Fuzzy Rough Approximations: A Novel Approach

T. K. Sheeja; A. Sunny Kuriakose

doi:https://doi.org/10.14445/22315373/IJMTT-V67I5P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 5 | Year 2021 | Article Id. IJMTT-V67I5P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I5P504

Fuzzy Rough Approximations: A Novel Approach

T. K. Sheeja, A. Sunny Kuriakose

Citation :

T. K. Sheeja, A. Sunny Kuriakose, "Fuzzy Rough Approximations: A Novel Approach," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 5, pp. 33-39, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I5P504

Abstract

Rough sets and fuzzy sets are two different but complementary concepts that provide effective mathematical tools for handling imperfect information. Their hybrid form, namely, fuzzy rough sets are very useful in dealing with real world data that involve vagueness and indiscernibility. In this paper, fuzzy rough approximations of a fuzzy set in a fuzzy approximation space are defined using normalized fuzzy divergence measures and their properties are investigated. Also, it is proved that the present approach is a generalization of both the Pawlak’s rough set approach and the fuzzy rough set approach. Moreover, the proposed definition gives better approximations to a set than the original fuzzy rough approximations.

Keywords

Approximations, Rough set, Fuzzy set, Divergence Measure, Fuzzy Rough Set

References

[1] Rough Sets on Topological Spaces, K. Anitha , P. Venkatesan, International Journal of Mathematics Trends and Technology (IJMTT) 10 (1) (2014) 47-50.
[2] L. D’eer, N. Verbiest, C. Cornelis and L. Godo, A Comprehensive Study of Implicator Conjunctor-based and Noise-Tolerant Fuzzy Rough Sets: Definitions, Properties and Robustness Analysis, Fuzzy Sets and Systems 275 (2015) 1-38.
[3] D. Dubois and H. Prade, Rough Fuzzy Sets and Fuzzy Rough Sets, International Journal of General Systems 17 (1990) 191-209.
[4] R. Jensen and Q. Shen, New Approaches to Fuzzy-Rough Feature Selection, IEEE Transactions on Fuzzy Systems, 17(4) (2009) 824-838.
[5] J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic, Prentice Hall, New Jersey, 1995.
[6] J.S. Mi, Y. Leung, H.Y. Zhao and T. Feng, Generalized Fuzzy Rough Sets Determined by a TriangularNorm, Information Sciences 178 (2008) 3203-3213.
[7] S. Montes, I. Couso, P. Gil and C. Bertoluzza, Divergence Measure Between Fuzzy Sets, International Journal of Approximate Reasoning 30 (2002) 91-105.
[8] A. Nakamura, ”Fuzzy Rough Sets”, Note on Multiple-Valued Logic in Japan 9(8) (1988) 1-8.
[9] N. R. Paul, Rough Topology Based Decision Making in Medical Diagnosis, International Journal of Mathematics Trends and Technology (IJMTT). 18(2015) 40-43.
[10] Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences 11(5), (1982) 341 - 356.
[11] Z. Pawlak, Rough Sets - Theoretical Aspect of Reasoning About Data, Kluwer Academic Publishers The Netherlands, 1991.
[12] A. M. Radzikowska and E. E. Kerre, A Comparative Study of Fuzzy Rough Sets, Fuzzy Sets and Systems 126(2) (2002) 137-155.
[13] Sheeja. T. K, Sunny Kuriakose A., Divergence Based Generalized Fuzzy Rough Sets, International Journal of Computer Sciences and Engineering 6(6) (2018) 809-815.
[14] Sheeja. T. K, Sunny Kuriakose A., A Novel Feature Selection Method Using Fuzzy Rough Sets, Computers in Industry 97 (2018) 111-116.
[15] Sheeja. T. K, Sunny Kuriakose A., Image Segmentation Using a Fuzzy Roughness Measure, International Journal of Engineering and Advanced Technology 8(6) (2019) 307-311.
[16] S. Vluymans, L. D'eer, Y. Saeys and C. Cornelis, Applications of Fuzzy Rough Set Theory in Machine Learning: a Survey, Fundamenta Informaticae, 142 (2015) 53-86.
[17] W. Z. Wu, J. S. Mi and W. X. Zhang, Generalized Fuzzy Rough Sets, Information Sciences, 151 (2003) 263-282.
[18] Y. Y. Yao, S. K. M. Wong and T. Y. Lin, A Review of Rough Set Models, in Rough Sets and Data mining analysis for Imprecise Data, eds T. Y. Lin, and N. Cerone, Kluwer Academic Publishers, Boston (1997) 47-75.
[19] L. A. Zadeh, Fuzzy Sets, Information and Control 8(3) (1965) 338-353.
[20] Q. Zhang, Q. Xie and G. Y. Wang, "A Survey on Rough Set Theory and its Applications, CAAI Transactions on Intelligence Technology 1(4) (2016) 323 - 333.