Fuzzy time series forecasting with a probabilistic smoothing hidden Markov model

Since its emergence, the study of fuzzy time series (FTS) has attracted more attention because of its ability to deal with the uncertainty and vagueness that are often inherent in real-world data resulting from inaccuracies in measurements, incomplete sets of observations, or difficulties in obtaining measurements under uncertain circumstances. The representation of fuzzy relations that are obtained from a fuzzy time series plays a key role in forecasting. Most of the works in the literature use the rule-based representation, which tends to encounter the problem of rule redundancy. A remedial forecasting model was recently proposed in which the relations were established based on the hidden Markov model (HMM). However, its forecasting performance generally deteriorates when encountering more zero probabilities owing to fewer fuzzy relationships that exist in the historical temporal data. This paper thus proposes an enhanced HMM-based forecasting model by developing a novel fuzzy smoothing method to overcome performance deterioration. To deal with uncertainty more appropriately, the roulette-wheel selection approach is applied to probabilistically determine the forecasting result. The effectiveness of the proposed model is validated through real-world forecasting experiments, and performance comparison with other benchmarks is conducted by a Monte Carlo method.