A pliant arithmetic-based fuzzy time series model

Abstract

In this study, a fuzzy arithmetics-based fuzzy time series modeling method is introduced. After input data normalization, the fuzzy c-means clustering algorithm is used for fuzzification and establishment of antecedents of the fuzzy rules. Here, each rule consequent is treated as a fuzzy number composed of a left and a right hand side fuzzy set, each of which is given by a sigmoid membership function. The novelty of the proposed method lies in the application of pliant arithmetics to aggregate separately the left and the right hand sides of the individual fuzzy consequents, taking the activation levels of the corresponding antecedents into account. Here, Dombi’s conjunction operator is applied to form the fuzzy output from the aggregates of the left and right hand side sigmoid functions. The introduced defuzzification method does not require any numerical integration and runs in constant time. The output of the pliant arithmetic based fuzzy time series model is obtained by denormalizing the crisp output produced by the fuzzy inference. Lastly, the modeling capability of the introduced methodology was tested on empirical data. Based on these results, our method may be viewed as a viable alternative prediction technique.