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A Novel Approach to Similarity of Soft Sets

Year 2019, Volume: 9 Issue: 1, 23 - 35, 28.06.2019

Hüseyin Kamacı

Abstract

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.

Keywords

Soft set Soft set operations Similarity coefficient

References

  • [1] Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Comput. Math. Appl., 59, 3458-3463, 2010.
  • [2] Aktaş, H., Çağman, N., Soft sets and soft groups, Inform. Sci., 177, 2726-2735, 2007.
  • [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] 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] Ali, M. I., Shabir, M., Naz, M., Algebraic structures of soft sets associated with new operations, Comput. Math. Appl., 61, 2647-2654, 2011.
  • [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] 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] Atagün, A. O., Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, 592-601, 2011.
  • [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] Çağman, N., Çıtak, F., Aktaş, H., Soft int-group and its applications to group theory, Neural. Comput. Appl., 21, 151-158, 2012.
  • [11] Çağman, N., Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl., 59, 3308-3314, 2010.
  • [12] Çağman, N., Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207, 848-855, 2010.
  • [13] Çağman, N., Karatas, S., Enginoğlu, S., Soft topology, Comput. Math. Appl., 62, 351-358, 2011.
  • [14] Çelik, Y., Ekiz, C., Yamak, S., A new view on soft rings, Hacet. J. Math. Stat., 40, 273-286, 2011.
  • [15] Çıtak, F., Çağman, N., Soft int-rings and its algebraic applications, J. Intell. Fuzzy Syst., 28, 1225-1233, 2015.
  • [16] Feng, F., Jun, Y. B., Zhao, X., Soft semirings, Comput. Math. Appl., 56, 2621-2628, 2008.
  • [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] Karaaslan, F., Çağman, N., Enginoğlu, S., Soft lattices, Journal of New Results in Science, 1, 5-17, 2012.
  • [19] Kharal, A., Distance and similarity measures for soft sets, New Math. Nat. Comput., 6, 321-334, 2010.
  • [20] Liu, X., Xiang, D., Zhan, J., Shum, K. P., Isomorphism theorems for soft rings, Algebra Colloq., 19, 649-656, 2012.
  • [21] Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Comput. Math. Appl., 45, 555-562, 2003.
  • [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] Majumdar, P., Samanta, S. K., Similarity measure of soft sets, New Math. Nat. Comput., 4, 1-12, 2008.
  • [24] Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37, 19-31, 1999.
  • [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] Sezgin, A., Atagün, A. O., On operations of soft sets, Comput. Math. Appl., 61, 1457-1467, 2011.
  • [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] Shabir, M., Naz, M., On soft topological spaces, Comput. Math. Appl., 61, 1786-1799, 2011.
  • [29] Sun, Q. M., Zhang, Z. L., Liu, J., Soft sets and soft modules, Lecture Notes in Comput. Sci., 5009, 403-409, 2008.
  • [30] Tunçay, M., Sezgin, A., Soft union ring and its applications to ring theory, International Journal of Computer Applications, 151, 7-13, 2016.
  • [31] Varol, B. P., Shostak, A., Aygün, H., A new approach to soft topology, Hacet. J. Math. Stat., 41, 731-741, 2012.
  • [32] Yang, W., New similarity measures for soft sets and their application, Fuzzy Inf. Eng., 1, 19-25, 2013.
  • [33] Yang, Y., Zeng, L., Tan, X., Chen, H., Similarity coefficient in soft set theory, Fuzzy Inf. Eng., 1, 119-126, 2013.
  • [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] Zhu, P., Wen, Q., Operations of soft set revisited, J. Appl. Math., 2013, Article ID 105752, 7 pages, 2013.

Esnek Kümelerin Benzerliğine Yeni Bir Yaklaşım

Year 2019, Volume: 9 Issue: 1, 23 - 35, 28.06.2019

Hüseyin Kamacı

Abstract

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.

Keywords

Esnek küme Esnek küme işlemleri Benzerlik Katsayısı

References

  • [1] Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Comput. Math. Appl., 59, 3458-3463, 2010.
  • [2] Aktaş, H., Çağman, N., Soft sets and soft groups, Inform. Sci., 177, 2726-2735, 2007.
  • [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] 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] Ali, M. I., Shabir, M., Naz, M., Algebraic structures of soft sets associated with new operations, Comput. Math. Appl., 61, 2647-2654, 2011.
  • [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] 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] Atagün, A. O., Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, 592-601, 2011.
  • [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] Çağman, N., Çıtak, F., Aktaş, H., Soft int-group and its applications to group theory, Neural. Comput. Appl., 21, 151-158, 2012.
  • [11] Çağman, N., Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl., 59, 3308-3314, 2010.
  • [12] Çağman, N., Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res., 207, 848-855, 2010.
  • [13] Çağman, N., Karatas, S., Enginoğlu, S., Soft topology, Comput. Math. Appl., 62, 351-358, 2011.
  • [14] Çelik, Y., Ekiz, C., Yamak, S., A new view on soft rings, Hacet. J. Math. Stat., 40, 273-286, 2011.
  • [15] Çıtak, F., Çağman, N., Soft int-rings and its algebraic applications, J. Intell. Fuzzy Syst., 28, 1225-1233, 2015.
  • [16] Feng, F., Jun, Y. B., Zhao, X., Soft semirings, Comput. Math. Appl., 56, 2621-2628, 2008.
  • [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] Karaaslan, F., Çağman, N., Enginoğlu, S., Soft lattices, Journal of New Results in Science, 1, 5-17, 2012.
  • [19] Kharal, A., Distance and similarity measures for soft sets, New Math. Nat. Comput., 6, 321-334, 2010.
  • [20] Liu, X., Xiang, D., Zhan, J., Shum, K. P., Isomorphism theorems for soft rings, Algebra Colloq., 19, 649-656, 2012.
  • [21] Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Comput. Math. Appl., 45, 555-562, 2003.
  • [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] Majumdar, P., Samanta, S. K., Similarity measure of soft sets, New Math. Nat. Comput., 4, 1-12, 2008.
  • [24] Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37, 19-31, 1999.
  • [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] Sezgin, A., Atagün, A. O., On operations of soft sets, Comput. Math. Appl., 61, 1457-1467, 2011.
  • [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] Shabir, M., Naz, M., On soft topological spaces, Comput. Math. Appl., 61, 1786-1799, 2011.
  • [29] Sun, Q. M., Zhang, Z. L., Liu, J., Soft sets and soft modules, Lecture Notes in Comput. Sci., 5009, 403-409, 2008.
  • [30] Tunçay, M., Sezgin, A., Soft union ring and its applications to ring theory, International Journal of Computer Applications, 151, 7-13, 2016.
  • [31] Varol, B. P., Shostak, A., Aygün, H., A new approach to soft topology, Hacet. J. Math. Stat., 41, 731-741, 2012.
  • [32] Yang, W., New similarity measures for soft sets and their application, Fuzzy Inf. Eng., 1, 19-25, 2013.
  • [33] Yang, Y., Zeng, L., Tan, X., Chen, H., Similarity coefficient in soft set theory, Fuzzy Inf. Eng., 1, 119-126, 2013.
  • [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] Zhu, P., Wen, Q., Operations of soft set revisited, J. Appl. Math., 2013, Article ID 105752, 7 pages, 2013.
There are 35 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Hüseyin Kamacı

Publication Date June 28, 2019
Submission Date June 8, 2018
Acceptance Date May 26, 2019
Published in Issue Year 2019 Volume: 9 Issue: 1

Cite

APA Kamacı, H. (2019). A Novel Approach to Similarity of Soft Sets. Adıyaman University Journal of Science, 9(1), 23-35.
AMA Kamacı H. A Novel Approach to Similarity of Soft Sets. ADYU J SCI. June 2019;9(1):23-35.
Chicago Kamacı, Hüseyin. “A Novel Approach to Similarity of Soft Sets”. Adıyaman University Journal of Science 9, no. 1 (June 2019): 23-35.
EndNote Kamacı H (June 1, 2019) A Novel Approach to Similarity of Soft Sets. Adıyaman University Journal of Science 9 1 23–35.
IEEE H. Kamacı, “A Novel Approach to Similarity of Soft Sets”, ADYU J SCI, vol. 9, no. 1, pp. 23–35, 2019.
ISNAD Kamacı, Hüseyin. “A Novel Approach to Similarity of Soft Sets”. Adıyaman University Journal of Science 9/1 (June 2019), 23-35.
JAMA Kamacı H. A Novel Approach to Similarity of Soft Sets. ADYU J SCI. 2019;9:23–35.
MLA Kamacı, Hüseyin. “A Novel Approach to Similarity of Soft Sets”. Adıyaman University Journal of Science, vol. 9, no. 1, 2019, pp. 23-35.
Vancouver Kamacı H. A Novel Approach to Similarity of Soft Sets. ADYU J SCI. 2019;9(1):23-35.
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