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Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix

Year 2017, Volume: 5 Issue: 2, 229 - 236, 30.03.2017

Riyaz Ahmad Padder P. Murugadas

Abstract

In this paper various properties of s-transitive intuitionistic fuzzy matrices are discussed. We obtain some results regarding convergence of powers of s-transitive intuitionistic fuzzy matrices. By using the properties of s-transitive intuitionistic fuzzy matrices  we formulated and constructed canonical form.

Keywords

Intuitionistic fuzzy set intuitionistic fuzzy matrix s-transitive convergence powers of intuitionistic fuzzy matrix

References

  • L. A. Zadeh ., Fuzzy Sets, Journal of Information and Control, 8, (1965).
  • K. Atanassov ., Intuitionistic Fuzzy Sets , VII ITKR’s Session, Sofia, June (1983).
  • K. Atanassov ., Intuitionistic Fuzzy Sets ; Theory and Applications, Physica Verlag, (1999).
  • K. Atanassov., Intuitionistic Fuzzy Implications and Modus Ponens, Notes On Intuitionistic Fuzzy Sets, . 11(1), (2005), 1-5.
  • K. Atanassov ., On Some Types of Fuzzy Negations, Notes on Intuitionistic Fuzzy Sets 11(4), (2005), 170-172.
  • K. Atanassov., A New Intuitionistic Fuzzy Implication from a Modal Type, Advance Studies In Contemporary Mathematics 12(1), (2006), 117-122.
  • K. Atanassov, and G. Gargov., Elements of Intuitionistic Fuzzy Logic.Part I, Fuzzy Sets and Systems, 95(1998),39-52.
  • Y. B. Im, E. P Lee., The determinant of square intuitionistic fuzzy matrices. Far-East Journal of Mathematical Sciences 5 (2001) 789-796
  • S.K Khan , M. Pal and A. K. Shyamal.,Intuitionistic Fuzzy Matrices, Notes on Intuitionistic Fuzzy Sets, 8(2) (2002), 51-62.
  • A. K. Shyamal , M. Pal., Distances between intuitionistics fuzzy matrices. V. U. J. Physical Sciences 8, (2002) 81-91.
  • 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.
  • M. Bhowmik , M. Pal., Generalized intuitionistic fuzzy matrices. Far-East Journal of Mathematical Sciences 29(3), (2008), 533-554
  • A. R. Meenakshi , and T. Gandhimathi., Intuitionistic Fuzzy Relational Equations, Advances in Fuzzy Mathematics, 5 (3), (2010), 239-244.
  • S. Sriram and P. Murugadas.,On Semi-ring of Intuitionistic Fuzzy Matrices, Applied Mathematical Science, 4(23), (2010), 1099-1105.
  • S. Sriram and P.Murugadas., Sub-inversesof Intuitionistic Fuzzy Matrices, Acta Ciencia Indica Mathematics, Vol.XXXVII,M No. 1, (2011), 41-56.
  • P. Murugadas and K. Lalitha., Dual implication Operator in Intuitionistic Fuzzy Matrices, Int.Conference on Mathematical Modelling and its Applications, Dec 22-24,2012, Organized by Department of Mathematics, Annamalai University.
  • 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.
  • P. Murugadas and K. Lalitha.,Implication Operator on Intuitionistic Fuzzy Tautological Matrix, Int.Journal of Fuzzy Mathematical Archive, 5(2), (2014), 79-87.
  • P. Murugadas and R. A .Padder ., Reduction of an intuitionistic fuzzy rectangular matrix,Annamalai University Science Journal, 49,(2015) 15-18.
  • M. G Thomason ; Convergence of powers of a fuzzy matrix, J.Math.Anal.Appl. 57, (1977), 476-480.
  • J. J Buckley; Note on convergence of powers of a fuzzy matrix ; Fuzzy sets and systems. 121, (2001), 363-364.
  • Z. T Ran and D.F Liu ; On the oscillating power sequence of a fuzzy matrix , Fuzzy sets and systems. 93, (1998) 75-85.
  • D. A Gregory, S.Kirkland and N.J Pullman; Power convergent Boolean matrices, Linear algebra and its applications. 179, (1993) 105-117.
  • H. Hashimoto; Convergence of powers of a fuzzy transitive matrix , Fuzzy sets and systems. 9, (1983),153-160.
  • Y. Y Lur, Y.KWu and S.MGuu. Convergence of powers for a fuzzy matrix with convex combination of maxmin and max-arithmetic mean operations, Information Sciences. 179, (2009) 938-944.
  • W. Kolodziejczyk, Convergence of powers of s-transitive fuzzy matrix, Fuzzy Sets and Systems, 26, (1988) 127-130.
  • L. J Xin, Convergence of powers of controllable fuzzy matrices, Fuzzy Sets and Systems, 45, (1994) 83-88.
  • A. D. Nola,Convergence of powers of reciprocal fuzzy matrices, Information Sciences, 75, (1993) 99-107.
  • W. Kolodziejczyk. Canonical form of a strongly transitive fuzzy matrix, Fuzzy Sets and Systems. 22, (1987), 297-302.
  • H. Chenggong. Canonical form of strongly transitive matrices over lattices , Fuzzy Sets and Systems. 45, (1992), 219-222.
  • H. Hashimoto. Canonical form of transitive fuzzy matrix, Fuzzy Sets and Systems. 11, (1983), 157-162.
  • H. Y. Lee and N. G Jeong. Canonical form of a transitive intuitionistic fuzzy matrices, Honam Mathematical Journal. 27(4), (2005), 543-550.
  • M. Pal and S. K. Khan, Intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets, 8(2), (2002), 51-62.

Year 2017, Volume: 5 Issue: 2, 229 - 236, 30.03.2017

Riyaz Ahmad Padder P. Murugadas

Abstract

References

  • L. A. Zadeh ., Fuzzy Sets, Journal of Information and Control, 8, (1965).
  • K. Atanassov ., Intuitionistic Fuzzy Sets , VII ITKR’s Session, Sofia, June (1983).
  • K. Atanassov ., Intuitionistic Fuzzy Sets ; Theory and Applications, Physica Verlag, (1999).
  • K. Atanassov., Intuitionistic Fuzzy Implications and Modus Ponens, Notes On Intuitionistic Fuzzy Sets, . 11(1), (2005), 1-5.
  • K. Atanassov ., On Some Types of Fuzzy Negations, Notes on Intuitionistic Fuzzy Sets 11(4), (2005), 170-172.
  • K. Atanassov., A New Intuitionistic Fuzzy Implication from a Modal Type, Advance Studies In Contemporary Mathematics 12(1), (2006), 117-122.
  • K. Atanassov, and G. Gargov., Elements of Intuitionistic Fuzzy Logic.Part I, Fuzzy Sets and Systems, 95(1998),39-52.
  • Y. B. Im, E. P Lee., The determinant of square intuitionistic fuzzy matrices. Far-East Journal of Mathematical Sciences 5 (2001) 789-796
  • S.K Khan , M. Pal and A. K. Shyamal.,Intuitionistic Fuzzy Matrices, Notes on Intuitionistic Fuzzy Sets, 8(2) (2002), 51-62.
  • A. K. Shyamal , M. Pal., Distances between intuitionistics fuzzy matrices. V. U. J. Physical Sciences 8, (2002) 81-91.
  • 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.
  • M. Bhowmik , M. Pal., Generalized intuitionistic fuzzy matrices. Far-East Journal of Mathematical Sciences 29(3), (2008), 533-554
  • A. R. Meenakshi , and T. Gandhimathi., Intuitionistic Fuzzy Relational Equations, Advances in Fuzzy Mathematics, 5 (3), (2010), 239-244.
  • S. Sriram and P. Murugadas.,On Semi-ring of Intuitionistic Fuzzy Matrices, Applied Mathematical Science, 4(23), (2010), 1099-1105.
  • S. Sriram and P.Murugadas., Sub-inversesof Intuitionistic Fuzzy Matrices, Acta Ciencia Indica Mathematics, Vol.XXXVII,M No. 1, (2011), 41-56.
  • P. Murugadas and K. Lalitha., Dual implication Operator in Intuitionistic Fuzzy Matrices, Int.Conference on Mathematical Modelling and its Applications, Dec 22-24,2012, Organized by Department of Mathematics, Annamalai University.
  • 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.
  • P. Murugadas and K. Lalitha.,Implication Operator on Intuitionistic Fuzzy Tautological Matrix, Int.Journal of Fuzzy Mathematical Archive, 5(2), (2014), 79-87.
  • P. Murugadas and R. A .Padder ., Reduction of an intuitionistic fuzzy rectangular matrix,Annamalai University Science Journal, 49,(2015) 15-18.
  • M. G Thomason ; Convergence of powers of a fuzzy matrix, J.Math.Anal.Appl. 57, (1977), 476-480.
  • J. J Buckley; Note on convergence of powers of a fuzzy matrix ; Fuzzy sets and systems. 121, (2001), 363-364.
  • Z. T Ran and D.F Liu ; On the oscillating power sequence of a fuzzy matrix , Fuzzy sets and systems. 93, (1998) 75-85.
  • D. A Gregory, S.Kirkland and N.J Pullman; Power convergent Boolean matrices, Linear algebra and its applications. 179, (1993) 105-117.
  • H. Hashimoto; Convergence of powers of a fuzzy transitive matrix , Fuzzy sets and systems. 9, (1983),153-160.
  • Y. Y Lur, Y.KWu and S.MGuu. Convergence of powers for a fuzzy matrix with convex combination of maxmin and max-arithmetic mean operations, Information Sciences. 179, (2009) 938-944.
  • W. Kolodziejczyk, Convergence of powers of s-transitive fuzzy matrix, Fuzzy Sets and Systems, 26, (1988) 127-130.
  • L. J Xin, Convergence of powers of controllable fuzzy matrices, Fuzzy Sets and Systems, 45, (1994) 83-88.
  • A. D. Nola,Convergence of powers of reciprocal fuzzy matrices, Information Sciences, 75, (1993) 99-107.
  • W. Kolodziejczyk. Canonical form of a strongly transitive fuzzy matrix, Fuzzy Sets and Systems. 22, (1987), 297-302.
  • H. Chenggong. Canonical form of strongly transitive matrices over lattices , Fuzzy Sets and Systems. 45, (1992), 219-222.
  • H. Hashimoto. Canonical form of transitive fuzzy matrix, Fuzzy Sets and Systems. 11, (1983), 157-162.
  • H. Y. Lee and N. G Jeong. Canonical form of a transitive intuitionistic fuzzy matrices, Honam Mathematical Journal. 27(4), (2005), 543-550.
  • M. Pal and S. K. Khan, Intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets, 8(2), (2002), 51-62.
There are 33 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Riyaz Ahmad Padder This is me

P. Murugadas This is me

Publication Date March 30, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Padder, R. A., & Murugadas, P. (2017). Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix. New Trends in Mathematical Sciences, 5(2), 229-236.
AMA Padder RA, Murugadas P. Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix. New Trends in Mathematical Sciences. March 2017;5(2):229-236.
Chicago Padder, Riyaz Ahmad, and P. Murugadas. “Convergence of Powers and Canonical Form of S-Transitive Intuitionistic Fuzzy Matrix”. New Trends in Mathematical Sciences 5, no. 2 (March 2017): 229-36.
EndNote Padder RA, Murugadas P (March 1, 2017) Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix. New Trends in Mathematical Sciences 5 2 229–236.
IEEE R. A. Padder and P. Murugadas, “Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 229–236, 2017.
ISNAD Padder, Riyaz Ahmad - Murugadas, P. “Convergence of Powers and Canonical Form of S-Transitive Intuitionistic Fuzzy Matrix”. New Trends in Mathematical Sciences 5/2 (March 2017), 229-236.
JAMA Padder RA, Murugadas P. Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix. New Trends in Mathematical Sciences. 2017;5:229–236.
MLA Padder, Riyaz Ahmad and P. Murugadas. “Convergence of Powers and Canonical Form of S-Transitive Intuitionistic Fuzzy Matrix”. New Trends in Mathematical Sciences, vol. 5, no. 2, 2017, pp. 229-36.
Vancouver Padder RA, Murugadas P. Convergence of powers and Canonical form of s-transitive intuitionistic fuzzy matrix. New Trends in Mathematical Sciences. 2017;5(2):229-36.
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