diagnosis selection problems. This approach aims to provide a more flexible and comprehensive framework for evaluating complex medical data and improving diagnostic accuracy.

Keywords :

[1] L. A. Zadeh, "Fuzzy sets," Information Control, vol. 8, no. 3, pp. 338-353, 1965.

[2] K. Alhazaymeh, Y. Al-Qudah, N. Hassan, and A. M. Nasruddin, "Cubic vague set and its application in decision-making," Entropy, vol. 22, no. 9, p. 963, 2020.

[3] T. R. Patel and S. K. Gupta, "Exploring Neutrosophic Sets in Decision-Making Processes," International Journal of Fuzzy Systems, vol. 23, no. 4, pp. 789-802, 2021.

[4] S. H. Zail, M. M. Abed, and A. S. Faisal, "Neutrosophic BCK-algebra and &Omega , -BCK-algebra," International Journal of Neutrosophic Science, vol. 19, no. 3, pp. 8-15, 2022.

[5] A. B. Kumar, R. C. Singh, and L. T. Zhang, "Neutrosophic Sets and Their Applications in Decision-Making," Journal of Intelligent Systems, vol. 30, no. 4, pp. 567-580, 2023.

[6] F. Smarandache, a Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logics, American Research Press, Reoboth, NM, USA, 1998.

[7] Deli, "Interval-valued neutrosophic soft sets and its decision-making," International Journal of Machine Learning and Cybernetics, vol. 8, pp. 665-676, 2017.

[8] J. P. Chen and H. Y. Wu, "A Comprehensive Review of Neutrosophic Decision-Making Techniques," International Journal of Fuzzy Systems, vol. 25, no. 2, pp. 345-360, 2023.

[9] M. M. Abed, N. Hassan, and F. Al-Sharqi, "On neutrosophic multiplication module," Neutrosophic Sets and Systems, vol. 49, no. 1, pp. 198-208, 2022.

[10] M. U. Romdhini, F. Al-Sharqi, A. Nawawi, A. Al-Quran, and H. Rashmanlou, "Signless Laplacian energy of interval-valued fuzzy graph and its applications," Sains Malaysiana, vol. 52, no. 7, pp. 2127&ndash , 2137, 2023.

[11] Al-Quran et al., "The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups," International Journal of Neutrosophic Science, vol. 22, no. 1, pp. 60-77, 2023.

[12] J. N. Ismail et al., "The Integrated Novel Framework: Linguistic Variables in Pythagorean Neutrosophic Set with DEMATEL for Enhanced Decision Support," Int. J. Neutrosophic Sci., vol. 21, no. 2, pp. 129-141, 2023.

[13] M. U. Romdhini et al., "Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields," International Journal of Neutrosophic Science, vol. 22, no. 04, pp. 93&ndash , 105, 2023.

[14] A. H. Al-Omari and M. A. Al-Khalidi, "Algebraic Structures of Topological Groups," Journal of Algebra, vol. 559, pp. 1-15, 2020.

[15] M. A. Khan and S. H. Ali, "Fuzzy Neutrosophic Sets: Theory and Applications in Real-World Problems," Applied Mathematical Modelling, vol. 110, pp. 456-470, 2023.

[16] J. D. H. Smith and L. K. Johnson, "Topology and Group Theory: A Comprehensive Overview," Mathematical Reviews, vol. 45, no. 3, pp. 234-250, 2021.

[17] T. R. Patel and A. R. Sharma, "Multi-Criteria Decision Analysis Based on Neutrosophic Logic," Soft Computing, vol. 27, no. 8, pp. 2151-2165, 2024.

[18] A. Al-Quran, F. Al-Sharqi, A. U. Rahman, and Z. M. Rodzi, "The q-rung orthopair fuzzy-valued neutrosophic sets: Axiomatic properties, aggregation operators, and applications," AIMS Mathematics, vol. 9, no. 2, pp. 5038&ndash , 5070, 2024. DOI: https://doi.org/10.3934/math.202424.

[19] F. Al-Sharqi, A. Al-Quran, and Z. M. Rodzi, "Multi-attribute group decision-making based on aggregation operator and score function of bipolar neutrosophic hypersoft environment," Neutrosophic Sets and Systems, vol. 61, no. 1, pp. 465&ndash , 492, 2023. DOI: https://doi.org/10.54216/NSS.610123.

[20] Z. A. Khalaf and F. M. Mohammed, "An Introduction to M-Open Sets in Fuzzy Neutrosophic Topological Spaces," International Journal of Neutrosophic Science, vol. 4, pp. 36-45, 2023.

[21] R. K. Gupta, A. S. Kumar, and L. T. Zhang, "Decision-making in Medical Robotics: A Fuzzy Neutrosophic Approach," International Journal of Medical Robotics and Computer Assisted Surgery, vol. 16, no. 5, pp. 1-12, 2020.

[22] M. Palanikumar et al., "Multiple attribute decision-making model for artificially intelligent last-mile delivery robots selection in neutrosophic square root environment," Engineering Applications of Artificial Intelligence, vol. 136, p. 108878, 2024.

[23] H. L. Chen and M. A. Wong, "Fuzzy Soft Sets and Their Applications in Real-Life Problems," Journal of Computational and Theoretical Nanoscience, vol. 18, no. 5, pp. 1234-1240, 2021.

[24] R. A. Alahmadi et al., "Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure," Granular Computing, vol. 8, no. 6, pp. 1385-1405, 2023.

[25] R. S. Thompson and P. Q. Lee, "Applications of Topological Groups in Analysis," Journal of Mathematical Sciences, vol. 29, no. 4, pp. 567-580, 2019.

[26] U. Rahman et al., "An innovative mathematical approach to the evaluation of susceptibility in liver disorder based on fuzzy parameterized complex fuzzy hypersoft set," Biomedical Signal Processing and Control, vol. 86, pp. 105-204, 2023.

[27] M. Arshad et al., "A robust framework for the selection of optimal COVID-19 mask based on aggregations of interval-valued multi-fuzzy hypersoft sets," Expert Systems with Applications, vol. 238, p. 121944, 2024.

[28] G. F. Martinez and R. S. Alvi, "A New Approach to Fuzzy Neutrosophic Decision-Making," in Proceedings of the International Conference on Intelligent Systems, pp. 201-206, Sep. 2022.

[29] K. M. Patel and S. R. Gupta, "Fundamental Concepts of Topological Groups," International Journal of Pure and Applied Mathematics, vol. 118, no. 2, pp. 345-360, 2018.

[30] E. Ghazi and S. O. Al-Salihi, "A robust framework for medical diagnostics based on interval valued Q-neutrosophic soft sets with aggregation operators," Neutrosophic Sets and Systems, vol. 68, pp. 165-186, 2024.

[31] Y. Z. Wang and F. L. Zhang, "Aggregation Operators for Neutrosophic Sets in Decision-Making Processes," Expert Systems with Applications, vol. 220, no. 1, pp. 103-115, 2024.

[32] A. Auad and F. Al-Sharqi, "Identical Theorem of Approximation Unbounded Functions by Linear Operators," Journal of Applied Mathematics & , Informatics, vol. 41, no. 4, pp. 801&ndash , 810, 2023.

[33] L. J. Smith and P. Q. Lee, "Applications of Fuzzy Soft Sets in Decision-Making under Uncertainty," Journal of Computational and Theoretical Nanoscience, vol. 19, no. 3, pp. 789-798, 2023.

[34] Bataihah, T. Qawasmeh, and M. Shatnawi, "Discussion on b-metric spaces and related results in metric and G-metric spaces," Nonlinear Functional Analysis and Applications, vol. 27, no. 2, pp. 233-247, 2022.

[35] Bataihah, "Some fixed point results with application to fractional differential equation via new type of distance spaces," Results in Nonlinear Analysis, vol. 7, pp. 202&ndash , 208, 2024.

[36] J. N. Ismail et al., "Enhancing Decision Accuracy in DEMATEL using Bonferroni Mean Aggregation under Pythagorean Neutrosophic Environment," Journal of Fuzzy Extension & , Applications (JFEA), vol. 4, no. 4, pp. 281 - 298, 2023.

[37] G. F. Martinez and R. S. Alvi, "Neutrosophic Decision-Making Models: A Review and Future Directions," International Journal of Neutrosophic Science, vol. 23, no. 4, pp. 200-215, 2024.

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