References
1. Liu, S.-F. and Lin, Y., Grey Systems: Theory and
Applications, Springer, Berlin, Germany (2010).
2. Kayacan, E., Ulutas, B., and Kaynak, O. \Grey system
theory-based models in time series prediction", Expert
Syst. Appl., 37(2), pp. 1784-1789 (2010).
3. Xia, M. and Wong, W.K. \A seasonal discrete grey
forecasting model for fashion retailing", Knowl. Based
Syst., 57, pp. 119-126 (2014).
4. Jin, M., Zhou, X., Zhang, Z.M., and Tentzeris, M.M.
\Short-term power load forecasting using grey correlation
contest modeling", Expert Syst. Appl., 39(1), pp.
773-779 (2012).
5. Bezuglov, A. and Comert, G. \Short-term freeway traf-
c parameter prediction: Application of grey system
theory models", Expert Syst. Appl., 62, pp. 284-292
(2016).
6. Chang, B.-R. \A tunable epsilon-tube in support
vector regression for re ning parameters of GM(1,1j )
prediction model - SVRGM(1,1j ) approach", IEEE
Int. Conf. on Systems, Man and Cybernetics (SMC),
Washington D.C., USA, pp. 4700-4704 (2003).
7. Chuang, C.-W. and Kao, C.-C. \PC-based pseudomodel
following discrete integral variable structure
control of positions in slider-crank mechanisms", J.
Sound Vib., 301(3-5), pp. 510-520 (2007).
8. Hsu, L.-C. \Using improved grey forecasting models
to forecast the output of opto-electronics industry",
Expert Syst. Appl., 38(11), pp. 13879-13885 (2011).
9. Li, D.-C., Chang, C.-J., Chen, W.-C., and Chen, C.-
C. \An extended grey forecasting model for omnidirectional
forecasting considering data gap di erence",
Appl. Math. Model., 35(10), pp. 5051-5058 (2011).
10. Li, G.-D., Wang, C.-H., Masuda, S., and Nagai, M. \A
research on short term load forecasting problem applying
improved grey dynamic model", Int. J. Electr.
Power Energy Syst., 33(4), pp. 809-816 (2011).
11. Li, H. and Xiao, T.-Y. \Improved Generalized Energy
Index method for comprehensive evaluation and prediction
of track irregularity", J. Stat. Comput. Simul.,
84(6), pp. 1213-1231 (2014).
12. Wu, L.-F., Liu, S.-F., Yao, L.-G., Xu, R.-T., and Lei,
X.-P. \Using fractional order accumulation to reduce
M. Hashem-Nazari et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2867{2880 2879
errors from inverse accumulated generating operator of
grey model", Soft Comput., 19(2), pp. 483-488 (2015).
13. Wu, L.-F., Liu, S.-F., and Yang, Y.-J. \A gray model
with a time varying weighted generating operator",
IEEE Trans. Syst. Man Cybern. Syst., 46(3), pp. 427-
433 (2016).
14. Zhou, W. and He, J.-M. \Generalized GM (1,1) model
and its application in forecasting of fuel production",
Appl. Math. Model., 37(9), pp. 6234-6243 (2013).
15. Wang, J.-Z., Zhu, S.-L., Zhao, W.-G., and Zhu, W.-
J. \Optimal parameters estimation and input subset
for grey model based on chaotic particle swarm optimization
algorithm", Expert Syst. Appl., 38(7), pp.
8151-8158 (2011).
16. Chang, C.-J., Li, D.-C., Chen, C.-C., and Chen, C.-S.
\A forecasting model for small non-equigap data sets
considering data weights and occurrence possibilities",
Comput. Ind. Eng., 67, pp. 139-145 (2014).
17. Chiang, H.-K. and Tseng, C.-H. \The grey GM(2,1)
integral variable structure controller of synchronous
reluctance motor drive", IEEE Int. Conf. on Control
Applications, Taipei, Taiwan, pp. 278-283 (2004).
18. Cui, J., Liu, S.-F., Zeng, B., and Xie, N.-M. \A novel
grey forecasting model and its optimization", Appl.
Math. Model., 37(6), pp. 4399-4406 (2013).
19. Kayacan, E. and Kaynak, O. \Single-step ahead prediction
based on the principle of concatenation using
grey predictors", Expert Syst. Appl., 38(8), pp. 9499-
9505 (2011).
20. Li, G.-D., Masuda, S., and Nagai, M. \Predictor design
using an improved grey model in control systems", Int.
J. Comput. Integr. Manuf., 28(3), pp. 297-306 (2015).
21. Li, K.-T. and Chen, Y.-P. \Predictor design of a
novel grey model PGM21 using pseudo second-order
information", JSME Int. J. Ser. C: Mech. Syst. Mach.
Elem. Manuf., 49(2), pp. 395-400 (2006).
22. Lin, C.-B., Su, S.-F., and Hsu, Y.-T. \High-precision
forecast using grey models", Int. J. Syst. Sci., 32(5),
pp. 609-619 (2001).
23. Luo, X. and Chang, X.-H. \A novel data fusion scheme
using grey model and extreme learning machine in
wireless sensor networks", Int. J. Control Autom.
Syst., 13(3), pp. 539-546 (2015).
24. Evans, M. \An alternative approach to estimating the
parameters of a generalised Grey Verhulst model: An
application to steel intensity of use in the UK", Expert
Syst. Appl., 41(4, Part 1), pp. 1236-1244 (2014).
25. Wang, Y., Song, Q.-B., Macdonell, S., Shepperd, M.,
and Shen, J.-Y. \Integrate the GM(1,1) and Verhulst
models to predict software stage e ort", IEEE Trans.
Syst. Man Cybern. C Appl. Rev., 39(6), pp. 647-658
(2009).
26. Xiao, X.-P. and Qin, L.-F. \A new type solution and
bifurcation of grey Verhulst model", J. Grey Syst.,
24(2), pp. 165-174 (2012).
27. Xu, J., Tan, T., Tu, M., and Qi, L. \Improvement
of grey models by least squares", Expert Syst. Appl.,
38(11), pp. 13961-13966 (2011).
28. Zhu, X.-L. \Application of composite grey BP neural
network forecasting model to motor vehicle fatality
risk", 2nd Int. Conf. on Computer Modeling and
Simulation, Sanya, China, pp. 236-240 (2010).
29. Wang, J.-Z., Dong, Y., Wu, J., Mu, R., and Jiang, H.
\Coal production forecast and low carbon policies in
China", Energy Policy, 39(10), pp. 5970-5979 (2011).
30. Wang, K., Wu, L.-Y., and Liu, Y.-W. \Condition
prediction of power transformer based on discrete
gray model", IEEE Conf. on Power Engineering and
Automation (PEAM), Wuhan, China, pp. 280-283
(2011).
31. Wang, Z.-X., Dang, Y.-G., and Liu, S.-F. \Unbiased
grey Verhulst model and its application", Syst. Eng.
Theory Pract., 29(10), pp. 138-144 (2009).
32. Xie, N.-M. and Liu, S.-F. \Discrete grey forecasting
model and its optimization", Appl. Math. Model.,
33(2), pp. 1173-1186 (2009).
33. Xie, N.-M., Liu, S.-F., Yang, Y.-J., and Yuan, C.-
Q. \On novel grey forecasting model based on nonhomogeneous
index sequence", Appl. Math. Model.,
37(7), pp. 5059-5068 (2013).
34. Guo, X.-J., Liu, S.-F., and Fang, Z.-G. \Study on
a grey Verhulst self-memory model and application",
IEEE Int. Conf. on Grey Systems and Intelligent
Services (GSIS), Macao, Macao, pp. 118-122 (2013).
35. Li, G.-D., Masuda, S., Yamaguchi, D., Nagai, M., and
Wang, C.-H. \An improved grey dynamic GM(2, 1)
model", Int. J. Comput. Math., 87(7), pp. 1617-1629
(2010).
36. Choi, T.-M., Hui, C.-L., Liu, N., Ng, S.-F., and Yu, Y.
\Fast fashion sales forecasting with limited data and
time", Decis. Support Syst., 59, pp. 84-92 (2014).
37. Liu, L., Wang, Q.-R., Wang, J.-Z., and Liu, M.
\A rolling grey model optimized by particle swarm
optimization in economic prediction", Comput. Intell.,
32(3), pp. 391-419 (2014).
38. Shih, C.-S., Hsu, Y.-T., Yeh, J., and Lee, P.-C.
\Grey number prediction using the grey modi cation
model with progression technique", Appl. Math.
Model., 35(3), pp. 1314-1321 (2011).
39. Stewart, J. Multivariable Calculus: Concepts and Contexts,
Thomson Brooks/Cole, Belmont, USA (2009).
40. Tsai, C.-F. \Dynamic grey platform for ecient forecasting
management", J. Comput. Syst. Sci., 81(6),
pp. 966-980 (2015).
41. Wu, L.-F., Liu, S.-F., Yang, Y.-J., Ma, L.-H., and Liu,
H.-X. \Multi-variable weakening bu er operator and
its application", Inf. Sci., 339, pp. 98-107 (2016).
42. Tsaur, R.-C. \Forecasting analysis by using fuzzy grey
regression model for solving limited time series data",
Soft Comput., 12(11), pp. 1105-1113 (2008).
2880 M. Hashem-Nazari et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2867{2880
43. Tien, T.-L. \The deterministic grey dynamic model
with convolution integral DGDMC(1,n)", Appl. Math.
Model., 33(8), pp. 3498-3510 (2009).
44. Wu, L.-F., Liu, S.-F., Cui, W., Liu, D.-L., and
Yao, T.-X. \Non-homogenous discrete grey model with
fractional-order accumulation", Neural Comput. Appl.,
25(5), pp. 1215-1221 (2014).
45. Xia, T.-B., Jin, X.-N., Xi, L.-F., Zhang, Y.-J., and
Ni, J. \Operating load based real-time rolling grey
forecasting for machine health prognosis in dynamic
maintenance schedule", J. Intell. Manuf., 26(2), pp.
269-280 (2015).
46. Hashem-Nazari, M., Esfahanipour, A., and Fatemi
Ghomi, S.M.T. \Non-equidistant 'Basic Form'-
focused Grey Verhulst Models (NBFGVMs) for illstructured
socio-economic forecasting problems", J.
Bus. Econ. Manag, 18(4), pp. 676-694 (2017).
http://dx.doi.org/10.3846/16111699.2017.1337045.
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