Journal of Guangxi Normal University(Natural Science Edition) ›› 2014, Vol. 32 ›› Issue (3): 57-60.

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The Perimeter and Its Preserving Operators of Rank-1 Matrices over Inclines

ZHANG Ting-hai   

  1. College of Mathematics and Informatics, Jiangxi Normal University, Nanchang Jiangxi 330022, China
  • Received:2014-03-10 Online:2014-09-25 Published:2018-09-25

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Abstract: Inclines are the additively idempotent semirings in which products are less than or equal to factors. They generalize Boolean algebra, fuzzy algebra and distributive lattice. This paper defines that the perimeter of rank-1 matrices over inclines is the sum of nonzero elements of its left and right factors, and proves the inequality about the perimeter of the sum of rank-1 matrices over inclines and gives the preserving operators of rank-1 matrices over inclines. The results in the present paper generalize and develop correlated results over Boolean matrices and fuzzy matrices.

Key words: inclines matrices , rank-1, perimeter, dominate, operator

CLC Number: 

  • O151.21
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