A Fuzzy Measure and Choquet Integral-Based Approach in the Predictive Knowledge-Based Systems: Application to the Electricity Demand Forecasting

Abstract

In a data-driven knowledge-based forecasting system, knowledge can be extracted from historical data by machine learning methods, and represented in the knowledge base. In the inference engine of such a system, the current inputs are used to forecast the likely outputs. The unpredictability of one (or more) inputs in the forecasting horizon, gives rise to one source of uncertainty in the reasoning process, named evidence uncertainty, which is the main focus of this article. To deal with this sort of uncertainty numerical scenarios are generated from historical data to substitute the uncertain input parameter using two approaches: Uniform sampling, and a classical nonuniform sampling acceptance–rejection method. Each input scenario has particular output, and at the end these outputs are aggregated with the discrete Choquet integral to account for outputs' dependencies. Fuzzy measures, also called capacities or nonadditive measures, assign the importance weight not to just each scenario but also to groups of scenarios. A fuzzy measure for the Choquet integral is learned from the historical data. The proposed reasoning approach is evaluated in a long-term relative electricity load forecasting, and treats the uncertainty which arises from unpredictability of the daily temperature in the long run. The results show the superiority of the proposed Choquet integral-based approach with respect to the $k$-interactive, $k$-additive, and $k$-tolerant fuzzy measures compared to traditional aggregators: the weighted arithmetic mean, and the ordered weighted averaging.