DOI QR코드

DOI QR Code

EXTREME PRESERVERS OF FUZZY MATRIX PAIRS DERIVED FROM ZERO-TERM RANK INEQUALITIES

  • Song, Seok-Zun (Department of Mathematics, Jeju National University) ;
  • Park, Eun-A (Department of Mathematics, Jeju National University)
  • Received : 2011.04.01
  • Accepted : 2011.09.04
  • Published : 2011.09.25

Abstract

In this paper, we construct the sets of fuzzy matrix pairs. These sets are naturally occurred at the extreme cases for the zero-term rank inequalities derived from the multiplication of fuzzy matrix pairs. We characterize the linear operators that preserve these extreme sets of fuzzy matrix pairs.

Keywords

References

  1. L. B. Beasley and A. E. Guterman, Rank inequalities over semirings, J. Korean Math. Soc. 42(2)(2005), 223-241. https://doi.org/10.4134/JKMS.2005.42.2.223
  2. L. B. Beasley, A. E. Guterman, and C. L. Neal, Linear preservers for Sylvester and Frobenius bounds on matrix rank, Rocky Mountains J. Math. 36(1)(2006), 67-75. https://doi.org/10.1216/rmjm/1181069488
  3. L. B. Beasley, A. E. Guterman, Y. B. Jun and S. Z. Song, Linear preservers of extremes of rank inequalities over semirings: Row and Column ranks, Linear Algebra Appl., 413(2006), 495-509. https://doi.org/10.1016/j.laa.2005.03.024
  4. L. B. Beasley, S. G. Lee, and S. Z. Song, Linear operators that preserve pairs of matrices which satisfy extreme rank properties, Linear ALgebra Appl. 350 (2002), 263-272. https://doi.org/10.1016/S0024-3795(02)00293-8
  5. L. B. Beasley, S. G. Lee, S. Z. Song, Linear operators that preserve zero-term rank of Boolean matrices, J. Korean Math. Soc., 36 (1999), 1181-1190.
  6. P. Pierce and others, A Survey of Linear Preserver Problems, Linear and Multi-linear Algebra, 33 (1992), 1-119. https://doi.org/10.1080/03081089208818176
  7. S. Z. Song, Topics on linear preserver problems - a brief introduction (Korean), Commun. Korean Math. Soc., 21 (2006), 595-612. https://doi.org/10.4134/CKMS.2006.21.4.595
  8. S. Z. Song, Linear operators that preserve column rank of fuzzy matrices, Fuzzy Sets and Systems, 62 (1994), 311-317. https://doi.org/10.1016/0165-0114(94)90115-5