A Fuzzy Time Series Model with Customized Membership Functions

In this study, a fuzzy time series modeling method that utilizes a class of customized and flexible parametric membership functions in the fuzzy rule consequents is introduced. The novelty of the proposed methodology lies in the flexibility of this membership function, which we call the composite kappa membership function, and its curve may take various shapes, such as a symmetric or asymmetric bell, triangular, or quasi trapezoid. In our approach, the fuzzy c-means clustering algorithm is used for fuzzification and for the establishment of fuzzy rule antecedents and a heuristic is introduced for identifying the quasi optimal number of clusters to be formed. The proposed technique does not require any preliminary parameter setting, hence it is easy-to-use in practice. In a real-life example, the modeling capability of the proposed method was compared to those of Winters’ method, the Autoregressive Integrated Moving Average technique and Adaptive Neuro-Fuzzy Inference System. Based on the empirical results, the proposed method may be viewed as a viable time series modeling technique.