Research Article
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Year 2019, , 28 - 38, 30.04.2019
https://doi.org/10.36753/mathenot.559242

Abstract

References

  • [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

Year 2019, , 28 - 38, 30.04.2019
https://doi.org/10.36753/mathenot.559242

Abstract

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.

References

  • [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.
There are 27 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Zehra Güzel Ergül

Saziye Yüksel

Publication Date April 30, 2019
Submission Date August 2, 2018
Published in Issue Year 2019

Cite

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. April 2019;7(1):28-38. doi:10.36753/mathenot.559242
Chicago Ergül, Zehra Güzel, and 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, no. 1 (April 2019): 28-38. https://doi.org/10.36753/mathenot.559242.
EndNote Ergül ZG, Yüksel S (April 1, 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 and 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, vol. 7, no. 1, pp. 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 (April 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 and 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, vol. 7, no. 1, 2019, pp. 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.

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