In this paper, based on the concept of $alpha$-values of fuzzy random variables, the fuzzy moving average model of order $q$ is introduced. In this regard, first, the definitions of variance, covariance, and correlation coefficient between fuzzy random variables are presented, and their properties are investigated. In the following, while introducing the fuzzy moving average model of order $q$, this model's autocovariance and autocorrelation functions are calculated. Finally, some examples are presented for the obtained results.
Type of Study: Applied |
Subject: Fuzzy Statistics Received: 2023/09/18 | Accepted: 2024/08/31 | Published: 2024/06/4
References
1. A'yun, K., Abadi, A. M. and Saptaningtyas, F. Y. (2015), Application of Weighted Fuzzy Time Series Model to Forecast Trans Jogja's Passengers, International Journal of Applied Physics and Mathematics, 5(2), 76. [DOI:10.17706/ijapm.2015.5.2.76-85]
2. Chen. S.M. (2002), Forecasting Enrollments Based on High-order Fuzzy Time Series, Cybernetics and Systems, 33, 1-16. [DOI:10.1080/019697202753306479]
3. D'Urso, P.and Gastaldi, T.(2002), An Orderwise Polynomial Regression Procedure for Fuzzy Data, Fuzzy Sets and Systems, 130, 1-19. [DOI:10.1016/S0165-0114(02)00055-6]
4. Hesamian, G. and Akbari, M. G. (2022), A Fuzzy Quantile Method for AR Time Series Model Based on Triangular Fuzzy Random Variables, Computational and Applied Mathematics, 41(3), 123. [DOI:10.1007/s40314-022-01826-1]
5. Hesamian, G. and Akbari, M. G. (2018a). A Semiparametric Model for Time Series Based on Fuzzy Data, IEEE Transactions on Fuzzy Systems, 26(5), 2953-2966. [DOI:10.1109/TFUZZ.2018.2791931]
6. Hesamian, G. and Akbari, M. G. (2018b). Fuzzy Absolute Error Distance Measure Based on a Generalised Difference Operation, International Journal of Systems Science, 49(11), 2454-2462. [DOI:10.1080/00207721.2018.1505002]
7. Hesamian, G. R. and Chachi, J. (2015), Two-Sample Kolmogorov-Smirnov Fuzzy Test for Fuzzy Random Variables, Statistical Papers, 56, 61-82. [DOI:10.1007/s00362-013-0566-2]
8. Kruse, R. and Meyer, K. D. (1987), Statistics with Vague Data, Netherlands, Springer. [DOI:10.1007/978-94-009-3943-1]
9. Kwakernaak, H. (1978), Fuzzy Random Variables-I. Definition and Theorem, Information Sciences, 15, 1-29. [DOI:10.1016/0020-0255(78)90019-1]
10. Kwakernaak, H. (1979), Fuzzy Random Variables-II. Algorithms and Examples for the Discrete Case, Information Sciences, 17, 253-278. [DOI:10.1016/0020-0255(79)90020-3]
12. Puri, M. L. and Ralescu, D. A. (1986), Fuzzy Random Variables, Journal of Mathematical Analysis and Applications, 114, 409-422. [DOI:10.1016/0022-247X(86)90093-4]
13. Song. Q. and Chissom. B. S. (1993), Fuzzy Time Series and its Models, Fuzzy Sets and Systems, 54, 269-277. [DOI:10.1016/0165-0114(93)90372-O]
15. Zarei, R., Akbari, M. G., and Chachi, J. (2020), Modeling Autoregressive Fuzzy Time Series Data Based on Semi-parametric Methods, Soft Computing, 24, 7295- 7304. [DOI:10.1007/s00500-019-04349-w]