Study on the possibility degree of the optimal solution of grey dynamic programming model base on standard interval grey number

Considering the uncertainty of information, the paper puts forward an improved grey dynamic programming model. After that, treating profit value as positive interval grey number, the paper researches on dynamic programming model, and we could get the optimal strategy after solution by means of defining standard interval grey number. Furthermore, as we can not make the judgment of standard interval grey number, the author puts forward the possibility degree of the optimal solution, which represented as beta u(y) (k) is only related with f(i+1) (circle times)(S-i+1,S-k) and it has the features of 0 < beta u(ij) (k) < 1 and Sigma(t)(k=1) beta(uj) (k) = 1. Finally, the author verifies the practicability of the model by case study.