Properties of the GM(1,1) with fractional order accumulation

•The changing of initial condition does not affect the simulative value of GM(1,1) model.•Simulative value is an exponential model when actual sequence is nonnegative increased.•Practical examples are used to validate the effectiveness of proposed GM(1,1). For traditional grey model (GM(1,1)), it is...

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Bibliographic Details
Published in:Applied mathematics and computation 2015-02, Vol.252, p.287-293
Main Authors: Wu, Lifeng, Liu, Sifeng, Fang, Zhigeng, Xu, Haiyan
Format: Article
Language:English
Subjects:
Computation
Computer simulation
Convexity
Fractional order accumulation
Grey system theory
Initial conditions
Mathematical models
Sequences
The initial condition
The monotonicity and convexity
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Summary:•The changing of initial condition does not affect the simulative value of GM(1,1) model.•Simulative value is an exponential model when actual sequence is nonnegative increased.•Practical examples are used to validate the effectiveness of proposed GM(1,1). For traditional grey model (GM(1,1)), it is proved theoretically that the initial condition is not utilized, and the simulative value is convex and increased or is the decreased and concave when the actual sequence is nonnegative increased. These shortcomings are the results of traditional first order accumulation on grey system model. However, for the GM(1,1) with fractional order accumulation, the initial condition is utilized, and the monotonicity and convexity of simulative value are uncertain when the actual value is nonnegative increased. The results of practical numerical examples demonstrate that the GM(1,1) with fractional order accumulation provides very remarkable predication performance compared with the traditional GM(1,1) model.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.12.014