International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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On Idempotent Intuitionistic Fuzzy Matrices of T-Type

  • Padder, Riyaz Ahmad (Department of Mathematics, Annamalai University) ;
  • Murugadas, P. (Department of Mathematics, Annamalai University)
  • Received : 2016.08.30
  • Accepted : 2016.09.19
  • Published : 2016.09.25
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Abstract

In this paper, we examine idempotent intuitionistic fuzzy matrices and idempotent intuitionistic fuzzy matrices of T-type. We develop some properties on both idempotent intuitionistic fuzzy matrices and idempotent intuitionistic fuzzy matrices of T-type. Several theorems are provided and an numerical example is given to illustrate the theorems.

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References

  1. L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no. 3, pp. 338-353, 1965. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
  2. K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986. http://dx.doi.org/10.1016/S0165-0114(86)80034-3
  3. L. C. Jang, W. J. Kim, and T. Kim, "A note on distances between interval-valued intuitionistic fuzzy sets," International Journal of Fuzzy Logic and Intelligent Systems, vol. 11, no. 1, pp. 8-11, 2011. http://dx.doi.org/10.5391/IJFIS.2011.11.1.008
  4. J. H. Park, Y. C. Kwun, and M. J. Son, "A generalized intuitionistic fuzzy soft set theoretic approach to decision making problems," International Journal of Fuzzy Logic and Intelligent Systems, vol. 11, no. 2, pp. 71-76, 2011. http://dx.doi.org/10.5391/IJFIS.2011.11.2.071
  5. K. H. Kim and F.W. Roush, "Generalized fuzzy matrices," Fuzzy Sets and Systems, vol. 4, no. 3, pp. 293-315, 1980. http://dx.doi.org/10.1016/0165-0114(80)90016-0
  6. M. G. Thomason, "Convergence of powers of a fuzzy matrix," Journal of Mathematical Analysis and Applications, vol. 57, no. 2, pp. 476-480, 1977. http://dx.doi.org/10.1016/0022-247X(77)90274-8
  7. J. B. Kim, "Idempotents and inverse in fuzzy matrices," Bulletin of the Malaysian Mathematical Sciences Society, vol. 6, no. 2, pp. 57-61, 1983.
  8. M. A. Mishref and E. G. Emam, "Transitivity and subinverses in fuzzy matrices," Fuzzy Sets and Systems, vol. 52, no. 3, pp. 337-343, 1992. http://dx.doi.org/10.1016/0165-0114(92)90241-U
  9. M. Z. Ragab and E. G. Emam, "The determinant and adjoint of a square fuzzy matrix," Information Sciences, vol. 84, no. 3-4, pp. 209-220, 1995. http://dx.doi.org/10.1016/0020-0255(93)00064-5
  10. J. B. Kim, "On fuzzy idempotent matrices of T-Type," Information Sciences, vol. 80, no. 3-4, pp. 311-318, 1994. http://dx.doi.org/10.1016/0020-0255(94)90082-5
  11. A. R. Meenakshi, Fuzzy Matrix: Theory and Applications. Chennai: MJP Publishers, 2008.
  12. M. Pal, "Intuitionistic fuzzy determinant," V.U.J. Physical Sciences, vol. 7, pp. 87-93, 2001.
  13. Y. B. Im, E. P. Lee, and S. W. Park, "The determinant of square intuitionistic fuzzy matrices," Far East Journal of Mathematical Sciences, vol. 3, no. 5, pp. 789-796, 2001.
  14. M. Pal, S. K. Khan, and A. K. Shyamal, "Intuitionistic fuzzy matrices," Notes on Intuitionistic Fuzzy Sets, vol. 8, no. 2, pp. 51-62, 2002.
  15. A. K. Shyamal and M. Pal, "Two new operators on fuzzy matrices," Journal of Applied Mathematics and Computing, vol. 15, no. 1, pp. 91-107, 2004. http://dx.doi.org/10.1007/BF02935748
  16. A. K. Shyamal and M. Pal, "Distances between intuitionistics fuzzy matrices," V.U.J. Physical Sciences, vol. 8, pp. 81-91, 2002.
  17. M. Bhowmik and M. Pal, "Generalized intuitionistic fuzzy matrices," Far East Journal of Mathematical Science, vol. 29, no. 3, pp. 533-554, 2008.
  18. M. Bhowmik and M. Pal, "Generalized interval-valued intuitionistic fuzzy sets," The Journal of Fuzzy Mathematics, vol. 18, no. 2, pp. 357-371, 2010.
  19. M. Bhowmik and M. Pal, "Some results on generalized interval-valued intuitionistic fuzzy sets," International Journal of Fuzzy Systems, vol. 14, no. 2, pp. 193-203, 2012.
  20. S. K. Khan and A. Pal, "The generalized inverse of intuitionistic fuzzy matrices," Journal of Physical Sciences, vol. 11, pp. 62-67, 2007.
  21. A. K. Adak, M. Bhowmik, and M. Pal, "Some properties of generalized intuitionistic fuzzy nilpotent matrices over distributive lattice," Fuzzy Information and Engineering, vol. 4, no. 4, pp. 371-387, 2012. http://dx.doi.org/10.1007/s12543-012-0121-1
  22. R. A. Padder and P. Murgadas, "Max-max operation on intuitionistic fuzzy matrix," Annals of Fuzzy Mathematics and Informatics, in press.
  23. P. Murugadas and R. A. Padder, "Reduction of an intuitionistic fuzzy rectangular Matrix," Annamalai University Science Journal, vol. 49, pp. 15-18, 2015.
  24. R. Pradhan and M. Pal, "Convergence of maxarithmetic mean-minarithmetic mean powers of intuitionistic fuzzy matrices," International Journal of Fuzzy Mathematical Archive, vol. 2, pp. 58-69, 2013.
  25. S. Sriram and P. Murugadas, "On semiring of intuitionstic fuzzy matrices," Applied Mathematical Sciences, vol. 4, no. 23, pp. 1099-1105, 2010.
  26. S. Sriram and P. Murugadas, "Sub-inverses of intuitionistic fuzzy matrices," Acta Ciencia Indica Mathematics, vol. 37, no. 1, pp. 41-56, 2011.
  27. H. Y. Lee and N. G. Jeong, "Canonical form of a transitive intuitionistic fuzzy matrices," Honam Mathematical Journal, vol. 27 no. 4, pp. 543-550, 2005.
  28. K. Atanassov, "Generalized index matrices," Comptes Rendus de L'academie Bulgare des Sciences, vol. 40, no. 11, pp. 15-18, 1987.
  29. K. T. Atanassov, "Intuitionistic fuzzy sets," in Proceedings of the Polish Symposium on Interval and Fuzzy Mathematics (VII ITKR's Session), Sofia, 1983.
  30. Y. B. Im, E. P. Lee, and S. W. Park, "The adjoint of square intuitionistic fuzzy matrices," Journal of Applied Mathematics and Informatics, vol. 11, no. 1-2, pp. 401-412, 2003.