Volume 9 • Issue 2 • PP: 01–14 • 2024
Fuzzy and Neutrosophic Systems for Medical Diagnosis: A Mathematical Review of Uncertainty Representation and Decision Models
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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Medical diagnosis is an uncertainty-sensitive decision problem in which a patient state x = (x1, . . . , xm) is mapped to a candidate disease dk ∈ C using incomplete, gradual, and sometimes conflicting evidence. Fuzzy systems represent such evidence by a membership grade µ(x) ∈ [0, 1]; intuitionistic fuzzy systems use inde-pendently assigned (µ, ν) with the derived hesitation π = 1 − µ − ν; and single-valued neutrosophic systems use an independently specified triple (T, I, F ) ∈ [0, 1 ]3. This article provides a structured mathematical re-view of these models in medical diagnosis using literature available no later than 31 May 2024. The literature is synthesized by representation space, constraints, distance and similarity measures, aggregation operators, temporal structure, and diagnostic decision rules. A common embedding Φ places fuzzy and intuitionistic fuzzy states inside the neutrosophic cube Ω = [0, 1]3, making the geometric relation among the three model families explicit. Within this space, a weighted diagnostic distance is written as D(r) k = Xm j=1 wj 3 (|Tpj − Tkj |r + |Ipj − Ikj |r + |Fpj − Fkj |r) 1/r, and the normalization residual κ = T + I + F − 1 is used to distinguish normalized states from under-specified or overlapping evidence without interpreting (T, I, F ) as probabilities. The review further devel-ops a synthesis-derived decision layer that combines distance, indeterminacy, and diagnostic margin through Sk = (1 + Dk)−1, Ck = Sk(1 − I¯p)γ , and ∆C = C(1) − C(2). The analysis indicates that fuzzy systems remain appropriate when uncertainty is predominantly gradual and rule interpretability is central, whereas neutrosophic systems are better justified when independent support, opposition, and indeterminacy must be retained. The resulting taxonomy clarifies when additional uncertainty dimensions are mathematically infor-mative and identifies calibration, metric stability, explainability, temporal modeling, and clinical validation as the principal unresolved problems.
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References
[1] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. doi: 10.1016/S0019-9958(65)90241-X.
[2] K.-P. Adlassnig, “Fuzzy set theory in medical diagnosis,” IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-16, no. 2, pp. 260–265, 1986. doi: 10.1109/TSMC.1986.4308946.
[3] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. doi: 10.1016/S0165-0114(86)80034-3.
[4] H. Wang, F. Smarandache, Y.-Q. Zhang, and R. Sunderraman, “Single valued neutrosophic sets,” Review of the Air Force Academy, vol. 1, no. 16, pp. 10–14, 2010.
[5] A. Torres and J. J. Nieto, “Fuzzy logic in medicine and bioinformatics,” Journal of Biomedicine and Biotechnology, vol. 2006, Art. 91908, 2006. doi: 10.1155/JBB/2006/91908.
[6] I. B. de Medeiros, M. A. S. Machado, W. J. Damasceno, A. M. Caldeira, R. C. dos Santos, and J. B. da Silva Filho, “A fuzzy inference system to support medical diagnosis in real time,” Procedia Computer Science, vol. 122, pp. 167–173, 2017. doi: 10.1016/j.procs.2017.11.356.
[7] E. Szmidt and J. Kacprzyk, “Distances between intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 114, no. 3, pp. 505–518, 2000. doi: 10.1016/S0165-0114(98)00244-9.
[8] E. Szmidt and J. Kacprzyk, “A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning,” in Artificial Intelligence and Soft Computing—ICAISC 2004, LNCS 3070, Springer, pp. 388–393, 2004. doi: 10.1007/978-3-540-24844-6 56.
[9] S. K. De, R. Biswas, and A. R. Roy, “An application of intuitionistic fuzzy sets in medical diagnosis,” Fuzzy Sets and Systems, vol. 117, no. 2, pp. 209–213, 2001. doi: 10.1016/S0165-0114(98)00235-8.
[10] Y. C¸ elik and S. Yamak, “Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations,” Journal of Inequalities and Applications, vol. 2013, Art. 82, 2013. doi: 10.1186/1029-242X-2013-82.
[11] P. Majumdar and S. K. Samanta, “On similarity and entropy of neutrosophic sets,” Journal of Intelligent & Fuzzy Systems, vol. 26, no. 3, pp. 1245–1252, 2014. doi: 10.3233/IFS-130810.
[12] J. Ye, “Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses,” Artificial Intel-ligence in Medicine, vol. 63, no. 3, pp. 171–179, 2015. doi: 10.1016/j.artmed.2014.12.007.
[13] J. Ye and J. Fu, “Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function,” Computer Methods and Programs in Biomedicine, vol. 123, pp. 142–149, 2016. doi: 10.1016/j.cmpb.2015.10.002.
[14] H. Garg and Nancy, “Some new biparametric distance measures on single-valued neutrosophic sets with applications to pattern recognition and medical diagnosis,” Information, vol. 8, no. 4, Art. 162, 2017. doi: 10.3390/info8040162.
[15] J. Fu and J. Ye, “Simplified neutrosophic exponential similarity measures for the initial evaluation/diagnosis of benign prostatic hyperplasia symptoms,” Symmetry, vol. 9, no. 8, Art. 154, 2017. doi: 10.3390/sym9080154.
[16] M. Ali, L. H. Son, N. D. Thanh, and N. V. Minh, “A neutrosophic recommender system for medical diag-nosis based on algebraic neutrosophic measures,” Applied Soft Computing, vol. 71, pp. 1054–1071, 2018. doi: 10.1016/j.asoc.2017.10.012.
[17] C. Zhang, D. Li, S. Broumi, and A. K. Sangaiah, “Medical diagnosis based on single-valued neutrosophic proba-bilistic rough multisets over two universes,” Symmetry, vol. 10, no. 6, Art. 213, 2018. doi: 10.3390/sym10060213.
[18] M. Abdel-Basset, M. Mohamed, M. Elhoseny, L. H. Son, F. Chiclana, and A. E.-N. H. Zaied, “Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases,” Artificial Intelligence in Medicine, vol. 101, Art. 101735, 2019. doi: 10.1016/j.artmed.2019.101735.
[19] J. S. Chai, G. Selvachandran, F. Smarandache, V. C. Gerogiannis, L. H. Son, Q.-T. Bui, and B. Vo, “New simi-larity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems,” Complex & Intelligent Systems, vol. 7, no. 2, pp. 703–723, 2021. doi: 10.1007/s40747-020-00220-w.
[20] A. U. Rahman, M. Saeed, M. A. Mohammed, S. Krishnamoorthy, S. Kadry, and F. Eid, “An integrated algorithmic MADM approach for heart diseases’ diagnosis based on neutrosophic hypersoft set with possibility degree-based setting,” Life, vol. 12, no. 5, Art. 729, 2022. doi: 10.3390/life12050729.
[21] P. Dutta and G. Borah, “Medical decision-making and pattern recognition via an advanced similarity measure based on single-valued neutrosophic sets,” SN Computer Science, vol. 5, no. 1, Art. 105, 2024. doi: 10.1007/s42979-023-02429-1.
[22] V. Khatibi and G. A. Montazer, “Intuitionistic fuzzy set vs. fuzzy set application in medical pattern recognition,” Artificial Intelligence in Medicine, vol. 47, no. 1, pp. 43–52, 2009. doi: 10.1016/j.artmed.2009.03.002.
[23] D. Liu, G. Liu, and Z. Liu, “Some similarity measures of neutrosophic sets based on the Euclidean distance and their application in medical diagnosis,” Computational and Mathematical Methods in Medicine, vol. 2018, Art. 7325938, 2018. doi: 10.1155/2018/7325938.
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