Dealing with the time series forecasting problem attracts much attention from the fuzzy community. Many models and methods have been proposed in the literature since the publication of the study by Song and Chissom in 1993, in which they proposed fuzzy time series together with its fuzzy forecasting model for time series data and the fuzzy formalism to handle their uncertainty. Unfortunately, the proposed method to calculate this fuzzy model was very complex. Then, in 1996, Chen proposed an efficient method to reduce the computational complexity of the mentioned formalism. Hwang et al. in 1998 proposed a new fuzzy time series forecasting model, which deals with the variations of historical data instead of these historical data themselves. Though fuzzy sets are concepts inspired by fuzzy linguistic information, there is no formal bridge to connect the fuzzy sets and the inherent quantitative semantics of linguistic words. This study proposes the so-called linguistic time series, in which words with their own semantics are used instead of fuzzy sets. By this, forecasting linguistic logical relationships can be established based on the time series variations and this is clearly useful for human users. The effect of the proposed model is justified by applying the proposed model to forecast student enrollment historical data.

The linguistic time-series forecasting model (LTS-FM), which has been recently proposed, uses linguistic words of linguistic variable domains generated by hedge algebras (HAs) to describe historical numeric time-series data. Then, the LTS-FM was established by utilizing real numeric semantics of words induced by the fuzziness parameter values (FPVs) of HAs. In the existing LTS-FMs, just the FPVs of HAs are optimized, while the used word set is still chosen by human experts. This paper proposes a co-optimization method of selecting the optimal used word set that best describes numeric time-series data in parallel with choosing the best FPVs of HAs to improve the accuracy of LTS-FMs by utilizing particle swarm optimization (PSO). In this co-optimization method, the outer loop optimizes the FPVs of HAs, while the inner loop optimizes the used word set. The experimental results on three datasets, i.e., the “enrollments of the University of Alabama” (EUA), the “killed in car road accidents in Belgium” (CAB), and the “spot gold in Turkey” (SGT), showed that our proposed forecasting model outperformed the existing forecasting models in terms of forecast accuracy.

Fuzzy time series forecasting model was first introduced by Song and Chissom, in 1993. Then, Chen examined this model, in 1996, applying fuzzy rules in the form A i → A j , where A i and A j are fuzzy sets associated with linguistic labels representing their corresponding values in a time series. Since then, many methods have been proposed to improve the accuracy of time series forecasting results or decrease processing times. In this study, we propose another approach dealing directly with human words with their own inherent semantics. That is, we assume that the above rules are of form X i → X j , in which X i and X j are human expert words describing their corresponding time series values. Therefore, we should deal with a so-called linguistic time series forecasting model using the inherent semantics of words and their quantitative semantics based on the hedge algebras formalism. A comparative experiment is made to show the usefulness of the proposed model.

Linguistic time series forecasting model (LTS-FM) which is proposed by Hieu et al. by utilizing hedge algebras theory is an efficient forecasting model. Instead of partitioning the universe of discourse (UD) of the linguistic variable into subintervals and assigning fuzzy sets to them, it establishes a formalism to convert historical numeric time series data into linguistic one based on numerical semantics of words which are transformed from the semantically quantifying mapping (SQM) values of the corresponding words. Therefore, a LTS-FM is established in such a way that it handles directly words of linguistic variable and their qualitative semantics. However, the fuzziness parameter values of the LTS-FM which determine the SQM values of words are currently specified by human experts, so the forecasted results may not be optimal. This paper proposes a hybrid LTS-FM in which particle swarm optimization is utilized to optimize the fuzziness parameter values. A new formula of computing crisp forecasted values is also proposed. The experimental studies carried out over two practical forecasting problems of the enrollments of University of Alabama and killed in car road accident in Belgium show that the proposed forecasting model obtains better forecasted results.