Generalized Z-fuzzy soft β-covering based rough matrices and its application to magdm problem based on AHP method
Abstract
Fuzzy, rough, and soft sets are different mathematical tools mainly developed to deal with uncertainty. Combining these theories has a wide range of applications in decision analysis. In this paper, we defined a generalized Z-fuzzy soft -covering-based rough matrices. Some algebraic properties are explored for this newly constructed matrix. The main aim of this paper is to propose a novel MAGDM model using generalized Z-fuzzy soft -covering-based rough matrices. A MAGDM algorithm based on the AHP method is created to recruit the best candidate for an assistant professor job in an institute, and a numerical example is presented to demonstrate the created method.
Downloads
References
Ali, M. I. (2011). A note on soft sets, rough soft sets and fuzzy soft sets. Applied Soft Computing, 11 (4), 3329-3332. DOI: https://doi.org/10.1016/j.asoc.2011.01.003
Cagman, N., & Enginoglu, S. (2010). Soft matrix theory and its decision making. Computers & Mathematics with Applications, 59 (10), 3308-3314. DOI: https://doi.org/10.1016/j.camwa.2010.03.015
Cagman, N., & Enginoglu, S. (2012). Fuzzy soft matrix theory and its application in decision making. Iranian Journal of Fuzzy Systems, 9 (1), 109-119.
Dubois, D., & Prade, H. (1990). Rough fuzzy sets and fuzzy rough sets. International Journal of General System, 17(2-3), 191-209. DOI: https://doi.org/10.1080/03081079008935107
Feng, F., Li, C., Davvaz, B., & Ali, M. I. (2010). Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft computing, 14, 899-911. DOI: https://doi.org/10.1007/s00500-009-0465-6
Greco, S., Matarazzo, B., & Slowinski, R. (2001). Rough sets theory for multicriteria decision analysis. European journal of operational research, 129 (1), 1-47. DOI: https://doi.org/10.1016/S0377-2217(00)00167-3
Gurmani, S. H., Chen, H., & Bai, Y. (2022). Multi-attribute group decision-making model for selecting the most suitable construction company using the linguistic interval-valued T-spherical fuzzy TOPSIS method. Applied Intelligence. https://doi.org/10.1007/s10489-022-04103-0.
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. DOI: https://doi.org/10.1016/S0898-1221(02)00216-X
Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & Mathematics with Applications, 45 (4-5), 555-562. DOI: https://doi.org/10.1016/S0898-1221(03)00016-6
Molodtsov, D. (1999). Soft set theory - First results. Computers & Mathematics with Applications, 37 (4-5), 19-31. DOI: https://doi.org/10.1016/S0898-1221(99)00056-5
Muthukumar, P., & Krishnan, G. (2018). Generalized Fuzzy Soft Rough Matrices and Their Applications in Decision-Making Problems. International Journal of Fuzzy Systems, 20(2), 500-514. DOI: https://doi.org/10.1007/s40815-017-0350-x
Pawlak, Z. (1982). Rough sets. International journal of computer & information sciences, 11 (5), 341-356. DOI: https://doi.org/10.1007/BF01001956
Saaty, T. L. (1980). The Analytic Hierarchy Process. McGraw-Hill, New York. DOI: https://doi.org/10.21236/ADA214804
Saaty, T. L. (2008). Decision making with the analytic hierarchy process. International journal of services sciences, 1 (1), 83-98. DOI: https://doi.org/10.1504/IJSSCI.2008.017590
Sharma, H. K., Kumari, K., & Kar, S. (2018). Air passengers forecasting for Australian airline based on hybrid rough set approach. Journal of Applied Mathematics, Statistics and Informatics, 14(1), 5-18.
Sharma, H. K., Kumari, K., & Kar, S. (2021). Forecasting Sugarcane Yield of India based on rough set combination approach. Decision Making: Applications in Management and Engineering, 4(2), 163-177. DOI: https://doi.org/10.31181/dmame210402163s
Sharma, H. K., Singh, A., Yadav, D., & Kar, S. (2022). Criteria selection and decision making of hotels using Dominance Based Rough Set Theory. Operational Research in Engineering Sciences: Theory and Applications, 5(1), 41-55. DOI: https://doi.org/10.31181/oresta190222061s
Tufail, F., Shabir, M., & Abo-Tabl, E. S. A. (2022). A Comparison of Promethee and TOPSIS Techniques Based on Bipolar Soft Covering-Based Rough Sets. IEEE Access, 10, 37586-37602.
Vijayabalaji, S. (2014). Multi-decision making in generalized soft-rough matrices. Mathematical Sciences-International Research Journal, 3 (1), 19-24.
Yang, B. (2022). Fuzzy covering-based rough set on two different universes and its application. Artificial Intelligence Review, 55, 4717-4753.
Yüksel, Ş., Ergül, Z. G., & Tozlu, N. (2014). Soft covering based rough sets and their application. The Scientific World Journal, Article ID 970893, 1-9. DOI: https://doi.org/10.1155/2014/970893
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
Zhan, J., & Wang, Q. (2019). Certain types of soft coverings based rough sets with applications. International Journal of Machine Learning and Cybernetics, 10 (5), 1065-1076. DOI: https://doi.org/10.1007/s13042-018-0785-x
Zhan, J., & Sun, B. (2019). Covering-based soft fuzzy rough theory and its application to multiple criteria decision making. Computational and Applied Mathematics, 38 (4), 1-27.
Zhang, H., Liang, H., & Liu, D. (2004). Two new operators in rough set theory with applications to fuzzy sets. Information Sciences, 166 (1-4), 147-165. DOI: https://doi.org/10.1016/j.ins.2003.11.003
Zhang, L., & Zhan, J. (2019). Fuzzy soft β-covering based fuzzy rough sets and corresponding decision-making applications. International Journal of Machine Learning and Cybernetics, 10 (6), 1487-1502. DOI: https://doi.org/10.1007/s13042-018-0828-3
Zhu, W., & Wang, F. Y. (2007). On three types of covering-based rough sets. IEEE transactions on knowledge and data engineering, 19 (8), 1131-1144. DOI: https://doi.org/10.1109/TKDE.2007.1044
Zhu, W., & Wang, F. Y. (2012). The fourth type of covering-based rough sets. Information Sciences, 201, 80-92. DOI: https://doi.org/10.1016/j.ins.2012.01.026
