Kyungpook Mathematical Journal

  • 제50권4호
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  • Pages.465-472
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  • 2010
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Extreme Preservers of Zero-term Rank Sum over Fuzzy Matrices

  • Song, Seok-Zun (Department of Mathematics, Jeju National University) ;
  • Na, Yeon-Jung (Department of Mathematics, Jeju National University)
  • 투고 : 2010.08.26
  • 심사 : 2010.10.06
  • 발행 : 2010.12.31
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초록

In this paper, we consider two extreme sets of zero-term rank sum of fuzzy matrix pairs: $$\cal{z}_1(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=min\{z(X),z(Y)\}\};$$ $$\cal{z}_2(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=0\}$$. We characterize the linear operators that preserve these two extreme sets of zero-term rank sum of fuzzy matrix pairs.

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참고문헌

  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(6)(1999), 1181-1190
  6. P. Pierce and others, A Survey of Linear Preserver Problems, Linear and Multilinear 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