Geodesic
DFIS: A novel data filling approach for an incomplete soft set
International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 4, pp. 817-828.

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The research on incomplete soft sets is an integral part of the research on soft sets and has been initiated recently. However, the existing approach for dealing with incomplete soft sets is only applicable to decision making and has low forecasting accuracy. In order to solve these problems, in this paper we propose a novel data filling approach for incomplete soft sets. The missing data are filled in terms of the association degree between the parameters when a stronger association exists between the parameters or in terms of the distribution of other available objects when no stronger association exists between the parameters. Data filling converts an incomplete soft set into a complete soft set, which makes the soft set applicable not only to decision making but also to other areas. The comparison results elaborated between the two approaches through UCI benchmark datasets illustrate that our approach outperforms the existing one with respect to the forecasting accuracy.
Keywords: soft sets, incomplete soft sets, data filling, association degree
Mots-clés : zbiór rozmyty, napełnianie danych 
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Qin, H.; Ma, X.; Herawan, T.; Zain, J. M. DFIS: A novel data filling approach for an incomplete soft set. International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 4, pp. 817-828. http://geodesic.mathdoc.fr/item/IJAMCS_2012_22_4_a2/

[1] Aktas, H. and Cagman, N. (2007). Soft sets and soft groups, Information Sciences 177(13): 2726-2735.

[2] Ali, M., Feng, F., Liu, X., Min, W. and Shabira, M. (2009). On some new operations in soft set theory, Computers and Mathematics with Applications 57(9): 1547-1553.

[3] Atanassov, K. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1): 87-96.

[4] Çağman, N. and Enginoğlu, S. (2010). Soft matrix theory and its decision making, Computers and Mathematics with Applications 59(10): 3308-3314.

[5] Chen, D., Tsang, E., Yeung, D. and Wang, X. (2005). The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications 49(5-6): 757-763.

[6] Feng, F. (2009). Generalized rough fuzzy sets based on soft sets, Proceedings of the 2009 International Workshop on Intelligent Systems and Applications, ISA 2009, Wuhan, China, pp. 1-4.

[7] Feng, F., Jun, Y., Liu, X. and Li, L. (2010a). An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics 234(1): 10-20.

[8] Feng, F., Li, Y. and Leoreanu-Fotea, V. (2010b). Application of level soft sets in decision making based on interval-valued fuzzy soft sets, Computers and Mathematics with Applications 60(6): 1756-1767.

[9] Feng, F., Jun, Y. and Zhao, X. (2008). Soft semirings, Computers and Mathematics with Applications 56(10): 2621-2628.

[10] Feng, F., Li, C., Davvaz, B. and Ali, M. (2009). Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Computing 14(9): 899-911.

[11] Gau, W. and Buehrer, D. (1993). Vague sets, IEEE Transactions on System, Man, and Cybernetics 23(2): 610-614.

[12] Gorzalzany, M. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21(1): 1-17.

[13] Herawan, T. and Mat Deris, M. (2009). A direct proof of every rough set is a soft set, Proceedings of the 3rd Asia International Conference on Modeling and Simulation, AMS'09, Bali, Indonesia, pp. 119-124.

[14] Herawan, T. and Mat Deris, M. (2011). A soft set approach for association rules mining, Knowledge Based Systems 24(1): 186-195.

[15] UCI (2012). Benchmark datasets, http://www.ics.uci.edu/mlearn/.

[16] Hyndman, R. and Koehler, A. (2006). Another look at measures of forecast accuracy, International Journal of Forecasting 22(4): 679-688.

[17] Jiang, Y., Tang, Y., Chen, Q., Liu, H. and Tang, J. (2010). Interval-valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications 60(3): 906-918.

[18] Jiang, Y., Tang, Y., and Chen, Q. (2011). An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling 35(2): 824-836.

[19] Jun, Y. and Park, C. (2008). Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences 178(11): 2466-2475.

[20] Kong, Z., Gao, L. and Wang, L. (2009). Comment on "A fuzzy soft set theoretic approach to decision making problems", Journal of Computational and Applied Mathematics 223(2): 540-542.

[21] Kong, Z., Gao, L., Wang, L. and Li, S. (2008). The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications 56(12): 3029-3037.

[22] Li, C. and Chiang, T.-W. (2011). Function approximation with complex neuro-fuzzy system using complex fuzzy sets-A new approach, New Generation Computing 29(3): 261-276.

[23] Ma, X., Sulaiman, N., Qin, H., Herawan, T. and Zain, J. (2011). A new efficient normal parameter reduction algorithm of soft sets, Computers and Mathematics with Applications 62(2): 588-598.

[24] Maji, P. (2009). More on intuitionistic fuzzy soft sets, in H. Sakai, M. Chakraborty, A. Hassanien, D. Slezak and W. Zhu (Eds.), Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2009), Lecture Notes in Computer Science, Vol. 5908, Springer, Berlin/Heidelberg, pp. 231-240.

[25] Maji, P., Biswas, R. and Roy, A. (2001a). Fuzzy soft sets, Journal of Fuzzy Mathematics 9(3): 589-602.

[26] Maji, P., Biswas, R. and Roy, A. (2001b). Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics 9(3): 677-692.

[27] Maji, P., Biswas, R. and Roy, A. (2003). Soft set theory, Computers and Mathematics with Applications 45(4-5): 555-562.

[28] Maji, P. and Roy, A. (2002). An application of soft sets in a decision making problem, Computers and Mathematics with Applications 44(8-9): 1077-1083.

[29] Maji, P. and Roy, A. (2007). A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics 203(2): 412-418.

[30] Maji, P., Roy, A. and Biswas, R. (2004). On intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics 12(3): 669-683.

[31] Majumdar, P. and Samanta, S. (2010). Generalized fuzzy soft sets, Computers and Mathematics with Applications 59(4): 1425-1432.

[32] Molodtsov, D. (1999). Soft set theory first results, Computers and Mathematics with Applications 37(4-5): 19-31.

[33] Molodtsov, D. (2004). The Theory of Soft Sets, URSS Publishers, Moscow, (in Russian).

[34] Nowicki, R. (2010). On classification with missing data using rough-neuro-fuzzy systems, International Journal of Applied Mathematics and Computer Science 20(1): 55-67, DOI: 10.2478/v10006-010-0004-8.

[35] Pawlak, Z. (1982). Rough sets, International Journal of Computing and Information Sciences 11(5): 341-356.

[36] Pei, D. and Miao, D. (2005). From soft sets to information systems, Proceedings of the 2005 IEEE International Conference on Granular Computing, IEEE GrC'05, Beijing, China, pp. 617-621.

[37] Qin, H., Ma, X., Herawan, T. and Zain, J. (2011a). An adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making, in N. Nguyen, C. Kim and A. Janiak (Eds.), ACIIDS 2011, Lecture Notes in Computer Science, Vol. 6592, Springer, Berlin/Heidelberg, pp. 80-89.

[38] Qin, H., Ma, X., Herawan, T. and Zain, J. (2011b). Data filling approach of soft sets under incomplete information, in N. Nguyen, C. G. Kim and A. Janiak (Eds.), ACIIDS 2011, Lecture Notes in Computer Science, Vol. 6592, Springer, Berlin/Heidelberg, pp. 302-311.

[39] Qin, K. and Kong, Z. (2010). On soft equality, Journal of Computational and Applied Mathematics 234(5,1): 1347-1355.

[40] Quinlan, J. (1989). Unknown attribute values in induction, Proceedings of the 6th International Machine Learning Workshop, San Mateo, Canada, pp. 164-168.

[41] Thiesson, B. (1995). Accelerated quantification of Bayesian networks with incomplete data, 1st International Conference on Knowledge Discovery and Data Mining, Montreal, Canada, pp. 306-311.

[42] Xiao, Z., Gong, K. and Zou, Y. (2009). A combined forecasting approach based on fuzzy soft sets, Journal of Computational and Applied Mathematics 228(1): 326-333.

[43] Xu, W., Ma, J., Wang, S. and Hao, G. (2010). Vague soft sets and their properties, Computers and Mathematics with Applications 59(2): 787-794.

[44] Yang, X., Lin, T., Yang, J. and Dongjun, Y. (2009). Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications 58(3): 521-527.

[45] Zadeh, L. (1965). Fuzzy sets, Information Control 8(3): 338-353.

[46] Zhang, D. and Li, X. (2006). An absolute information quantity-based data making-up algorithms of incomplete information system, Computer Engineering and Applications 42(22): 155-157.

[47] Zhong, N. and Skowron, A. (2001). A rough set-based knowledge discovery process, International Journal of Applied Mathematics and Computer Science 11(3): 603-619.

[48] Zou, Y. and Xiao, Z. (2008). Data analysis approaches of soft sets under incomplete information, Knowledge Based System 21(8): 941-945.