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**Fuzzy time series and its models.**
*(English)*
Zbl 0792.62087

Summary: Based upon the works by L. A. Zadeh [IEEE Trans. Syst. Man Cybern. SMC-3, 28–44 (1973; Zbl 0273.93002), Inf. Sci. 8, 199–249 (1975; Zbl 0397.68071); ibid., 301–357 (1975; Zbl 0404.68074); ibid. 9, 43–80 (1975; Zbl 0404.68075)], a special dynamic process with linguistic values as its observations is defined and studied. This dynamic process is called fuzzy time series. To describe fuzzy time series, fuzzy relational equations are employed as the models. There are two classes of fuzzy time series: time-variant and time-invariant. The definition of fuzzy time series is given, some properties of fuzzy time series are explored, and procedures to develop fuzzy time series models are discussed. Finally, a procedure for using fuzzy time series for forecasting is suggested.

### MSC:

62A86 | Fuzzy analysis in statistics |

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

03E72 | Theory of fuzzy sets, etc. |

### Keywords:

fuzzy conditional statements; dynamic process; linguistic values; fuzzy time series; fuzzy relational equations; time-variant; time-invariant; forecasting
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\textit{Q. Song} and \textit{B. S. Chissom}, Fuzzy Sets Syst. 54, No. 3, 269--277 (1993; Zbl 0792.62087)

Full Text:
DOI

### References:

[1] | Zadeh, L. A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man Cybernet., 3, 28-44 (1973) · Zbl 0273.93002 |

[2] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Parts 3, Inform. Sci., 9, 43-80 (1975) · Zbl 0404.68075 |

[3] | Zadeh, L. A., Fuzzy Sets, Inform and Control, 8, 338-353 (1965) · Zbl 0139.24606 |

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[8] | Zuoyong, Li, A model of weather forecast by fuzzy grade statistics, Fuzzy Sets and Systems, 26, 275-281 (1988) |

[9] | Song, Q.; Chissom, B. S., Forecasting enrollments with fuzzy time series: Part I, Fuzzy Sets and Systems, 54, 1-9 (1993) |

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