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Extreme Preservers of Zero-term Rank Sum over Fuzzy Matrices

Song, Seok-Zun;Na, Yeon-Jung

  • Received : 2010.08.26
  • Accepted : 2010.10.06
  • Published : 2010.12.31

Abstract

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.

Keywords

Linear operator;zero-term rank;fuzzy semiring;fuzzy matrix

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