Korean J. Math. Vol. 25 No. 1 (2017) pp.71-85
DOI: https://doi.org/10.11568/kjm.2017.25.1.71

An extension of soft rough fuzzy sets

Main Article Content

Ismat Beg
Tabasam Rashid

Abstract

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.



Article Details

References

[1] H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences 177 (2007), 2726–2735. Google Scholar

[2] M. I. Ali, A note on soft sets, rough sets and fuzzy soft sets, Applied Soft Computing 11 (2011), 3329–3332. Google Scholar

[3] I. Beg and S. Ashraf, Fuzzy relational calculus, Bulletin of the Malaysian Mathematical Sciences Society (2) 37 (1) (2014), 203–237. Google Scholar

[4] I. Beg and T. Rashid, TOPSIS for hesitant fuzzy linguistic term sets, International Journal of Intelligent Systems 28 (2013), 1162-1171. Google Scholar

[5] R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management Science 17 (4) (1970), 141–164. Google Scholar

[6] D. Dubois and H. Prade, Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Dordrecht - 2000. Google Scholar

[7] F. Feng, C. X. Li, B. Davvaz and M. I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14 (2010), 899–911. Google Scholar

[8] F. Feng, X. Liu, V. Leoreanu-Fotea and Y. B. Jun, Soft sets and soft rough sets, Information Sciences 181 (2011), 1125–1137. Google Scholar

[9] X. Ge, Z. Li and Y. Ge, Topological spaces and soft sets, Journal of Computational Analysis and Applications 13 (2011), 881–885. Google Scholar

[10] S. Greco, B. Matarazzo and R. Slowinski, Rough set theory for multicriteria decision analysis, European Journal of Operational Research 129 (2001), 1–47. Google Scholar

[11] T. Herawan and M. M. Deris, A soft set approach for association rules mining, Knowledge-Based Systems 24 (2011), 186–195. Google Scholar

[12] T. B. Iwinski, Algebraic approach to rough sets, Bulletin of the Polish Academy of Sciences, Mathematics 35 (9–10) (1987). Google Scholar

[13] Y. B. Jun, Roughness of ideals in BCK-algebra, Scientiae Mathematicae Japonica 57 (1) (2003), 165–169. Google Scholar

[14] S. J. Kalayathankal and G. S. Singh, A fuzzy soft flood alarm model, Mathematics and Computers in Simulation 80 (2010), 887–893. Google Scholar

[15] P. K. Maji, R. Biswas and R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (2003), 555–562. Google Scholar

[16] D. Meng, X. Zhang and K. Qin, Soft rough fuzzy sets and soft fuzzy rough sets, Computers and Mathematics with Applications 62 (2011), 4635–4645. Google Scholar

[17] D. Molodtsov, Soft set theory - first results, Computers and Mathematics with Applications 37 (1999), 19–31. Google Scholar

[18] M. M. Musharif, S. Sengupta and A. K. Ray, Texture classification using a novel, soft set theory based classification algorithm, Lecture Notes in Computer Science 3851 (2006), 246–254. Google Scholar

[19] Z. Pawlak, Rough sets, International Journal of Computing and Information Sciences 11 (1982), 341–356. Google Scholar

[20] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Boston, 1991. Google Scholar

[21] Z. Pawlak, Rough set approach to knowledge-based decision support, European Journal of Operational Research 99 (1997), 48–57. Google Scholar

[22] Z. Pawlak, Rough set theory and its applications, Journal of Telecommunications and Information Technology 3 (2002). Google Scholar

[23] Z. Pawlak and A. Skowron, Rudiments of rough sets, Information Sciences 177 (2007), 3–27. Google Scholar

[24] H. Qin, X. Ma, J. M. Zain and T. Herawan, A novel soft set approach in selecting clustering attribute, Knowledge-Based Systems 36 (2012), 139–145. Google Scholar

[25] A. S. Sezer, A new view to ring theory via soft union rings, ideals and bi-ideals, Knowledge-Based Systems 36 (2012), 300–314. Google Scholar

[26] M. Shabir, M. I. Ali and T. Shaheen, Another approach to soft rough sets, Knowledge-Based Systems 40 (2013), 72–80. Google Scholar

[27] L. Shanmei and X. Xiaohao, Vulnerability analysis for airport networks based on fuzzy soft sets: from the structural and functional perspective, Chinese Journal of Aeronautics 28 (2015) DOI:http://dx.doi.org/10.1016/j.cja.2015.04.002 Google Scholar

[28] H. Tang, A novel fuzzy soft set approach in decision making based on grey relational analysis and Dempster–Shafer theory of evidence, Applied Soft Computing 31 (2015), 317–325. Google Scholar

[29] Z. Tao, H. Chen, X. Song, L. Zhou and J. Liu, Uncertain linguistic fuzzy soft sets and their applications in group decision making, Applied Soft Computing 34 (2015), 587–605. Google Scholar

[30] Z. Xio, K. Gong and Y. Zou, A combined forecasting approach based on fuzzy soft sets, Journal of Computational and Applied Mathematics 228 (2009), 326–333. Google Scholar

[31] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338–353. Google Scholar

[32] H. J. Zimmermann, Fuzzy Set Theory and its Applications, second edition, Kluwer Academic Publishers, Boston, (1991). Google Scholar