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Arithmetic mean, geometric mean and harmonic mean of fuzzy matrices on the basis of reference function

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In this article, our main intention is to deal with the fuzzy matrices on the basis of reference function and thereafter to define arithmetic mean, geometric mean and harmonic mean of such matrices. Various properties of arithmetic, geometric and harmonic mean of these matrices are also studied. Further the concept discussed is illustrated with the help of numerical examples.

Abstract

In this article, our main intention is to deal with the fuzzy matrices on the basis of reference function and thereafter to define arithmetic mean, geometric mean and harmonic mean of such matrices. Various properties of arithmetic, geometric and harmonic mean of these matrices are also studied. Further the concept discussed is illustrated with the help of numerical examples.

참고문헌 (15)

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  3. M. Dhar, "Representation of fuzzy matrices Based on Reference Function", International Journal of Intelligent Systems and Applications, 5(2), pp.84~90 (2013)
  4. M. Dhar, "A Note on Determinant and Adjoint of Fuzzy Square Matrix", International Journal of Intelligent Systems and Applications, 5(5), pp.58~67 (2013)
  5. M. Dhar, "The De nition of Complement of fuzzy numbers : An Exposition", International Journal of Intelligent Systems and Applications, 5(8), pp.7~82 (2013)
  6. H. Hasimato, "Convergence of powers of fuzzy transitive matrix", Fuzzy Sets and Systems, 9, pp.153~160 (1983)
  7. J. B. Kim, "Determinant theory for Fuzzy and Boolean Matices", pp.273~276 (1988), Congressus Numerantium Utilitus Mathematica Pub
  8. J. B. Kim, "Inverses of Boolean Matrices", Bull.Inst. Math. Acod, Science, 12(2), pp.125~128 (1984)
  9. J. B. Kim, "Idempotents and Inverses in Fuzzy Matrices", Malayasian Math, 6(2), pp.57~61 (1988)
  10. J. B. Kim, "Determinant Theory for Fuzzy Matrices", Fuzzy Sets and Systems, 29, pp.349~356 (1989)
  11. S. V. Ovehinnikov, "Structure of fuzzy relations", Fuzzy Sets and Systems, 6, pp.169~195 (1981)
  12. M. Z. Ragab, "The determinant and adjoint of square fuzzy matrix", Fuzzy Sets and Systems, 61, pp.297~307 (1994)
  13. A. K. Shymal, "Two new operators on fuzzy matrices", J. Applied Mathematics and Computing, 15, pp.91~107 (2004)
  14. A. K., Shymal, "Distance between fuzzy matrices and its applications", Acta Siencia, XXXI(1), pp.476~480 (2005)
  15. M. G. Thomason, "Convergence of powers of a fuzzy matrix", J. Math. Anal. Appl, 57, pp.476~480 (1977)

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