A Novel Approach to Similarity of Soft Sets

Öz

The main objective of this paper is to present a new perspective for the similarity between soft sets. Therefore, the concept of similarity coefficient for soft sets are defined. Also, some theoretical investigations for this concept are presented. Finally, it is given examples of how this similarity coefficient can be used to solve the problems in various fields involving the uncertainty.

Anahtar Kelimeler

• Soft set,Soft set operations,Similarity coefficient

Esnek Kümelerin Benzerliğine Yeni Bir Yaklaşım

Öz

Bu çalışmanın temel amacı esnek kümeler arasındaki benzerlik için yeni bir bakış açısı sunmaktır. Bu bağlamda, ilk olarak esnek kümeler için benzerlik katsayısı kavramı tanımlanmıştır. Ayrıca, bu kavram için bazı teorik araştırmalar sunulmuştur. Son olarak, bu benzerlik katsayısının belirsizlik içeren çeşitli alanlardaki problemleri çözmede nasıl kullanılabileceğinin örnekleri verilmiştir.

Anahtar Kelimeler

• Esnek küme,Esnek küme işlemleri,Benzerlik Katsayısı

Kaynakça

1. [1] Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Comput. Math. Appl., 59, 3458-3463, 2010.
2. [2] Aktaş, H., Çağman, N., Soft sets and soft groups, Inform. Sci., 177, 2726-2735, 2007.
3. [3] Ali, M. I., Mahmood, T., Rehman M. M. U., Aslam, M. F., On lattice ordered soft sets, Appl. Soft Comput., 36, 499-505, 2015.
4. [4] Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M., On some new operations in soft set theory, Comput. Math. Appl., 57, 1547-1553, 2009.
5. [5] Ali, M. I., Shabir, M., Naz, M., Algebraic structures of soft sets associated with new operations, Comput. Math. Appl., 61, 2647-2654, 2011.
6. [6] Alshehri, N. O., Akram, M., Al-ghami, R. S., Applications of soft sets in K-algebras, Adv. Fuzzy Syst., 2013, Article ID 319542, 8 pages, 2013.
7. [7] Atagün, A. O., Kamacı, H., Oktay, O., Reduced soft matrices and generalized products with applications in decision making, Neural Comput. Appl., 29, 445-456, 2018.
8. [8] Atagün, A. O., Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, 592-601, 2011.

9. [9] Basu, T. M., Mahapatra, N. M., Mondal, S. K., Matrices in soft set theory and their applications in decision making problems, South Asian J. Math., 2, 126-143, 2012.
10. [10] Çağman, N., Çıtak, F., Aktaş, H., Soft int-group and its applications to group theory, Neural. Comput. Appl., 21, 151-158, 2012.
11. [11] Çağman, N., Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl., 59, 3308-3314, 2010.
12. [12] Çağman, N., Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207, 848-855, 2010.
13. [13] Çağman, N., Karatas, S., Enginoğlu, S., Soft topology, Comput. Math. Appl., 62, 351-358, 2011.
14. [14] Çelik, Y., Ekiz, C., Yamak, S., A new view on soft rings, Hacet. J. Math. Stat., 40, 273-286, 2011.
15. [15] Çıtak, F., Çağman, N., Soft int-rings and its algebraic applications, J. Intell. Fuzzy Syst., 28, 1225-1233, 2015.
16. [16] Feng, F., Jun, Y. B., Zhao, X., Soft semirings, Comput. Math. Appl., 56, 2621-2628, 2008.
17. [17] Kamacı, H., Atagün, A. O., Sönmezoğlu, A., Row-products of soft matrices with applications in multiple-disjoint decision making, Appl. Soft Comput., 62, 892-914, 2018.
18. [18] Karaaslan, F., Çağman, N., Enginoğlu, S., Soft lattices, Journal of New Results in Science, 1, 5-17, 2012.
19. [19] Kharal, A., Distance and similarity measures for soft sets, New Math. Nat. Comput., 6, 321-334, 2010.
20. [20] Liu, X., Xiang, D., Zhan, J., Shum, K. P., Isomorphism theorems for soft rings, Algebra Colloq., 19, 649-656, 2012.
21. [21] Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Comput. Math. Appl., 45, 555-562, 2003.
22. [22] 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.
23. [23] Majumdar, P., Samanta, S. K., Similarity measure of soft sets, New Math. Nat. Comput., 4, 1-12, 2008.
24. [24] Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37, 19-31, 1999.
25. [25] Pei, D., Miao, D., From soft sets to information systems, in: Hu, X., Liu, Q., Skowron, A., Lin, T. Y., Yager, R. R., Zhang, B. (Eds.) Proceedings of Granular Computing, IEEE, 2, 617-621, 2005.
26. [26] Sezgin, A., Atagün, A. O., On operations of soft sets, Comput. Math. Appl., 61, 1457-1467, 2011.
27. [27] Sezgin, A., Atagün, A. O., Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat, 25, 53-68, 2011.
28. [28] Shabir, M., Naz, M., On soft topological spaces, Comput. Math. Appl., 61, 1786-1799, 2011.
29. [29] Sun, Q. M., Zhang, Z. L., Liu, J., Soft sets and soft modules, Lecture Notes in Comput. Sci., 5009, 403-409, 2008.
30. [30] Tunçay, M., Sezgin, A., Soft union ring and its applications to ring theory, International Journal of Computer Applications, 151, 7-13, 2016.
31. [31] Varol, B. P., Shostak, A., Aygün, H., A new approach to soft topology, Hacet. J. Math. Stat., 41, 731-741, 2012.
32. [32] Yang, W., New similarity measures for soft sets and their application, Fuzzy Inf. Eng., 1, 19-25, 2013.
33. [33] Yang, Y., Zeng, L., Tan, X., Chen, H., Similarity coefficient in soft set theory, Fuzzy Inf. Eng., 1, 119-126, 2013.
34. [34] Yücel, C. C., Acar, U., A note on soft modules, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66, 66-74, 2017.
35. [35] Zhu, P., Wen, Q., Operations of soft set revisited, J. Appl. Math., 2013, Article ID 105752, 7 pages, 2013.