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**A combined forecasting approach based on fuzzy soft sets.**
*(English)*
Zbl 1161.91472

Summary: Forecasting the export and import volume in international trade is the prerequisite of a government’s policy-making and guidance for a healthier international trade development. However, an individual forecast may not always perform satisfactorily, while combination of forecasts may result in a better forecast than component forecasts. We believe the component forecasts employed in combined forecasts are a description of the actual time series, which is fuzzy. This paper attempts to use forecasting accuracy as the criterion of fuzzy membership function, and proposes a combined forecasting approach based on fuzzy soft sets. This paper also examines the method with data of international trade from 1993 to 2006 in the Chongqing Municipality of China and compares it with a combined forecasting approach based on rough sets and each individual forecast. The experimental results show that the combined approach provided in this paper improves the forecasting performance of each individual forecast and is free from a rough sets approach’s restrictions as well. It is a promising forecasting approach and a new application of soft sets theory.

### MSC:

91B84 | Economic time series analysis |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

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\textit{Z. Xiao} et al., J. Comput. Appl. Math. 228, No. 1, 326--333 (2009; Zbl 1161.91472)

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### References:

[1] | Bates, J. M.; Granger, C. W., The combination of forecasts, Operational Research Quarterly, 20, 451-468 (1969) |

[2] | Dickinson, J. P., Some comments on the combination of forecasts, Operational Research Quarterly, 26, 205-210 (1975) · Zbl 0312.62068 |

[3] | Makridakis, S.; Andersen, A.; Carbone, R.; Fildes, R.; Hibon, M.; Lewandowski, R.; Newton, J.; Parzen, E.; Winkler, R., The accuracy of extrapolation (time series) methods: Results of a forecasting competition, Journal of Forecasting., 1, 111-153 (1982) |

[4] | Deutsch, M.; Granger, C. W.; Terasvirta, T., The combination of forecasts using changing weights, International Journal of Forecasting, 10, 47-57 (1994) |

[5] | Chan, C. K.; Kingsman, B. G.; Wong, H., The value of combining forecasts in inventory management—a case study in banking, European Journal of Operational Research, 117, 199-210 (1999) · Zbl 0998.90504 |

[6] | Zhong, B.; Xiao, Z., Determination to weighting coefficient of combination forecast based on rough set theory, Journal of Chongqing University (Natural Science)., 25, 127-130 (2002) |

[7] | Zhong, B.; Xiao, Z., A compound projection method based on coarse aggregate theory, Statistical Research, 11, 37-39 (2002) |

[9] | Zhang, F., An application of vector GARCH model in semiconductor demand planning, European Journal of Operational Research, 181, 288-297 (2007) · Zbl 1121.90382 |

[10] | Molodtsov, D., Soft set theory-first results, Computers & Mathematics With Applications, 4/5, 19-31 (1999) · Zbl 0936.03049 |

[11] | Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606 |

[12] | Maji, P. K.; Biswas, R.; Roy, A. R., Soft set theory, Computers & Mathematics With Applications., 555-562 (2003) · Zbl 1032.03525 |

[13] | Aktaş, Hacı; Çağman, Naim, Soft sets soft groups, Information Sciences, 177, 2726-2735 (2007) · Zbl 1119.03050 |

[14] | Jun, Y. B.; Park, C. H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences, 178, 2466-2475 (2008) · Zbl 1184.06014 |

[15] | Maji, P. K.; Roy, A. R., An application of soft sets in a decision making problem, Computers & Mathematics With Applications, 1077-1083 (2002) · Zbl 1044.90042 |

[16] | Xiao, Z.; Li, Y.; Zhong, B.; Yang, X., Research on synthetically evaluating method for business competitive capacity based on soft set, Statistical Research, 52-54 (2003) |

[17] | Mushrif, M. M.; Sengupta, S.; Ray, A. K., Texture classification using a novel, soft-set theory based classification algorithm, Lecture Notes in Computer Science, 3851, 246-254 (2006) |

[18] | Chen, D.; Tsang, E. C.C.; Yeung, D. S.; Wang, X., The parameterization reduction of soft sets and its applications, Computers & Mathematics with Applications, 49, 757-763 (2005) · Zbl 1074.03510 |

[19] | Roy, A. R.; Maji, P. K., A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, 203, 412-418 (2007) · Zbl 1128.90536 |

[20] | Kong, Z.; Gao, L.; Wang, L., Comment on “A fuzzy soft set theoretic approach to decision making problems”, Journal of Computational and Applied Mathematics (2008) |

[21] | Zou, Y.; Xiao, Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems (2008) |

[22] | Maji, P. K.; Biswas, R.; Roy, A. R., Fuzzy soft sets, Journal of Fuzzy Mathematics, 9, 589-602 (2001) · Zbl 0995.03040 |

[23] | Box, G. E.P.; Jenkins, G., Time Series Analysis, Forecasting and Control (1990), Holden-Day: Holden-Day San Francisco |

[24] | Hyndman, R. J.; Koehler, A. B., Another look at measures of forecast accuracy, International Journal of Forecasting, 22, 679-688 (2006) |

[25] | Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11, 341-356 (1982) · Zbl 0501.68053 |

[26] | Pawlak, Z.; Skowron, A., Rudiments of rough sets, Information Sciences, 177, 3-27 (2007) · Zbl 1142.68549 |

[27] | Wang, G. Y.; Yu, H.; Yang, D. C., Decision table reduction based on conditional information entropy, Chinese Journal of Computers, 25, 759-766 (2002) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.