Table of Contents
ISRN Algebra
Volume 2014 (2014), Article ID 635783, 8 pages
http://dx.doi.org/10.1155/2014/635783
Research Article

An Investigation on Algebraic Structure of Soft Sets and Soft Filters over Residuated Lattices

1Department of Mathematics, Persian Gulf University, Bushehr 75169, Iran
2Department of Mathematics, Yazd University, Yazd, Iran

Received 23 September 2013; Accepted 29 October 2013; Published 13 March 2014

Academic Editors: H. S. Kim, T. Nakatsu, and S. Yang

Copyright © 2014 S. Rasouli and B. Davvaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Z. Pawlak and A. Skowron, “Rudiments of rough sets,” Information Sciences, vol. 177, no. 1, pp. 3–27, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. W. L. Gau, D. J. Buehrer, and Vague sets, IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 2, pp. 610–614, 1993. View at Publisher · View at Google Scholar
  5. M. B. Gorzałczany, “A method of inference in approximate reasoning based on interval-valued fuzzy sets,” Fuzzy Sets and Systems, vol. 21, no. 1, pp. 1–17, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. Molodtsov, “Soft set theory—first results,” Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19–31, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. K. Maji, A. R. Roy, and R. Biswas, “An application of soft sets in a decision making problem,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1077–1083, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. Chen, E. C. C. Tsang, D. S. Yeung, and X. Wang, “The parameterization reduction of soft sets and its applications,” Computers & Mathematics with Applications, vol. 49, no. 5-6, pp. 757–763, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. K. Maji, R. Biswas, and A. R. Roy, “Soft set theory,” Computers & Mathematics with Applications, vol. 45, no. 4-5, pp. 555–562, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir, “On some new operations in soft set theory,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1547–1553, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. H. Aktaş and N. Çağman, “Soft sets and soft groups,” Information Sciences, vol. 177, no. 13, pp. 2726–2735, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. K. V. Babitha and J. J. Sunil, “Soft set relations and functions,” Computers & Mathematics with Applications, vol. 60, no. 7, pp. 1840–1849, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. I. Ali, M. Shabir, and M. Naz, “Algebraic structures of soft sets associated with new operations,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2647–2654, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. B. Jun, K. J. Lee, and C. H. Park, “Soft set theory applied to ideals in d-algebras,” Computers & Mathematics with Applications, vol. 57, no. 3, pp. 367–378, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  15. J. Zhan and Y. B. Jun, “Soft BL-algebras based on fuzzy sets,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 2037–2046, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  16. F. Feng, C. Li, B. Davvaz, and M. I. Ali, “Soft sets combined with fuzzy sets and rough sets: a tentative approach,” Soft Computing, vol. 14, no. 9, pp. 899–911, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. F. Feng, X. Liu, V. Leoreanu-Fotea, and Y. B. Jun, “Soft sets and soft rough sets,” Information Sciences, vol. 181, no. 6, pp. 1125–1137, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Yamak, O. Kazancı, and B. Davvaz, “Soft hyperstructure,” Computers & Mathematics with Applications, vol. 62, no. 2, pp. 797–803, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. W. Krull, “Axiomatische Begrundung der allgemeinen Idealtheo rie,” Sitzungsberichte der Physikalisch Medizinischen Societat der Erlangen, vol. 56, pp. 47–63, 1924. View at Google Scholar
  20. P. Hájek, Metamathematics of Fuzzy Logic, vol. 4 of Trends in Logic, Kluwer Academic, Dodrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  21. E. Turunen, Mathematics behind Fuzzy Logic, Advances in Soft Computing, Physica, Heidelberg, Germany, 1999. View at MathSciNet
  22. D. Mundici, “MV-algebras are categorically equivalent to bounded commutative BCK-algebras,” Mathematica Japonica, vol. 31, no. 6, pp. 889–894, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. M. Ward and R. P. Dilworth, “Residuated lattices,” Transactions of the American Mathematical Society, vol. 45, no. 3, pp. 335–354, 1939. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. L. Leustean, Representations of many-valued algebras [Ph.D. thesis], Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania, 2003.
  25. F. Feng, Y. B. Jun, and X. Zhao, “Soft semirings,” Computers & Mathematics with Applications, vol. 56, no. 10, pp. 2621–2628, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet