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

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.