Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

THE CANONICAL FORM OF INVOLUTARY FUZZY MATRICES

  • Kim, Chang Il (Department of Mathematics Education Dankook University) ;
  • Park, Se Won (Department of Liberal arts and Science Shingyeong University)
  • Received : 2014.08.11
  • Accepted : 2014.10.10
  • Published : 2014.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

We study special types of matrices. The involutary fuzzy matrices are important in various applications and have many interesting properties. Using the graphical method, we have the zero patterns of involutary fuzzy matrix, that is, involutary Boolean matrices. And we give the construction of all involutary fuzzy matrices for some dimensions and suggest the canonical form of involutary fuzzy matrix.

Keywords

References

  1. K. H. Kim and F. W. Roush, Generalized fuzzy matrices, Fuzzy Sets and Systems 4 (1980), 293-315. https://doi.org/10.1016/0165-0114(80)90016-0
  2. K. H. Kim and F. W. Roush, Idempotent fuzzy matrices, Seminar Report, Alabama State Univ., Montgomery, AL (1981).
  3. H. Hashimoto, Canonical form of a transitive fuzzy matrix, Fuzzy Sets and Systems 11 (1983), 157-162. https://doi.org/10.1016/S0165-0114(83)80077-3
  4. H. Schneider, The in uence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties, Linear Algebra Appl. 84 (1986), 161-189. https://doi.org/10.1016/0024-3795(86)90313-7
  5. H. Y. Lee and S. W. Park, The Boolean idempotent matrices, Journal of Applied Math. and computing. 15 (2004), 475-484.
  6. F. Zhang, Matrix theory; Basic results and Techniques, Springer-Verlag New York Inc. 15 (1999).