Abstract
In the fuzzy set theory introduced by Zadeh [15], membership degree of a fuzzy set is determined by a static membership function, i.e., it does not change over time. To improve this condition, then Wang introduced the dynamic fuzzy logic. In this concept, the membership degree of a fuzzy set is changing over time. Intan and Mukaido [5] introduced the knowledge-based fuzzy set, by means that the membership degree of a set is dependent on the knowledge of a person. Since the knowledge of a person is not static, the knowledge-based fuzzy set can be measured dynamically over time, so that we have the knowledge-based dynamic fuzzy set. In this paper, we approximate the learning process as a knowledge-based dynamic fuzzy set. We consider that the process of learning is dependent on the knowledge of a person from time to time so that we can model the learning process is a Markov process of dynamic knowledge. Additionally, using the triangular fuzzy number, we follow Yabuuchi et al. (2014), for modeling the time difference in the dynamic knowledge fuzzy set as an autoregressive model of order one.
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References
Brockwell, P. J., Davis, R. A.: Time series: theory and methods, pp. 238–272. Springer, New York (1991)
Cheng, C.H., Chen, C.H.: Fuzzy time series model based on weighted association rule for financial market forecasting. Expert Systems. Wiley online Library (2018)
Ellis, A.B., Ozgur, Z., Kulow, M., Dogan, M.F., Amidon, J.: An exponential growth learning trajectory: student’s emerging understanding of exponential growth through covariation. Math. Thinking Learning 18(3), 151–181 (2016)
Fukuda, T., Sunahara, Y.: Parameter identification of fuzzy autoregressive models. IFAC Proc., 26(2) Part 5, 689–692, (1993)
Intan, R., Mukaidono, M.: On knowledge-based fuzzy sets. Int. J. Fuzzy Syst. 4(2), 655–664 (2002)
Jónás, T.: Sigmoid functions in reliability based management. Soc. Manag. Sci. 15(2), 67–72 (2007)
Kallenberg, O.: Foundation of Modern Probability. Springer, New-York (2002)
Kucharavy, D., De Guio, R.: Application of S-shaped Curve. Proc. Eng. 9, 559–572 (2011)
Lee, H.S., Chou, M.T.: Fuzzy forecasting based on fuzzy time series. Int. J. Comput. Math. 81(7), 781–789 (2004)
Leonid, P.: Dynamic fuzzy logic, denotational mathematics, and cognition modeling. J. Adv. Math. Appl. 1(1), 27–41 (2012)
Li, F.: Dynamic fuzzy logic and its applications. Nova-Science Publisher, New York (2008)
Silva, J. L. P., Rosano, F. L.: Dynamic fuzzy logic. In: Mexican International Conference on Artificial Intelligence (Micai), Lectures Notes in Computer Science, 1793, 661–670, (2000)
Tanaka, H., Shimomura, T., Watada, J.: Identification of learning curve based on fuzzy regression model. Japn. J. Ergon. 22(5), 253–258 (1986)
Yabuuchi, Y., Watada, J., Toyoura, Y.: Fuzzy AR model of stock price. Scientiae Mathematicae Japonicae 10, 485–492 (2004)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: Fuzzy sets and systems. Int. J. Gen Syst. 17, 129–138 (1990)
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Halim, S., Intan, R., Dewi, L.P. (2019). Learning Curve as a Knowledge-Based Dynamic Fuzzy Set: A Markov Process Model. In: Bhatia, S., Tiwari, S., Mishra, K., Trivedi, M. (eds) Advances in Computer Communication and Computational Sciences. Advances in Intelligent Systems and Computing, vol 924. Springer, Singapore. https://doi.org/10.1007/978-981-13-6861-5_29
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DOI: https://doi.org/10.1007/978-981-13-6861-5_29
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