Learning Curve as a Knowledge-based Dynamic Fuzzy Set: A Markov Process Model

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. [14], for modeling the time difference in the dynamic knowledge fuzzy set as an autoregressive model of order one.