Cotangent similarity measure of n-valued interval neutrosophic sets for medical diagnosis
Abstract
Each illness presents with specific signs and symptoms. The proposed approach effectively identifies relationships between groups of illnesses and the symptoms that patients experience, supporting medical professionals in reaching a likely diagnosis. Medical diagnosis relies heavily on n-valued interval neutrosophic sets and their applications. This study examines aspects of cotangent similarity among n-valued interval neutrosophic sets and proposes a method utilizing these concepts. This approach serves as a valuable tool for addressing uncertainties and limitations in existing diagnostic methods. The application of this method in medical diagnosis is evaluated to accurately identify the illness affecting the patient. The diagnostic results demonstrate the effectiveness of the proposed strategy.
Keywords:
n-valued interval neutrosophic sets, Cotangent similarity measure, Medical diagnosis uncertainty modeling, Fuzzy decision-making in healthcare, Neutrosophic logic in symptom analysisReferences
- [1] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
- [2] Li, Q., Rong, Y., Pei, Z., & Ren, F. (2023). A novel linguistic decision making approach based on attribute correlation and EDAS method. Soft computing, 27(12), 7751–7771. https://doi.org/10.1007/s00500-023-08079-y
- [3] Samuel, A. E., & Narmadhagnanam, R. (2018). Intuitionistic fuzzy sets in medical diagnosis. International journal of mathematical archive, 9(1), 1–5. https://doi.org/10.22457/ijfma.v16n1a3
- [4] Mohamed Kozae, A., Shokry, M., & Omran, M. (2020). Intuitionistic fuzzy set and its application in corona Covid-19. Applied and computational mathematics, 9(5), 146. https://doi.org/10.11648/j.acm.20200905.11
- [5] Rajkalpana, M., KavyaSri, R., Abarna, S., & Nishantini, M. (2020). An analysis of medical diagnosis using intuitionistic fuzzy set and its operators. International journal of advanced science and technology, 29(2), 2496–2500. http://sersc.org/journals/index.php/IJAST/article/view/3798
- [6] Shinoj, T. K., & John, S. J. (2012). Intuitionistic fuzzy multisets and its application in medical diagnosis. World academy of science, engineering and technology, 6(1), 1418–1421. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=be7b506060dda86ccab28deb5c9d4e01ff0996f3
- [7] Rajarajeswari, P., & Uma, N. (2013). Hausdroff similarity measures for intuitionistic fuzzy multi sets and its application in medical diagnosis. International journal of mathematical archive-4 (9), 4(9), 106–111.
- [8] Rajarajeswari, P., & Uma, N. (2014). Normalized hamming similarity measure for intuitionistic fuzzy multi sets and its application in medical diagnosis. International journal of mathematical trends and technology, 5(3), 219–225. https://doi.org/10.14445/22315373/ijmtt-v5p525
- [9] Samuel, A. E., & Narmadhagnanam, R. (2018). Intuitionistic fuzzy multisets in medical diagnosis. International journal of fuzzy mathematical archive, 16(01), 13–19. https://doi.org/10.22457/ijfma.v16n1a3
- [10] Smarandache, F. (1999). A unifying field in Logics: Neutrosophic Logic. In Philosophy (pp. 1–141). American Research Press. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=70f349e9c4e4dd0a2097d911d9dec36915eb7b13
- [11] Pawlak, Z. (1982). Rough sets. International journal of computer & information sciences, 11, 341–356. https://doi.org/10.1007/BF01001956
- [12] Nanda, S., & Majumdar, S. (1992). Fuzzy rough sets. Fuzzy sets and systems, 45(2), 157–160. https://doi.org/10.1016/0165-0114(92)90114-J
- [13] Broumi, S., Smarandache, F., & Dhar, M. (2014). Rough Neutrosophic sets. Italian journal of pure and applied mathematics, 32, 493–502. https://doi.org/10.5281/zenodo.30310
- [14] Pramanik, S., & Mondal, K. (2015). Cosine similarity measure of rough Neutrosophic sets and its application in medical diagnosis. Global journal of advanced research, 2(1), 212–220. https://fs.unm.edu/CosineSimilarityMeasureOfRough.pdf
- [15] Pramanik, S., & Mondal, K. (2015). Cotangent similarity measure of rough Neutrosophic sets and its application to medical diagnosis. Journal of new theory, 4, 90–102. https://dergipark.org.tr/en/pub/jnt/issue/34490/381119
- [16] Pramanik, S., Roy, R., Roy, T. K., & Smarandache, F. (2017). Multi criteria decision making using correlation coefficient under rough Neutrosophic environment. Neutrosophic sets and systems, 17, 29–36. https://doi.org/10.5281/zenodo.1012237
- [17] Samuel, A. E., & Narmadhagnanam, R. (2018). Utilization of Rough Neutrosophic sets in medical diagnosis. International journal of engineering science invention, 7(3), 1–5. https://fs.unm.edu/neut/UtilizationOfRoughNeutrosophicMedical.pdf
- [18] Samuel, A. E., & Narmadhagnanam, R. (2018). Neoteric techniques for Rough Neutrosophic set and their utilization in Medical Diagnosis. International journal for research in engineering application & management, 4(7), 253–258.
- [19] Samuel, A. E., & Narmadhagnanam, R. (2018). Rough Neutrosophic sets in medical diagnosis. International journal of pure and applied mathematics, 120(8), 79–87. https://www.acadpubl.eu/hub/2018-120-8/1/9.pdf
- [20] Samuel, A. E., & Narmadhagnanam, R. (2019). Pi-distance of rough Neutrosophic sets for medical diagnosis. Neutrosophic sets and systems, 28(1), 51–57. https://digitalrepository.unm.edu/nss_journal/vol28/iss1/6
- [21] Bera, T., & Mahapatra, N. K. (2019). Generalised single valued Neutrosophic number and its application to Neutrosophic linear programming. Neutrosophic sets and systems, 25, 85–103. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1258&context=nss_journal
- [22] Ulucay, V., Kilic, A., Yildiz, I., & Sahin, M. (2018). A new approach for multi-attribute decision-making problems in bipolar Neutrosophic sets. Neutrosophic sets and systems, 23(1), 142–159. https://digitalrepository.unm.edu/nss_journal/vol23/iss1/12
- [23] Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued Neutrosophic sets. Multispace & multistructure, 4(10), 410–413. https://fs.unm.edu/SingleValuedNeutrosophicSets.pdf
- [24] Majumdar, P., & Samanta, S. K. (2014). On similarity and entropy of Neutrosophic sets. Journal of intelligent & fuzzy systems, 26(3), 1245–1252. https://doi.org/10.3233/IFS-130810
- [25] Ye, J. (2017). Single-valued Neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft computing, 21(3), 817–825. https://doi.org/10.1007/s00500-015-1818-y
- [26] Broumi, S., Murugappan, M., Talea, M., Smarandache, F., Bakali, A., Singh, P. K., & Dey, A. (2019). Single valued (2N+ 1) sided polygonal Neutrosophic numbers and single valued (2N) sided polygonal Neutrosophic numbers. Neutrosophic sets and systems, 25, 54–65. https://fs.unm.edu/nss8/index.php/111/article/view/153
- [27] Li, C., Ye, J., Cui, W., & Du, S. (2019). Slope stability assessment method using the arctangent and tangent similarity measure of Neutrosophic numbers. Neutrosophic sets and systems, 27(1), 98–103. https://digitalrepository.unm.edu/nss_journal/vol27/iss1/9
- [28] Samuel, A. E., & Narmadhagnanam, R. (2018). Cosine logarithmic distance of singlevalued Neutrosophic sets in medical diagnosis. International journal of engineering, science and mathematics, 7(6), 14–19. https://www.indianjournals.com/ijor.aspx?target=ijor:ijesm&volume=7&issue=6&article=003
- [29] Samuel, A. E., & Narmadhagnanam, R. (2018). Tangent inverse similarity measure of singled valued Neutrosophic sets in medical diagnosis. International journal of creative research thoughts, 6(2), 77–79. https://www.ijcrt.org/papers/IJCRT1892673.pdf
- [30] Narmadhagnanam, R., & Samuel, A. E. (2022). Sine exponential measure of single valued Neutrosophic sets in medical diagnosis. Neutrosophic sets and systems, 51, 303–310. https://doi.org/10.5281/zenodo.7135305
- [31] Chai, J. S., Selvachandran, G., Smarandache, F., Gerogiannis, V. C., Son, L. H., Bui, Q. T., & Vo, B. (2021). New similarity measures for single-valued Neutrosophic sets with applications in pattern recognition and medical diagnosis problems. Complex and intelligent systems, 7(2), 703–723. https://doi.org/10.1007/s40747-020-00220-w
- [32] Ye, S., & Ye, J. (2014). Dice similarity measure between single valued Neutrosophic multisets and its application in medical diagnosis. Neutrosophic sets and systems, 6(1), 48–53. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1073&context=nss_journal
- [33] Samuel, A. E., & Narmadhagnanam, R. (2018). Cosine Exponential Distance of Single valued Neutrosophic multi sets in medical diagnosis. International journal of engineering research and application, 8(6), 26–29. https://fs.unm.edu/neut/CosineExponentialDistance.pdf
- [34] Smarandache, F. (2013). n-Valued refined Neutrosophic logic and its applications to physics. Progress in physics, 4, 143–146. https://doi.org/10.5281/zenodo.49149
- [35] Broumi, S., & Smarandache, F. (2014). Neutrosophic refined similarity measure based on cosine function. Neutrosophic sets and systems, 6, 4–10. https://philarchive.org/rec/BRONRS-2
- [36] Ye, J. (2014). Vector similarity measures of simplified Neutrosophic sets and their application in multicriteria decision making. International journal of fuzzy systems, 16(2), 204–211. https://fs.unm.edu/neut/VectorSimilarityMeasuresOfSimplified.pdf
- [37] Samuel, A. E., & Narmadhagnanam, R. (2017). Neutrosophic refined sets in medical diagnosis. International journal of fuzzy mathematical archive, 14(01), 117–123. https://doi.org/10.22457/ijfma.v14n1a14
- [38] Samuel, A. E., & Narmadhagnanam, R. (2018). Sine logarithmic distance of Neutrosophic refined sets in medical diagnoses. Journal of global research in mathematical archive, 5(6), 14–19. https://www.jgrma.com/index.php/jgrma/article/view/482
- [39] Samuel, A. E., & Narmadhagnanam, R. (2019). Contemporary techniques for Neutrosophic refined set and their exploitation in medical diagnosis. Journal of emerging technologies and innovative research, 6(1), 258–262. https://www.jetir.org/papers/JETIR1901027.pdf
- [40] Broumi, S., Deli, I., & Smarandache, F. (2015). N-valued interval Neutrosophic sets and their application in medical diagnosis. Critical review, 10, 45–69. https://doi.org/10.6084/M9.FIGSHARE.1502596
- [41] Samuel, A. E., & Narmadhagnanam, R. (2017). Innovative approaches for N-valued interval Neutrosophic sets and their execution in medical diagnosis. Journal of applied sciences, 17(9), 429–440. https://doi.org/10.3923/jas.2017.429.440
- [42] Samuel, A. E., & Narmadhagnanam, R. (2018). N-valued interval Neutrosophic set in medical diagnosis. International journal of pure and applied mathematics, 120(8), 59–67. https://acadpubl.eu/hub/2018-120-8/2/7.pdf
- [43] Samuel, A. E., & Narmadhagnanam, R. (2018). Execution of n-valued interval Neutrosophic sets in medical diagnosis. International journal of mathematics trends and technology, 58(1), 66–70. https://doi.org/10.14445/22315373/ijmtt-v58p509
- [44] Narmadhagnanam, R., & Samuel, A. E. (2024). Application of secant span in medical diagnosis. Neutrosophic systems with applications, 18, 40–45. https://doi.org/10.61356/j.nswa.2024.18254
- [45] Broumi, S., & Smarandache, F. (2015). Extended hausdorff distance and similarity measures for Neutrosophic refined sets and their application in medical diagnosis. Journal of new theory, 7, 64–78. https://dergipark.org.tr/en/pub/jnt/issue/34499/381190