Einstein-operations on fuzzy soft multi sets and decision making
DOI:
https://doi.org/10.5269/bspm.32546Abstract
In this paper, we define Einstein product and Einstein sum of fuzzy soft multi sets (FSM-sets) and using these products, we introduce an adjustable approach to FSM-set based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed FSM-set based decision-making procedure in practical application is shown by some numerical examples.
References
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27. Maji, P. K., Biswas, R., Roy, A. R., Fuzzy soft sets, J. Fuzzy Math. 9, 589-602 (2001).
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32. Mukherjee, A., Das, A. K., Topological structure formed by fuzzy soft multi sets, Rev. Bull. Cal. Math. Soc. 21, 193-212 (2013).
33. Mukherjee, A., Das, A. K., Topological structure formed by soft multi sets and soft multi compact space, Ann. Fuzzy Math. Inform. 7, 919-933 (2014).
34. Mukherjee, A., Das, A. K., Interval valued intuitionistic fuzzy soft multi set theoretic ap-proach to decision making problems, Proceedings of the 2015 IEEE Int. Conf. on Comp. Comm. Cont., IEEE Xplore Digital Library, DOI: 10.1109/IC4.2015.7375640, 1-5, (2015). https://doi.org/10.1109/IC4.2015.7375640
35. Mukherjee, A., Das, A. K., Application of interval valued intuitionistic fuzzy soft set in in-vestment decision making, Proc. of the IEEE 5th Int. Conf. on Advances in Computing and Communications, IEEE Xplore Digital Library, 61-64, (2015). https://doi.org/10.1109/ICACC.2015.37
36. Mukherjee, A., Das, A. K., Relations on intuitionistic fuzzy soft multi sets, Information Science and Applications, Lecture Notes in Electrical Engineering, (Springer), 339, 607-614 (2015). https://doi.org/10.1007/978-3-662-46578-3_71
37. Roy, A.R., Maji, P. K., A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203, 412-418 (2007) https://doi.org/10.1016/j.cam.2006.04.008
38. Sayed, O.R., Khalil, A. M., Some properties of soft-topology, Hacettepe Journal of Mathematics and Statistics, 44(5), 1133 - 1145 (2015).
39. She, Y., He, X., Uncertainty measures in rough algebra with applications to rough logic, Int. J Mach. Learn. Cyber., 5, 671-681 (2014). https://doi.org/10.1007/s13042-013-0206-0
40. Tokat, D., Osmanoglu, I., Soft multi set and soft multi topology, Nevsehir Universitesi Fen Bilimleri Enstitusu Dergisi Cilt. 2, 109-118 (2011)
41. Vamitha, V., Rajaram, S., A multiset based forecasting model for fuzzy time series, Hacet-tepe Journal of Mathematics and Statistics, 44(4), 965-973 (2015). https://doi.org/10.15672/HJMS.201511334
42. Yang, H-L, Liaoy, X., Liz, S-G., On soft continuous mappings and soft connectedness of soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(2), 385 - 398 (2015). https://doi.org/10.15672/HJMS.2015459876
43. Zadeh, L. A., Fuzzy sets, Inform. Control. 8, 338-353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X
44. Zhan, J., Dudek, W. A., Neggers, J., A new soft union set: characterizations of hemirings, Int. J. Mach. Learn. Cyber., (Springer), available as online first article, DOI 10.1007/s13042-015-0343-8 (2015). https://doi.org/10.1007/s13042-015-0343-8
45. Zhan, J., Liu, Q., Davvaz, B., A new rough set theory: rough soft hemirings, J. Intell. Fuzzy Systems, 28, 1687-1697 (2015). https://doi.org/10.3233/IFS-141455
46. Zhu, K., Zhan, J., Fuzzy parameterized fuzzy soft sets and decision making, International Journal of Machine Learning and Cybernetics, (Springer), available as online first article, 2015). https://doi.org/10.1007/s13042-015-0449-z
47. Zimmermann, H.J., Fuzzy set theory and its applications, Kluwer Academic, 2th edition, Dordrecht, (1991). https://doi.org/10.1007/978-94-015-7949-0
2. Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M., On some new operations in soft set theory, Comp. Math. Appl. 57, 1547-1553 (2009). https://doi.org/10.1016/j.camwa.2008.11.009
3. Alkhazaleh, S., Salleh, A.R., Fuzzy soft multi sets theory, Abstract and Applied Analysis, Vol. 2012, Article ID 350603, 20 pages, (2012). https://doi.org/10.1155/2012/350603
4. Alkhazaleh, S., Salleh, A.R., Hassan, N.: Fuzzy parameterized interval-valued fuzzy soft sets, Appl. Math. Sci., 67, 3335-3346(2011). https://doi.org/10.1155/2011/479756
5. Alkhazaleh, S., Salleh, A.R., Hassan, N., Soft multisets theory, App. Math. Sci. 5, 3561-3573 (2011) https://doi.org/10.1155/2011/479756
6. Atmaca, S., Zorlutuna, I., On topological structures of fuzzy parametrized soft sets, The Scientific World Journal, Article ID 164176, 8 pages (2014). https://doi.org/10.1155/2014/164176
7. Babitha, K. V., John, S. J., On soft multi sets. Ann. Fuzzy Math, Inform. 5, 35-44 (2013)
8. Balami, H. M., Ibrahim, A. M., Soft multiset and its application in information system, Int. J. Sci. Research and management. 1, 471-482 (2013).
9. Bashir, M., Salleh, A. R., Fuzzy parameterized soft expert set, Abstr. Appl. Anal., Ar-ticle ID 258361, 15 pages (2012). https://doi.org/10.1155/2012/258361
10. Cagman, N., Citak, F., Enginoglu, S., Fuzzy parameterized fuzzy soft set theory and its ap-plications, Turk. J. Fuzzy Systems, 1(1), 21-35 (2010).
11. Cagman, N., Citak, F., Enginoglu, S., FP-soft set theory and its applications, Ann. Fuzzy Math. Inform., 2, 219-226 (2011).
12. Cagman, N., Deli, I., Means of FP-soft sets and their applications, Hacett. J. Math. Stat., 41(5), 615-625 (2012).
13. Cagman, N., Deli, I., Products of FP-soft sets and their applications, Hacett. J. Math. Stat., 41(3), 365-374 (2012).
14. Cagman, N., Enginolu, S., Soft matrix theory and its decision making, Comput. Math.Appl., 59, 3308-3314 (2010). https://doi.org/10.1016/j.camwa.2010.03.015
15. Cagman, N., Enginoglu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207, 848-855 (2010). https://doi.org/10.1016/j.ejor.2010.05.004
16. Chen, D., Tsang, E.C.C., Yeung, D.S., Wang, X., The paramerization reduction of soft sets and applications, Comput. Math. Appl., 49, 757-763 (2005). https://doi.org/10.1016/j.camwa.2004.10.036
17. Das, A. K., On partially included intuitionistic fuzzy rough relations, Afrika Matematika (Springer), available as online first article, (2016). https://doi.org/10.1007/s13370-016-0395-2
18. Das, A. K., Weighted fuzzy soft multiset and decision-making, Int. J. Mach. Learn. Cyber, Springer, available as online first article, (2016). https://doi.org/10.1007/s13042-016-0607-y
19. Deli, I., Cagman, N., Intuitionistic fuzzy parameterized soft set theory and its decision making, Appl. Soft Comput., 28, 109-113 (2015). https://doi.org/10.1016/j.asoc.2014.11.053
20. Deli, I., Cagman, N., Relations on FP-soft sets applied to decision making problems, J. New Theory, 3, 98-107 (2015).
21. Feng, F., Liu, X.Y., Leoreanu-Fotea, V., Jun, Y.B., Soft sets and soft rough sets, Inform. Sci., 181, 1125-1137 (2011). https://doi.org/10.1016/j.ins.2010.11.004
22. Feng, F., Jun, Y.B., Liu, X., Li, L., An adjustable approach to fuzzy soft set based decision making, J. Comp. Appl. Math. 234, 10-20 (2010). https://doi.org/10.1016/j.cam.2009.11.055
23. Hussain, S., Ahmad, B., Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3), 559 - 568 (2015). https://doi.org/10.15672/HJMS.2015449426
24. Jamkhaneh, E.B., Nadarajah, S., A new generalized intuitionistic fuzzy set, Hacettepe Journal of Mathematics and Statistics, 44(6), 1537 - 1551 (2015).
25. Khan, M., Jun, Y.B., Yousafzai F., Fuzzy ideals in right regular LA-semigroups, Hacettepe Journal of Mathematics and Statistics, 44(3), 569 - 586 (2015). https://doi.org/10.15672/HJMS.2015449419
26. Kong, Z., Gao, L.Q., Wang, L.F., Comment on a fuzzy soft set theoretic approach to decision making problems, J. Comp. Appl. Math. 223, 540-542 (2009). https://doi.org/10.1016/j.cam.2008.01.011
27. Maji, P. K., Biswas, R., Roy, A. R., Fuzzy soft sets, J. Fuzzy Math. 9, 589-602 (2001).
28. Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Comp. Math. Appl. 45, 555-562 (2003). https://doi.org/10.1016/S0898-1221(03)00016-6
29. Maji, P. K., Roy, A. R., Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077-1083 (2002) https://doi.org/10.1016/S0898-1221(02)00216-X
30. Molodtsov, D., Soft set theory-first results, Comp. Math. Appl. 37, 19-31 (1999). https://doi.org/10.1016/S0898-1221(99)00056-5
31. Mukherjee, A., Das, A. K., Application of fuzzy soft multi sets in decision making problems, Smart Innovation Systems and Technologies, Springer Verlag, 43(1) 21-28 (2015). https://doi.org/10.1007/978-81-322-2538-6_3
32. Mukherjee, A., Das, A. K., Topological structure formed by fuzzy soft multi sets, Rev. Bull. Cal. Math. Soc. 21, 193-212 (2013).
33. Mukherjee, A., Das, A. K., Topological structure formed by soft multi sets and soft multi compact space, Ann. Fuzzy Math. Inform. 7, 919-933 (2014).
34. Mukherjee, A., Das, A. K., Interval valued intuitionistic fuzzy soft multi set theoretic ap-proach to decision making problems, Proceedings of the 2015 IEEE Int. Conf. on Comp. Comm. Cont., IEEE Xplore Digital Library, DOI: 10.1109/IC4.2015.7375640, 1-5, (2015). https://doi.org/10.1109/IC4.2015.7375640
35. Mukherjee, A., Das, A. K., Application of interval valued intuitionistic fuzzy soft set in in-vestment decision making, Proc. of the IEEE 5th Int. Conf. on Advances in Computing and Communications, IEEE Xplore Digital Library, 61-64, (2015). https://doi.org/10.1109/ICACC.2015.37
36. Mukherjee, A., Das, A. K., Relations on intuitionistic fuzzy soft multi sets, Information Science and Applications, Lecture Notes in Electrical Engineering, (Springer), 339, 607-614 (2015). https://doi.org/10.1007/978-3-662-46578-3_71
37. Roy, A.R., Maji, P. K., A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203, 412-418 (2007) https://doi.org/10.1016/j.cam.2006.04.008
38. Sayed, O.R., Khalil, A. M., Some properties of soft-topology, Hacettepe Journal of Mathematics and Statistics, 44(5), 1133 - 1145 (2015).
39. She, Y., He, X., Uncertainty measures in rough algebra with applications to rough logic, Int. J Mach. Learn. Cyber., 5, 671-681 (2014). https://doi.org/10.1007/s13042-013-0206-0
40. Tokat, D., Osmanoglu, I., Soft multi set and soft multi topology, Nevsehir Universitesi Fen Bilimleri Enstitusu Dergisi Cilt. 2, 109-118 (2011)
41. Vamitha, V., Rajaram, S., A multiset based forecasting model for fuzzy time series, Hacet-tepe Journal of Mathematics and Statistics, 44(4), 965-973 (2015). https://doi.org/10.15672/HJMS.201511334
42. Yang, H-L, Liaoy, X., Liz, S-G., On soft continuous mappings and soft connectedness of soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(2), 385 - 398 (2015). https://doi.org/10.15672/HJMS.2015459876
43. Zadeh, L. A., Fuzzy sets, Inform. Control. 8, 338-353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X
44. Zhan, J., Dudek, W. A., Neggers, J., A new soft union set: characterizations of hemirings, Int. J. Mach. Learn. Cyber., (Springer), available as online first article, DOI 10.1007/s13042-015-0343-8 (2015). https://doi.org/10.1007/s13042-015-0343-8
45. Zhan, J., Liu, Q., Davvaz, B., A new rough set theory: rough soft hemirings, J. Intell. Fuzzy Systems, 28, 1687-1697 (2015). https://doi.org/10.3233/IFS-141455
46. Zhu, K., Zhan, J., Fuzzy parameterized fuzzy soft sets and decision making, International Journal of Machine Learning and Cybernetics, (Springer), available as online first article, 2015). https://doi.org/10.1007/s13042-015-0449-z
47. Zimmermann, H.J., Fuzzy set theory and its applications, Kluwer Academic, 2th edition, Dordrecht, (1991). https://doi.org/10.1007/978-94-015-7949-0
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2022-02-01
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