On Characterization of Fuzzy Soft Rough Sets Based on a Pair of Border Implicators

• Autorzy: Gong Z. , Zhang X.

Identyfikatory

DOI

10.3233/FI-2015-1190

• Języki publikacji: EN

Abstrakty

EN

Fuzzy set theory, soft set theory and rough set theory are powerfulmathematical tools for dealing with various types of uncertainty. This paper is devoted to define a broad family of soft fuzzy rough sets, each one of which, called an (I, J)-soft fuzzy rough set, is determined by a pair of border implicators (I, J). Alternatively, it shows that a fuzzy soft set can induce a T -equivalence fuzzy relation which is used to granulate the universe. In particular, we prove that (I, J)-fuzzy soft rough sets in our work are equivalent to (I, J)-fuzzy rough sets of Yao et al. by using a T -equivalence fuzzy relation determined by a fuzzy soft set. Furthermore, basic properties of (I, J)-fuzzy soft rough sets are investigated. Meanwhile, an operator-oriented characterization of (I, J)-fuzzy soft rough sets is proposed. Finally, an example is given to illustrate the approach of present paper.

Słowa kluczowe

EN

fuzzy set; rough set; soft set; fuzzy soft set; fuzzy logical operation; (I, J)-soft fuzzy rough set; (I, J)-fuzzy rough set

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2015
• Tom: Vol. 137, nr 4
• Strony: 457--491
• Opis fizyczny: Bibliogr. 26 poz., tab.

Twórcy

autor

Gong Z.

• College of Mathematics and Statistics Northwest Normal University Lanzhou, 730070, PR China

autor

Zhang X.

• College of Mathematics and Statistics Northwest Normal University Lanzhou, 730070, PR China

Bibliografia

• [1] Aktas, H., Căgman, N.: Soft sets and soft groups, Information Sciences, 177, 2007, 2726–2735.
• [2] Belohlavek, R.: Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
• [3] Chen, D. G., Tsang, E. C. C., Yeung, D. S., Wang, X. Z.: The paremeterization reduction of soft sets and its applications, Computers and Mathematics with Applications, 49, 2005, 757–763.
• [4] Cornelis, C., Deschrijver, G., Kerre, E. E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application, International Journal of Approximate Reasoning, 35, 2004, 55–95.
• [5] Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together, in: Handbook of Applications and Advances of the Sets Theory: Intelligent Decision Support (Slowiński, R., Eds.), Kluwer Academic Publishers, Boston Dordrecht London, 1992, 233–250.
• [6] Feng, F., Li, C. X., Davvaz, B., Ali, M. I.: Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing, 14, 2010, 899–911.
• [7] Grzymala-Busse, J. W., LERS-A system for learning from examples based on rough sets, in: Intelligent Decision Support (Slowiński, R., Eds.), Kluwer Academic Publishers, Boston, 1992, 3–18.
• [8] Klement, E. P., Mesiar, R., Pap, E.: Triangular norms, Trends in Logic Studia Logica Libarary, vol. 8, Kluwer Academic Publishers, Dodrecht, 2000.
• [9] Klir, G. J., Yuan, B., Fuzzy logic: theory and applications, Prentice-Hall, Englewood Cliffs, NJ, 1995.
• [10] Maji, P. K., Biswas, R., Roy, A. R.: Fuzzy soft sets, The Journal of Fuzzy Mathematics, 9, 2001, 589–602.
• [11] Maji, P. K., Biswas, R., Roy, A. R.: Soft set theory, Computers and Mathematics with Applications, 45, 2003, 555–562.
• [12] Maji, P. K., Roy, A. R., Biswas, R.: An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44, 2002, 1077–1083.
• [13] Meng, D., Zhang, X. H., Qin, K. Y.: Soft rough fuzzy sets and soft fuzzy rough sets, Computers and Mathematics with Applications, 62, 2011, 4635–4645.
• [14] Mi, J. S., Wu, W. Z., Zhang, W. X.: Approaches to knowledge reduction based on variable precision rough set model, Information Science, 159, 2004, 255–272.
• [15] Molodtsov, D.: Soft set theory-first results, Computers and Mathematics with Applications, 37, 1999, 19–31.
• [16] Morsi, N. N., Yakout,M. M.: Axiomatics for fuzzy rough sets, Fuzzy Sets and Systems, 100, 1998, 327–342.
• [17] Nachtegael, M., Kerre, E. E.: The dizzy number of fuzzy implication operators on finite chains, in: Fuzzy Logic and Intelligent Technologies for Nuclear Science and Industry (Ruan, D., et al., Eds.),World Scientific, Singapore, 1998, 29–35.
• [18] Pawlak, Z.: Rough sets, International Journal of Computer and Information Science, 11(5), 1982, 341–356.
• [19] Radzikowska, A. M., Kerre, E. E.: A comparative study of fuzzy rough sets, Fuzzy Sets and Systems, 126, 2002, 137–155.
• [20] Radzikowska, A. M., Kerre, E. E.: Fuzzy rough sets based on residuated lattices, in: Transactions on Rough Sets II (Peter, J. F., et al., Eds.), LNCS, 3135, 2004, 278–296.
• [21] Roy, A. R., Maji, P. K.: A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, 203, 2007, 412–418.
• [22] Wu,W. Z.,Mi, J. S., Zhang,W. X.: Generalized fuzzy rough sets, Information Sciences, 151, 2003, 263–282.
• [23] Yang, X. B., Lin, T. Y., Yang, J. Y., Li, Y., Yu, D. J.: Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications, 58, 2009, 521–527.
• [24] Yao, Y. Y.: Combination of rough and fuzzy sets based on _-level sets, in: Rough Sets and Data Mining: Analysis for Imprecise Data (Lin, T. Y., Cercone, N., Eds.), Kluwer Academic Publishers, Boston, 1997, 301–321.
• [25] Yao, O. Y.,Wang, Z. D., Zhang,H. P.: On fuzzy rough sets based on tolerance relations, Information Sciences, 180, 2010, 532–542.
• [26] Zadeh, L. A.: Fuzzy sets, Information and Control, 8, 1965, 338–353.