Transitivity of generalized intuitionistic fuzzy matrices

Abstract

 In this paper, generalized intuitionistic fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra. We introduce the concept of transitivity of generalized intuitionistic fuzzy matrices. Some algebraic properties of generalized intuitionistic fuzzy matrices are developed. Also, we develop some properties of transitivity.

Keywords

• Intuitionistic fuzzy sets,Intuitionistic fuzzy matrix,Transitivity

Kaynakça

1. L. A. Zadeh, Fuzzy Sets, Journal of Information and Control, 8, (1965), 338-353.
2. K. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR’s Session, Sofia, June, 1983.
3. K. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy sets and systems, 20, (1986), 87-96.
4. M. G Thomason, Convergence of powers of a fuzzy matrix, J. Math. Anal. Appl, 57, (1977), 476-480.
5. K. H. Kim and F. W. Roush, Generalized fuzzy matrices, Fuzzy sets and systems, 4, (1980), 293-315.
6. D. Dubois and H. Prade, Fuzzy Sets and Systems, vol. 144 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1980.
7. J. A. Goguen, L-fuzzy sets Journal of Mathematical Analysis and Applications, 18 (1967) 145-174.
8. A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, NY, USA, 1975.

9. S. V. Ovchinnikov, Structure of fuzzy binary relations, Fuzzy Sets and Systems, 6(2), (1981), 169-195,
10. L. A. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3, (1971), 177-200.
11. V. Tahani, A fuzzy model of document retrieval systems, Information Processing Management, 12, (1976), 177-187.
12. S. Tamura, S. Higuchi, and K. Tanaka, Pattern classification based on fuzzy relations, IEEE Transictions on Systems, Man, and Cybernetics, 1(1), (1971), 61-66.
13. H. Hashimoto, Transitivity of generalized fuzzy matrices, Fuzzy Sets and Systems, 17(1), (1985), 83-90.
14. W. Koa‚odziejczyk, Convergence of powers of s-transitive fuzzy matrices, Fuzzy Sets and Systems, 26(1), (1988), 127-130.
15. H. Hashimoto, Convergence of powers of a fuzzy transitive matrix, Fuzzy Sets and Systems, 9(2), (1983), 153-160.
16. H. Hashimoto, Canonical form of a transitive fuzzy matrix, Fuzzy Sets and Systems, 11(2), (1983), 157-162.
17. W. Kołodziejczyk, Canonical form of a strongly transitive fuzzy matrix, Fuzzy Sets and Systems, 22(3), (1987), 297-302.
18. C. G. Hao, Canonical form of strongly transitive matrices over lattices, Fuzzy Sets and Systems, 45(2), (1992) 219-222.
19. Y. J. Tan, On the powers of matrices over a distributive lattice, Linear Algebra and its Applications, 336, (2001), 1-14.
20. Y. J. Tan, On the transitive matrices over distributive lattices, Linear Algebra and its Applications, 400, (2005), 169-191.
21. L. J.-Xin, Controllable fuzzy matrices, Fuzzy Sets and Systems, 45, (1992), 313-319.
22. L. J.-Xin, Convergence of powers of controllable fuzzy matrices, Fuzzy Sets and Systems, 62, (1994), 83-88.
23. J. Jiang, L. Shu, and X. Tian, On generalized transitive matrices, Journal of Applied Mathematics, 2011 ID 164371, (2011) 1-16.
24. Y. J. Tan, On transitivity of generalized fuzzy matrices, Fuzzy Sets and Systems, 210 (2013) 69-88
25. M.Pal, Intuitionistic fuzzy determinant, V.U.J.Physical Sciences, 7, (2001), 87-93.
26. M.Pal, S.Khan and A.K.Shyamal, Intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets, 8 (2), (2002), 51-62.
27. S.K.Khan and M.Pal, Intuitionistic fuzzy tautological matrices, V.U. Journal of Physical Sciences , 8, (2002-2003), 92-100.
28. S.K.Khan and M.Pal, Interval valued intuitionistic fuzzy matrices, Communicated.
29. M. Bhowmik , M. Pal , Some results on intuitionistic fuzzy matrices and intuitionistic circulant fuzzy matrices. International Journal of Mathematical Sciences 7(1-2): (2008), 177-192
30. M. Bhowmik , M. Pal, Generalized intuitionistic fuzzy matrices. Far-East Journal of Mathematical Sciences 29(3), (2008) 533-554.
31. S. K. Khan and A. Pal, The generalized inverse of intuitionistic fuzzy matrices, Journal of Physical Sciences, 11, 2007, 62-67.
32. H. Y. Lee and N. G. Jeong. Canonical form of a transitive intuitionistic fuzzy matrices, Honam Mathematical Journal, 27(4), (2005) 543-550.
33. A. K. Adak, M. Bhowmik and M. Pal, Some properties of generalized intuitionistic fuzzy nilpotent matrices over distributive lattice, Fuzzy Inf. Eng. 4, (2012), 371-387.
34. R. Pradhan and M. Pal, Some results on generalized Inverse of intuitionistic fuzzy matrices, Fuzzy Inf. Eng. 6, (2014), 133-145.
35. A. R.Meenakshi , and T. Gandhimathi, Intuitionistic fuzzy relational equations, advances in Fuzzy Mathematics, 5, (3), (2010), 239-244.
36. S. Mondal and M. Pal, Similarity relations, invertibility and eigenvalues of intuitionistic fuzzy matrix, International Journal of Fuzzy Information and Engineering, 4, (2013), 431-443.
37. S. Mondal and M. Pal, Intuitionistic fuzzy incline matrix and determinant, Annals of Fuzzy Mathematics and Informatics, 8(1), (2014), 19-32.
38. P. Murugadas and K. Lalitha, Sub-inverse and g-inverse of an Intuitionistic Fuzzy Matrix Using Bi-implication Operator, Int.Journal of Computer Application. 89, (1), (2014), 1-5.
39. R. Pradhan and M. Pal, Convergence of maxarithmetic mean-minarithmetic mean powers of intuitionistic fuzzy matrices, intern. J. Fuzzy Mathematical Archive, 2, (2013) 58-69.
40. R. Pradhan and M. Pal, Intuitionistic fuzzy linear transformations, Annals of pure and applied Mathematics, 1(1), (2012), 57-68.
41. R. Pradhan and M. Pal, The generalized inverse of Atanassov’s intuitionistic fuzzy matrices, International Journal of Computational Intelligence Systems, 7(6), (2014), 1083-1095.
42. S. Sriram and P. Murugadas, On semi-ring of intuitionistic fuzzy matrices, Applied Mathematical Science, 4(23), (2010), 1099-1105.
43. S. Sriram and P. Murugadas, Sub-inverses of intuitionistic fuzzy matrices, Acta Ciencia Indica Mathematics, Vol.XXXVII, M No.1, (2011), 41-56.
44. A. K. Shyamal and M. Pal, Distance between intuitionistic fuzzy matrices, V.U.J. Physical Sciences, 8, (2002), 81-91
45. R. A. Padder and P. Murugadas, Max-max operation on intuitionistic fuzzy matrix, Annals of Fuzzy Mathematics and Informatics, Article in press.
46. P.Murugadas and R. A. Padder, Reduction of an intuitionistic fuzzy rectangular Matrix, Annamalai University Science Journal, 49, (2015), 15-18.
47. R. A. Padder and P. Murugadas, Convergence of Power of Controllable Intuitionistic Fuzzy Matrices, ICTACT Journal on Soft Computing 07(01), (2016), 1332-1337.
48. R. A. Padder and P. Murugadas, On Idempotent Intuitionistic Fuzzy Matrices of T-type, International Journal of Fuzzy Logic and Intelligent Systems, 16(3), (2016), 181-187.