Fuzzy Time Series Models Using Pliant- and Asymptotically Pliant Arithmetic-Based Inference

The fuzzy time series modeling techniques proposed in this study are based on a fuzzy inference method in which the fuzzy output is either a so-called pliant or quasi pliant (q-pliant) number. The novelty of the introduced inference method lies in the fact that its fuzzy output is obtained by fuzzy arithmetic operations; namely, via weighted aggregation of pliant numbers or q-pliant numbers, which are the consequents of the fuzzy rules. These fuzzy inference systems are called the pliant arithmetic-based fuzzy inference system (PAFIS) and the quasi pliant arithmetic-based fuzzy inference system (QPAFIS). The advantage of the defuzzification methods of these two systems is twofold. On the one hand, they do not require any numerical integration to generate the crisp output, on the other hand, they run in a constant time. Here, it is discussed how the pliant arithmetic-based fuzzy time series and the quasi pliant arithmetic-based fuzzy time series models can be established by utilizing the PAFIS and QPAFIS methods. Lastly, the modeling capabilities of the introduced methods are also examined on some real-life time series, and the forecasting results are compared with those of some well-known and recent time series forecasting methods. Based on the experimental results, our methods may be viewed as novel viable time series modeling techniques.