Document Type : Research Paper

Author

Department of Mathematics, Umakanta Academy, Agartala-799001, Tripura, India.

10.22105/jfea.2021.275132.1083

Abstract

Hypersoft set is an extension of the soft set where there is more than one set of attributes occur and it is very much helpful in multi-criteria group decision making problem. In a hypersoft set, the function F is a multi-argument function. In this paper, we have used the notion of Fuzzy Hypersoft Set (FHSS), which is a combination of fuzzy set and hypersoft set. In earlier research works the concept of Fuzzy Soft Set (FSS) was introduced and it was applied successfully in various fields. The FHSS theory gives more flexibility as compared to FSS to tackle the parameterized problems of uncertainty. To overcome the issue where FSS failed to explain uncertainty and incompleteness there is a dire need for another environment which is known as FHSS. It works well when there is more complexity involved in the parametric data i.e the data that involves vague concepts. This work includes some basic set-theoretic operations on FHSSs and for the reliability and the authenticity of these operations, we have shown its application with the help of a suitable example. This example shows that how FHSS theory plays its role to solve real decision-making problems.

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Main Subjects

[1]       Abbas, M., Murtaza, G., & Smarandache, F. (2020). Basic operations on hypersoft sets and hypersoft point. Neutrosophic sets and systems, 35(1), 407-421.
[2]       Ajay, D., & Charisma, J. J. (2021). Neutrosophic hypersoft topological spaces. Neutrosophic sets and systems, 40(1), 11.27
[3]       Aktaş, H., & Çağman, N. (2007). Soft sets and soft groups. Information sciences, 177(13), 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
[4]       Ali, M. I., Feng, F., Liu, X., Min, W. K., & Shabir, M. (2009). On some new operations in soft set theory. Computers and mathematics with applications, 57(9), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
[5]       Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87-96.
[6]       Atanassov, K., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy sets and systems, 3, 343-349.
[7]       Çağman, N., & Enginoğlu, S. (2010). Soft set theory and uni–int decision making. European journal of operational research, 207(2), 848-855. https://doi.org/10.1016/j.ejor.2010.05.004
[8]       Çağman, N., & Enginoğlu, S. (2010). Soft matrix theory and its decision making. Computers and mathematics with applications, 59(10), 3308-3314. https://doi.org/10.1016/j.camwa.2010.03.015
[9]       Cagman, N., Enginoglu, S., & Citak, F. (2011). Fuzzy soft set theory and its applications. Iranian journal of fuzzy systems, 8(3), 137-147.
[10]    Cuong, B. C., & Kreinovich, V. (2014). Picture fuzzy sets. Journal of computer science and cybernetics, 30(4), 409-420.
[11]    Goguen, J. A. (1967). L-fuzzy sets. Journal of mathematical analysis and applications, 18(1), 145-174.
[12]    Gorzałczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy sets and systems, 21(1), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
[13]    Maji, P. K., Biswas, R., & Roy, A. R. (2001). Fuzzy soft sets. Journal of fuzzy mathematics, 9, 589-602.
[14]    Maji, P. K., Roy, A. R., & Biswas, R. (2002). An application of soft sets in a decision-making problem. Computers and mathematics with applications, 44(8-9), 1077-1083.
[15]    Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers and mathematics with applications, 45(4-5), 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
[16]    Molodtsov, D. (1999). Soft set theory—first results. Computers and mathematics with applications, 37(4-5), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
[17]    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
[18]    Saqlain, M., Moin, S., Jafar, M. N., Saeed, M., & Smarandache, F. (2020). Aggregate operators of neutrosophic hypersoft set. Infinite Study.
[19]    Saeed, M., Ahsan, M., Siddique, M. K., & Ahmad, M. R. (2020). A study of the fundamentals of hypersoft set theory. Infinite Study.
[20]    Smarandache, F. (2018). Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic sets syst, 22, 168-170.
[21]    Wang, F., Li, X., & Chen, X. (2014). Hesitant fuzzy soft set and its applications in multicriteria decision making. Journal of applied mathematics, 1-10. https://doi.org/10.1155/2014/643785
[22]    Xu, W., Ma, J., Wang, S., & Hao, G. (2010). Vague soft sets and their properties. Computers and mathematics with applications, 59(2), 787-794. https://doi.org/10.1016/j.camwa.2009.10.015
[23]    Yolcu, A., & Ozturk, T. Y. (2021). Fuzzy hypersoft sets and its application to decision-making. In Theory and application of hypersoft set. https://www.researchgate.net/profile/Naveed-Jafar/publication/349455966_HyperSoftSet-book/links/6030c5424585158939b7c455/HyperSoftSet-book.pdf#page=58
[24]    Zadeh, L. A. (1965). Fuzzy set. Information and control, 8, 338-353.
[25]    Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision-making with Pythagorean fuzzy sets. International journal of intelligent systems, 29(12), 1061-1078. https://doi.org/10.1002/int.21676
[26]    Zimmermann, H. J. (1993). Fuzzy set theory and its applications. Kluwer academic publishers.
[27]    Zulqarnain, R. M., Xin, X. L., & Saeed, M. (2020). Extension of TOPSIS method under intuitionistic fuzzy hypersoft environment based on correlation coefficient and aggregation operators to solve decision making problem. AIMS mathematics, 6(3), 2732-2755.
[28]    Zulqarnain, R. M., Xin, X. L., Saqlain, M., Saeed, M., Smarandache, F., & Ahamad, M. I. (2021). Some fundamental operations on interval valued neutrosophic hypersoft set with their properties. Neutrosophic sets and systems, 40(1), 134-148. https://digitalrepository.unm.edu/nss_journal/vol40/iss1/8