A FUZZY-SOFT-SET THEORYAPPROACH FOR SOLVING DECISION-MAKING PROBLEMS ON CERTAIN HYBRID SET MODEL
Keywords:Fuzzy Set, Fuzzy Soft Set, Rough Soft Set, Decision-Making, Hybrid Decision-Making Model
Uncertainty is a key aspect that arises in any actual mathematical model and may lead to a change in the situation. Because of the presence of uncertainty in the model, it is particularly challenging to manage these models using conventional techniques. Fuzzy set theory and its extensions, such as intuitionistic fuzzy set, hesitant fuzzy set, rough fuzzy set, and hybrid fuzzy-soft-set theory, have been included into mathematics to manage this uncertainty. Applications of these concepts for the expansion of fuzzy set information, particularly the application to circumstances involving decision-making problems, have made some headway in this article in terms of their practicality. The methods for generating judgments based on (fuzzy) soft sets, including soft, rough sets and rough, soft sets, are also examined in this article. Innovative techniques and numerical examples have been provided in this study, with a focus on the use of hybrid models to address decision-making issues. It might serve as the complexity of hybrid soft set models that address decision-making issues.
Agarwal, R., Nishad, A. K., Agrawal, A., & Husain, S. (2023). Evaluation and Selection of a Green and Sustainable Supplier by Using a Fuzzy Aras Mathematical Modeling. New Mathematics and Natural Computation. https://doi.org/10.1142/S1793005723500382.
Akram, M., Shahzadi, S., Rasool, A., & Sarwar, M. (2022). Decision-Making Methods Based on Fuzzy Soft Competition Hypergraphs. Complex & Intelligent Systems, 8(3), 2325-2348. https://doi.org/10.1007/s40747-022-00646-4.
Begam, S. S., Selvachandran, G., Ngan, T. T., & Sharma, R. (2020). Similarity Measure of Lattice Ordered Multi-Fuzzy-Soft-Sets Based on Set Theoretic Approach and its Application in Decision Making. Mathematics, 8(8), 1255. https://doi.org/10.3390/math8081255.
Chen, Z. H., Wan, S. P., & Dong, J. Y. (2022). An Efficiency-Based Interval Type-2 Fuzzy Multi-Criteria Group Decision Making for Makeshift Hospital Selection. Applied Soft Computing, 115, 108243. https://doi.org/10.1016/j.asoc.2021.108243.
Dalkılıç, O. (2021). A Novel Approach to Soft Set Theory in Decision-Making Under Uncertainty. International Journal of Computer Mathematics, 98(10), 1935-1945. https://doi.org/10.1080/00207160.2020.1868445.
Feng, F., Jun, Y. B., Liu, X., & Li, L. (2010). An Adjustable Approach to Fuzzy-Soft-Set Based Decision Making. Journal of Computational and Applied Mathematics, 234(1), 10-20. https://doi.org/10.1016/j.cam.2009.11.055.
Husain, S., & Shivani, K. (2018). A Study of Properties of Soft Set and its Applications. International Research Journal of Engineering and Technology (IRJET), 5(01), 2395-0056.
Husain, S., Kumari, A., & Tyagi, V. K. (2022). An Approach to Group Decision Problems Using Fuzzy-Soft-Set Theory and Lambda Cuts. International Journal of Early Childhood Special Education (INT-JECSE), 14(8).
Husain, S., Tyagi, V. K., & Gupta, M. K. (2022). A Fuzzy Soft Set-Theoretic New Methodology to Solve Decision-Making Problems. In Electronic Systems and Intelligent Computing: Proceedings of ESIC 2021 Singapore: Springer Nature Singapore. 671-683. https://doi.org/10.1007/978-981-16-9488-2_64.
Jana, C., & Pal, M. (2018). Application of Bipolar Intuitionistic Fuzzy-Soft-Sets in Decision Making Problem. International Journal of Fuzzy System Applications (IJFSA), 7(3), 32-55. https://doi.org/10.4018/IJFSA.2018070103.
Khalil, A. M., & Hassan, N. (2019). Inverse Fuzzy-Soft-Set and its Application in Decision Making. International Journal of Information and Decision Sciences, 11(1), 73-92. https://doi.org/10.1504/IJIDS.2019.096630.
Kong, Z., Gao, L. & Wang, L. (2009). Comment on a Fuzzy-Soft-Set Theoretic Approach to Decision Making Problems. Journal of Computational and Applied Mathematics, 223(2), 540-542. https://doi.org/10.1016/j.cam.2008.01.011.
Ma, X., Liu, Q., & Zhan, J. (2017). A Survey of Decision Making Methods Based on Certain Hybrid Soft Set Models. Artificial Intelligence Review, 47(4), 507-530. https://doi.org/10.1007/s10462-016-9490-x.
Maji, P. K., Roy, A. R., & Biswas, R. (2002). An Application of Soft Sets in a Decision Making Problem. Computers & Mathematics with Applications, 44(8-9), 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X.
Molodtsov, D. (1999). Soft Set Theory-First Results. Computers & Mathematics with Applications, 37(4-5), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5.
Rahman, A. U., Saeed, M., Khalifa, H. A. E. W., & Afifi, W. A. (2022). Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets. AIMS Math, 7(3), 3866-3895. https://doi.org/10.3934/math.2022214.
Riaz, M., & Tehrim, S. T. (2019). Bipolar fuzzy soft mappings with application to bipolar disorders. International Journal of Biomathematics, 12(07), 1950080. https://doi.org/10.1142/S1793524519500803.
Roy, A. R., & Maji, P. K. (2007). A Fuzzy-Soft-Set Theoretic Approach to Decision Making Problems. Journal of Computational and Applied Mathematics, 203(2), 412-418. https://doi.org/10.1016/j.cam.2006.04.008.
Shabir, M., Ali, M. I., & Shaheen, T. (2013). Another Approach to Soft Rough Sets. Knowledge-Based Systems, 40, 72-80. https://doi.org/10.1016/j.knosys.2012.11.012.
Yang, Y., Tan, X., & Meng, C. (2013). The Multi-Fuzzy-Soft-Set and its Application in Decision Making. Applied Mathematical Modelling, 37(7), 4915-4923. https://doi.org/10.1016/j.apm.2012.10.015.
Zadeh, L. (1965). Fuzzy sets. Inform Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.
Zulqarnain, R. M., Xin, X. L., Saqlain, M., & Khan, W. A. (2021). Topsis Method Based on the Correlation Coefficient of Interval-Valued Intuitionistic Fuzzy-Soft-Sets and Aggregation Operators with their Application in Decision-Making. Journal of Mathematics, 1-16. https://doi.org/10.1155/2021/6654657.
Çağman, N., & Karataş, S. (2013). Intuitionistic Fuzzy-Soft-Set Theory and its Decision Making. Journal of Intelligent & Fuzzy Systems, 24(4), 829-836. https://doi.org/10.3233/IFS-2012-0601.
How to Cite
Copyright (c) 2023 Shamshad Husain, Vipin Kumar Tyagi, Mridul Kumar Gupta
This work is licensed under a Creative Commons Attribution 4.0 International License.