A Co-Optimization Algorithm Utilizing Particle Swarm Optimization for Linguistic Time Series

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.