Generalized Fuzzy Time Series Based On Fermatean Fuzzification
Shiwei Pu, Yabin Shao · 2023
The membership degree of ordinary fuzzy sets is relatively single. Based on this situation, this paper proposes fermatean fuzzy time series(FFTS) based on fermatean fuzzy sets. The proposed time series not only covers the membership degree and non-membership degree of intuitionistic fuzzy sets but also has a wider range than the original intuitionistic fuzzy sets. Fermatean fuzzy time series, for some specific cases, such as when the membership and non-membership degrees of expert decision are greater than 1, are more suitable for the prediction of these time series data. We refer to the intuitionistic fuzzy time series(IFTS) fuzzification form and the generalized fuzzy time through the primary membership degree and secondary membership degree, combined with the scoring function prediction, putting forward the fermatean fuzzy time series. It is also proved that the calculation methods of membership functions and non-membership functions of fermatean fuzzy time series are normal, that is, they are constructed based on normal fermatean fuzzy sets. Then, the fuzzy c-means clustering algorithm (FCM) technology was used to obtain the optimal interval division at the same time. The proposed prediction method is superior to the existing prediction methods such as ordinary fuzzy time series and intuitionistic fuzzy time series in terms of prediction accuracy. It provides a useful way for us to deal with the prediction problem and achieves a higher prediction accuracy rate.