Abstract
Time series is an extremely important branch of prediction, and the research on it plays an important guiding role in production and life. To get more realistic prediction results, scholars have explored the combination of fuzzy theory and time series. Although some results have been achieved so far, there are still gaps in the combination of n-Pythagorean fuzzy sets and time series. In this paper, a pioneering n-Pythagorean fuzzy time series model (n-PFTS) and its forecasting method (n-IMWPFCM) are proposed to employ a n-Pythagorean fuzzy c-means clustering method (n-PFCM) to overcome the subjectivity of directly assigning membership and non-membership values, thus improving the accuracy of the partition the universe of discourse. A novel improved Markov prediction method is exploited to enhance the prediction accuracy of the model. The proposed prediction method is applied to the yearly University of Alabama enrollments data and the new COVID-19 cases data. The results show that compared with the traditional fuzzy time series forecasting method, the proposed method has better forecasting accuracy. Meanwhile, it has the characteristics of low computational complexity and high interpretability and demonstrates the superiority of this model from a realistic perspective.
Highlights
Using the known to derive the unknown, that is prediction, has important guiding significance for production and life, collecting long-term weather data to predict whether a ship is seaworthy, looking at seasonal variations in climate to predict suitability for farming, using stock trading data to predict the timing of purchases
Both data sets are analyzed by using the classical model which proposed by Chen and Chung (2006), Markov weighted fuzzy time series model based on an optimum partition method proposed by Alyousifi et al (2020) (MWFCM), Markov weighted fuzzy n-Pythagorean time series model which based on nPythagorean fuzzy c-means (n-MWPFCM)
According to the results of the simulation experiment, we can intuitively see that based on the n-Pythagorean fuzzy c-means clustering and using the Markov weighted method of MWFCM Li et al (2009) to carry out the de-fuzzed prediction, the prediction accuracy is significantly improved, which demonstrates the effectiveness of the n-Pythagorean fuzzy c-means algorithm
Summary
Using the known to derive the unknown, that is prediction, has important guiding significance for production and life, collecting long-term weather data to predict whether a ship is seaworthy, looking at seasonal variations in climate to predict suitability for farming, using stock trading data to predict the timing of purchases. After Zadeh (1965) completed the theoretical work of fuzzy sets, which provided an unprecedented idea for dealing with uncertain and fuzzy linguistic variables, Song and Chissom (1993, 1965a, b) developed the first fuzzy time series model and prediction method based on this. For a situation similar to the above example and the intuitionistic fuzzy time series cannot cope with, this paper proposes an improved Markov weighted nPythagorean fuzzy time series forecasting method based on n-Pythagorean fuzzy c-means(n-IMWPFCM). An improved Markov Weighted prediction algorithm is proposed and applied to the defuzzification of the n-Pythagorean fuzzy time series.
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