Bipolar Fuzzy Soft Set Theory Applied to Medical Diagnosis

Year 2024, Volume: 16 Issue: 2, 314 - 324, 31.12.2024

Orhan Dalkılıç , Naime Demirtaş

https://doi.org/10.47000/tjmcs.1254943

Abstract

The primary objective of this study is to advance Sanchez’s method for medical diagnosis by incorporating fuzzy arithmetic operations. To achieve this, we generalize the existing approach through the application of bipolar fuzzy soft set theory, which enables the identification of two distinct types of medical knowledge within a unified framework. Additionally, we propose a novel decision-making algorithm tailored to this enhanced approach. The application of this algorithm in the medical field is illustrated through practical examples, demonstrating its potential to improve diagnostic processes and decision-making in medical practice.

Keywords

Bipolar fuzzy soft sets, fuzzy numbers, defuzzification, decision making

References

• Abdullah, S., Aslam, M., Ullah, K., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent and Fuzzy Systems, 27(2)(2014), 729–742.
• Chetia, B., Das, P.K., An application of interval valued fuzzy soft set in medical diagnosis, International Journal of Contemporary Mathematical Sciences, 5(38)(2010), 1887–1894.
• Çelik, Y., Yamak S., Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations, Journal of Inequalities and Applications, 82(2013), 1–9.
• Dalkılıç, O., novel approach to soft set theory in decision-making under uncertainty, International Journal of Computer Mathematics, 98(2021)(10), 1935–1945.
• Dalkılıç, O., Relations on neutrosophic soft set and their application in decision making, Journal of Applied Mathematics and Computing, 67(2021), 257-–273.
• Dalkılıç, O., Approaches that take into account interactions between parameters: pure (fuzzy) soft sets, International Journal of Computer Mathematics, 99(2022)(7), 1428–1437.
• Dalkılıç, O., Two novel approaches that reduce the effectiveness of the decision maker in decision making under uncertainty environments, Iranian Journal of Fuzzy Systems, 19(2022)(2), 105–117.
• De, S.K., Biswas, R., Roy, A.R., An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets Systems, 117(2001), 209–213.
• Jaleel, A., WASPAS technique utilized for agricultural robotics system based on Dombi aggregation operators under bipolar complex fuzzy soft information, Journal of Innovative Research in Mathematical and Computational Sciences, 1(2)(2022), 67–95.
• Kamacı, H., Selectivity analysis of parameters in soft set and its effect on decision making, International Journal of Machine Learning and Cybernetics, 11(2020), 313-–324.
• Karaaslan, F., Deli, I., Soft neutrosophic classical sets and their applications in decision-making, Palestine Journal of Mathematics, 9(1)(2020), 312-–326.
• Kaufmann, A., Gupta, M.M., Introduction to Fuzzy Arithmetic Theory and Applications, Van Nostrand-Reinhold, New York, 1991.
• Lee, K.M., Bipolar-valued fuzzy sets and their basic operations, Proceeding International Conference, Bangkok, Thailand, (2000), 307–317.
• Liu, Z., Alcantud, J. C. R., Qin, K., Pei, Z., The relationship between soft sets and fuzzy sets and its application, Journal of Intelligent and Fuzzy Systems, 36(4)(2019), 3751–3764.
• Mahmood, T., Abdullah, S., Bilal, M., Rashid, S., Multiple criteria decision making based on bipolar valued fuzzy set, Annals of Fuzzy Mathematics and Informatics, 11(6)(2016), 1003–1009.
• Mahmood, T., Ullah, K., Ullah, M., Jan, N., Deli, I., Some aggregation operators for bipolar-valued hesitant fuzzy information based on einstein operational laws. Journal of Engineering and Applied Science, 36(2)(2017), 63-72.
• Mahmood, T., A novel approach towards bipolar soft sets and their applications, Journal of mathematics, (1)(2020), 4690808.
• Mahmood, T., Ur Rehman, U., A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures, International Journal of Intelligent Systems, 37(1)(2022), 535–567.
• Meenakshi, A.R., Kaliraja, M., An application of interval valued fuzzy matrices in medical diagnosis, International Journal of Mathematical Analysis, 5(36)(2011), 1791–1802.
• Molodtsov, D. Soft set theory-first results, Computers and Mathematics with Applications, 37(1999), 19-–31.
• Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11(5)(1982), 341-–356.
• Saikia, B.K., Das, P.K., Borkakati, A.K., An application of intuitionistic fuzzy soft sets in medical diagnosis, Bio-Science Research Bulletin, 19(2)(2003), 121–127.
• Sanchez, E., Resolution of composite fuzzy relation equations, Infornation Control, 30(1976), 38–48.
• Sanchez, E., Inverse of fuzzy relations, application to possibility distribution and medical diagnosis, Fuzzy Sets and Systems, 2(1979), 75–86.
• Ullah, K., Mahmood, T., Jan, N., Broumi, S., Khan, Q., On bipolar-valued hesitant fuzzy sets and their applications in multi-attribute decision making, The Nucleus, 55(2)(2018), 93–101.
• Zadeh, L.A., Fuzzy sets, Information and Control, 8(1965), 338–353.
• Zhang, W.R., Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, In Fuzzy Information Processing Society Biannual Conference, 1994.