JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (08): 51-56.doi: 10.6040/j.issn.1671-9352.0.2014.372

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On conditions for transfer function to preserve solution configuration of semiring-induced valuation algebras

XU Ge-ni1,2, LI Yong-ming1   

  1. 1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, Shaanxi, China;
    2. School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, Shaanxi, China
  • Received:2014-08-17 Online:2015-08-20 Published:2015-07-31

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Abstract: The map preserving solution configuration of valuation algebra induced by a semiring is studied. The transfer function f preserves solution configuration is obtained if f is an order-reflecting semiring homomorphism. In addition, if the transfer function f is monotonous, then there exists a solution configuration x0of the new valuation such that x0 is also a solution configuration of the primal valuation when the set of solution configuration of the two valuations are not empty.

Key words: valuation algebra, semiring, optimal solution, transfer function

CLC Number: 

  • O153.3
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