A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis

Zehra Güzel Ergül; Saziye Yüksel

doi:10.36753/mathenot.559242

Araştırma Makalesi

Yıl 2019, , 28 - 38, 30.04.2019

Zehra Güzel Ergül , Saziye Yüksel

https://doi.org/10.36753/mathenot.559242

Cited By: 5

Öz

Kaynakça

[1] Pawlak, Z., Rough sets. International Journal of Computer and Information Sciences. 11 (1982), no.5, 341-356.
[2] Molodtsov, D., Soft set theory-first results. Comput. Math. Appl. 37 (1999), 19-31.
[3] Yüksel, ¸S., Güzel Ergül, Z. and Tozlu, N., Soft covering based rough sets and their application. The Scientific World Journal. (2014), Article ID 970893, 9 pages.
[4] Zadeh, L. A., Fuzzy sets. Inform. Control. 8 (1965), 338-353.
[5] Zhu, W. and Wang, F. Y., On three types of covering based rough sets. IEEE Transactions on Knowledge and Data Engineering. 19 (2007), no.8, 1131-1143.
[6] Zhu, W., Topological approaches to covering rough sets. Information Science. 177 (2007), 1499-1508.
[7] Maji, P. K., Biswas, R. and Roy, A. R., Soft set theory. Computers and Mathematics with Applications. 45 (2003), 555-562.
[8] Ali, M. I., Feng, F., Liu, X., Min, W. K. and Shabir, M., On some new operations in soft set theory. Comput. Math. Appl. 57 (2009), 1547-1553.
[9] Akta¸s, H. and Ça˘gman, N., Soft sets and soft groups. Information Sciences. 177 (2007), 2726-2735.A tentative approach. Soft Comput. 14 (2010), 899-911.
[11] Feng, F., Liu, X., Violeta, F. L. and Young, J. B., Soft sets and soft rough sets. Information Sciences. 181 (2011), 1125-1137.
[12] Feng, F., Soft rough sets applied to multicriteria group decision making. Ann. Fuzzy Math. Inform. 2 (2011), no.1, 69-80.
[13] Catolona, W. J., Partin, A. W., Slawin, K. M., Brawer, M. K., Flanigan, R. C. and Patel, A., Use of the percentage of free prostate-specific antigen to enhance differentiation of prostate cancer from benign prostatic disease: A prospective multicenter clinical trial. Journal of American Medical Association. 279 (1998), no.19, 1542-1547.
[14] Egawa, S., Soh, S., Ohori, M., Uchida, T., Gohji, K., Fujii, A., Kuwao, S. and Koshiba, K., The ratio of free to total serum prostate specific antigen and its use in differential diagnosis of prostate carcinoma in Japan. Cancer. 79 (1997), 90-98.
[15] Van Cangh, P. J., De Nayer, P., Sauvage, P., Tombal, B., Elsen, M., Lorge, F., Opsomer, R. and Wese, F. X., Free to total prostate-specific antiden (PSA) ratio is superior to total PSA in differentiating benign prostate hypertrophy from prostate cancer. The prostate. 29 (1996), 30-34.
[16] Mettlin, C., Lee, F. and Drago, J., The American cancer society national prostate cancer detection, project: Findings on the detection of early prostate cancer in 2425 men. Cancer. 67 (1991), 2949-2958.
[17] Nguyen, H. P. and Kreinovich, V., Fuzzy logic and its applications in medicine. International Journal of Medical Informatics. 62 (2001), 165-173.
[18] Seker, H., Odetayo, M., Petrovic, D. and Naguib, R. N. G., A fuzzy logic based method for prognostic decision making in breast and prostate cancers. IEEE Transactions on Information Technology in Biomedicine. 7 (2003), 114-122.
[19] ¸Simsekler, T. and Yüksel, ¸S., Fuzzy soft topological spaces. Ann. Fuzzy Math. Inform. 5 (2013), no.1, 87-96.
[20] Chen, D., Tsang, E. C. C., Yeung, D. S. and Wang, X., The parametrization reduction of soft sets and its applications. Comput. Math. Appl. 49 (2005), 757-763.
[21] Zou, Y. and Xiao, Z., Data analysis approaches of soft sets under incomplete information. Knowl. Based Syst. 21 (2008), 941-945.
[22] Maji, P. K., Roy, A. R. and Biswas, R., Fuzzy soft sets. J. Fuzzy Math. 9 (2001), no.3, 589-602.
[23] Lashin, E. F., Kozae, A. M., Abo Khadra, A. A. and Medhat, T., Rough set theory for topological spaces. International Journal of Approximate Reasoning. (2005), 35-43.
[24] Kozae, A. M., Abo Khadra, A. A. and Medhat, T., Topological approach for approximation space (TAS). Proceeding of the 5th International Conference INFOS 2007 on Informatics and Systems. (2007), 289-302.
[25] Allam, A. A., Bakeir, M. Y. and Abo Tabl, E. A., Some methods for generating topologies by relations. Bulletin of the Malaysian Mathematical Sciences Society. (2) 31 (2008), no.1, 35-45.
[26] Wu, Q. E., Wang, T., Huang Y. X. and Li, J. S., Topology theory on rough sets. IEEE Transactions on Systems, Man, And Cybernetics-Part B:Cybernetics. 38 (2008), no.1, 68-77.
[27] Wu, M., Wu, X., Shen, T. and Cao, C., A new type of covering approximation operators. 2009 International Conference on Electronic Computer Technology. (2009), 334-338.
[28] Shabir, M. and Naz, M., On soft topological spaces. Computers and Mathematics with Applications. 61 (2011), no.7, 1786-1799.

A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis

Yıl 2019, , 28 - 38, 30.04.2019

Zehra Güzel Ergül , Saziye Yüksel

https://doi.org/10.36753/mathenot.559242

Cited By: 5

Öz

In this work we define a new type of soft covering upper approximation operator and study its basic

and topological properties. Comparing with other type of soft covering operation, our soft covering

upper approximation is more accurate and have more properties. Based on the new type of soft covering

upper approximation operator, we give a new kind of soft covering based rough sets. Also we present

an example in medicine which determines the risk of prostate cancer. Our aim is to gain results more

reasonable by using upper and lower approximations of a new kind of soft covering based rough sets

and to help the doctor to determine that the patient needs biopsy or not.

Anahtar Kelimeler

Soft set, rough set, soft covering approximation space, soft covering based rough set, prostate cancer

Kaynakça

[1] Pawlak, Z., Rough sets. International Journal of Computer and Information Sciences. 11 (1982), no.5, 341-356.
[2] Molodtsov, D., Soft set theory-first results. Comput. Math. Appl. 37 (1999), 19-31.
[3] Yüksel, ¸S., Güzel Ergül, Z. and Tozlu, N., Soft covering based rough sets and their application. The Scientific World Journal. (2014), Article ID 970893, 9 pages.
[4] Zadeh, L. A., Fuzzy sets. Inform. Control. 8 (1965), 338-353.
[5] Zhu, W. and Wang, F. Y., On three types of covering based rough sets. IEEE Transactions on Knowledge and Data Engineering. 19 (2007), no.8, 1131-1143.
[6] Zhu, W., Topological approaches to covering rough sets. Information Science. 177 (2007), 1499-1508.
[7] Maji, P. K., Biswas, R. and Roy, A. R., Soft set theory. Computers and Mathematics with Applications. 45 (2003), 555-562.
[8] Ali, M. I., Feng, F., Liu, X., Min, W. K. and Shabir, M., On some new operations in soft set theory. Comput. Math. Appl. 57 (2009), 1547-1553.
[9] Akta¸s, H. and Ça˘gman, N., Soft sets and soft groups. Information Sciences. 177 (2007), 2726-2735.A tentative approach. Soft Comput. 14 (2010), 899-911.
[11] Feng, F., Liu, X., Violeta, F. L. and Young, J. B., Soft sets and soft rough sets. Information Sciences. 181 (2011), 1125-1137.
[12] Feng, F., Soft rough sets applied to multicriteria group decision making. Ann. Fuzzy Math. Inform. 2 (2011), no.1, 69-80.
[13] Catolona, W. J., Partin, A. W., Slawin, K. M., Brawer, M. K., Flanigan, R. C. and Patel, A., Use of the percentage of free prostate-specific antigen to enhance differentiation of prostate cancer from benign prostatic disease: A prospective multicenter clinical trial. Journal of American Medical Association. 279 (1998), no.19, 1542-1547.
[14] Egawa, S., Soh, S., Ohori, M., Uchida, T., Gohji, K., Fujii, A., Kuwao, S. and Koshiba, K., The ratio of free to total serum prostate specific antigen and its use in differential diagnosis of prostate carcinoma in Japan. Cancer. 79 (1997), 90-98.
[15] Van Cangh, P. J., De Nayer, P., Sauvage, P., Tombal, B., Elsen, M., Lorge, F., Opsomer, R. and Wese, F. X., Free to total prostate-specific antiden (PSA) ratio is superior to total PSA in differentiating benign prostate hypertrophy from prostate cancer. The prostate. 29 (1996), 30-34.
[16] Mettlin, C., Lee, F. and Drago, J., The American cancer society national prostate cancer detection, project: Findings on the detection of early prostate cancer in 2425 men. Cancer. 67 (1991), 2949-2958.
[17] Nguyen, H. P. and Kreinovich, V., Fuzzy logic and its applications in medicine. International Journal of Medical Informatics. 62 (2001), 165-173.
[18] Seker, H., Odetayo, M., Petrovic, D. and Naguib, R. N. G., A fuzzy logic based method for prognostic decision making in breast and prostate cancers. IEEE Transactions on Information Technology in Biomedicine. 7 (2003), 114-122.
[19] ¸Simsekler, T. and Yüksel, ¸S., Fuzzy soft topological spaces. Ann. Fuzzy Math. Inform. 5 (2013), no.1, 87-96.
[20] Chen, D., Tsang, E. C. C., Yeung, D. S. and Wang, X., The parametrization reduction of soft sets and its applications. Comput. Math. Appl. 49 (2005), 757-763.
[21] Zou, Y. and Xiao, Z., Data analysis approaches of soft sets under incomplete information. Knowl. Based Syst. 21 (2008), 941-945.
[22] Maji, P. K., Roy, A. R. and Biswas, R., Fuzzy soft sets. J. Fuzzy Math. 9 (2001), no.3, 589-602.
[23] Lashin, E. F., Kozae, A. M., Abo Khadra, A. A. and Medhat, T., Rough set theory for topological spaces. International Journal of Approximate Reasoning. (2005), 35-43.
[24] Kozae, A. M., Abo Khadra, A. A. and Medhat, T., Topological approach for approximation space (TAS). Proceeding of the 5th International Conference INFOS 2007 on Informatics and Systems. (2007), 289-302.
[25] Allam, A. A., Bakeir, M. Y. and Abo Tabl, E. A., Some methods for generating topologies by relations. Bulletin of the Malaysian Mathematical Sciences Society. (2) 31 (2008), no.1, 35-45.
[26] Wu, Q. E., Wang, T., Huang Y. X. and Li, J. S., Topology theory on rough sets. IEEE Transactions on Systems, Man, And Cybernetics-Part B:Cybernetics. 38 (2008), no.1, 68-77.
[27] Wu, M., Wu, X., Shen, T. and Cao, C., A new type of covering approximation operators. 2009 International Conference on Electronic Computer Technology. (2009), 334-338.
[28] Shabir, M. and Naz, M., On soft topological spaces. Computers and Mathematics with Applications. 61 (2011), no.7, 1786-1799.

Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Articles
Yazarlar	Zehra Güzel Ergül Saziye Yüksel
Yayımlanma Tarihi	30 Nisan 2019
Gönderilme Tarihi	2 Ağustos 2018
Yayımlandığı Sayı	Yıl 2019

Kaynak Göster

APA	Ergül, Z. G., & Yüksel, S. (2019). A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis. Mathematical Sciences and Applications E-Notes, 7(1), 28-38. https://doi.org/10.36753/mathenot.559242
AMA	Ergül ZG, Yüksel S. A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis. Math. Sci. Appl. E-Notes. Nisan 2019;7(1):28-38. doi:10.36753/mathenot.559242
Chicago	Ergül, Zehra Güzel, ve Saziye Yüksel. “A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis”. Mathematical Sciences and Applications E-Notes 7, sy. 1 (Nisan 2019): 28-38. https://doi.org/10.36753/mathenot.559242.
EndNote	Ergül ZG, Yüksel S (01 Nisan 2019) A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis. Mathematical Sciences and Applications E-Notes 7 1 28–38.
IEEE	Z. G. Ergül ve S. Yüksel, “A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis”, Math. Sci. Appl. E-Notes, c. 7, sy. 1, ss. 28–38, 2019, doi: 10.36753/mathenot.559242.
ISNAD	Ergül, Zehra Güzel - Yüksel, Saziye. “A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis”. Mathematical Sciences and Applications E-Notes 7/1 (Nisan 2019), 28-38. https://doi.org/10.36753/mathenot.559242.
JAMA	Ergül ZG, Yüksel S. A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis. Math. Sci. Appl. E-Notes. 2019;7:28–38.
MLA	Ergül, Zehra Güzel ve Saziye Yüksel. “A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis”. Mathematical Sciences and Applications E-Notes, c. 7, sy. 1, 2019, ss. 28-38, doi:10.36753/mathenot.559242.
Vancouver	Ergül ZG, Yüksel S. A New Type of Soft Covering Based Rough Sets Applied to Multicriteria Group Decision Making for Medical Diagnosis. Math. Sci. Appl. E-Notes. 2019;7(1):28-3.