A hybrid learning method for the data-driven design of linguistic dynamic systems

In lots of data based prediction or modeling applications, uncertainties and/ or noises in the observed data cannot be avoided. In such cases, it is more preferable and reasonable to provide linguistic ( fuzzy ) predicted results described by fuzzy memberships or fuzzy sets instead of the crisp estimates depicted by numbers. Linguistic dynamic system ( LDS) provides a powerful tool for yielding linguistic ( fuzzy ) results. However, it is still difficult to construct LDS models from observed data. To solve this issue, this paper first presents a simplified LDS whose input-output mapping can be determined by closed-form formulas. Then, a hybrid learning method is proposed to construct the data-driven LDS model. The proposed hybrid learning method firstly generates fuzzy rules by the subtractive clustering method, then carries out further optimization of centers of the consequent triangular fuzzy sets in the fuzzy rules, and finally adopts multi-objective optimization algorithm to determine the left and right end-points of the consequent triangular fuzzy sets. The proposed approach is successfully applied to three real-world prediction applications which are: prediction of energy consumption of a building, forecasting of the traffic flow, and prediction of the wind speed. Simulation results show that the uncertainties in the data can be effectively captured by the linguistic ( fuzzy) estimates. It can also be extended to some other prediction or modeling problems, in which observed data have high levels of uncertainties.