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Two new operators on fuzzy matrices

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Abstract

The fuzzy matrices are successfully used when fuzzy uncertainty occurs in a problem. Fuzzy matrices become popular for last two decades. In this paper, two new binary fuzzy operators ⊕ and ⊙ are introduced for fuzzy matrices. Several properties on ⊕ and ⊙ are presented here. Also, some results on existing operators along with these new operators are presented.

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References

  1. H. Hashimoto,Canonical form of a transitive matrix, Fuzzy Sets and Systems,11 (1983) 157–162.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Hemasinha, N.R. Pal and J.C. Bezdek,Iterates of fuzzy circulant matrices, Fuzzy Sets and Systems,60 (1993) 199–206.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. K. Khan, A. K. Shyamal and M. Pal,Intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets,8(2) (2002) 51–62.

    MATH  Google Scholar 

  4. K. H. Kim and F. W. Roush,Generalised fuzzy matrices, Fuzzy Sets and Systems,4 (1980) 293–315.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Kolodziejczyk,Canonical form of a strongly transitive fuzzy matrix, Fuzzy Sets and Systems,22 (1987) 292–302.

    Article  MathSciNet  Google Scholar 

  6. J. B. Kim,Determinant theory for fuzzy and boolean matrices, Congressus Numerantium, (1988) 273–276.

  7. J. B. Kim, A. Baartmans and S. Sahadin,Determinant theory for fuzzy matrices, Fuzzy Sets and Systems,29 (1989) 349–356.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Pal,Intuitionistic fuzzy determinant, V. U. J. Physical Sciences,7 (2001) 87–93.

    Google Scholar 

  9. M. Z. Ragab and E. G. Emam,The determinant and adjoint of a square fuzzy matrix, Fuzzy Sets and Systems,61 (1994) 297–307.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. G. Ragab and E. G. Emam,On the min-max composition of fuzzy matrices, Fuzzy Sets and Systems,75 (1995) 83–92.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Tamura, S. Higuchi and K. Tanaka,Pattern classification based on fuzzy relations, IEEE Trans. Syst. Man Cybern, SMC,1(1) (1971) 61–66.

    MATH  MathSciNet  Google Scholar 

  12. M. G. Thomason,Convergence of powers of a fuzzy matrix, J. Math Anal. Appl.,57 (1977) 476–480.

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhou-Tian and De-Fu Liu,On the power sequence of a fuzzy matrix convergent power sequence, J. Appli. Math. & Computing(old: KJCAM)4 (1997) 147–166.

    MATH  Google Scholar 

  14. L. J. Xin,Controllable fuzzy matrices, Fuzzy Sets and Systems,45 (1992) 313–319.

    Article  MathSciNet  Google Scholar 

  15. L. J. Xin,Convergence of powers of controllable fuzzy matrices, Fuzzy Sets and Systems,62 (1994) 83–88.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, 721 102, Midnapore, West Bengal, India

    Amiya K. Shyamal & Madhumangal Pal

Authors
  1. Amiya K. Shyamal
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  2. Madhumangal Pal
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Additional information

Amiya K. Shyamal has started his Ph. D. work at Vidyasagar University on 2000. His research interests include fuzzy and intuitionistic fuzzy sets.

Madhumangal Pal received his M. Sc from Vidyasagar University, India and Ph. D from Indian Institute of Technology, Kharagpur, India in 1990 and 1996 respectively. He is engaged in research since 1991. In 1996, he received Computer Division Award from Institution of Engineers (India), for best research work. During 1997 to 1999 he was a faculty member of Midnapore College and since 1999 he has been at the Vidyasagar University, India. His research interest include computational graph theory, parallel algorithms, data structure, combinatorial algorithms, genetic algorithms, fuzzy sets and intuitionistic fuzzy sets.

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Shyamal, A.K., Pal, M. Two new operators on fuzzy matrices. JAMC 15, 91–107 (2004). https://doi.org/10.1007/BF02935748

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  • DOI: https://doi.org/10.1007/BF02935748

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