A novel probabilistic intuitionistic fuzzy set based model for high order fuzzy time series forecasting

The present research proposes a novel probabilistic intuitionistic fuzzy time series forecasting (PIFTSF) model using support vector machine (SVM) to address both uncertainty and non-determinism associated with real world time series data. In this model, the probability of membership values of crisp observation is determined to handle the statistical uncertainty. At the same time, the intuitionistic fuzzy element of crisp observation is determined to handle the non-statistical uncertainty along with non-determinism. Then, both the membership values are aggregated to obtain the probabilistic intuitionistic fuzzy element which handles both statistical and non-statistical uncertainty along with non-determinism due to hesitancy. Additionally, a novel trend-based discretization (TBD) method is proposed to determine the universe of discourse and number of intervals (NOIs) of fuzzy time series (FTS). For the first time, the fuzzy logical relationships (FLRs) are established for the probabilistic intuitionistic fuzzy set by considering the ratio trend variation (RTV) of crisp observation along with the mean of aggregated membership values which is modelled using SVM. The efficiency of the proposed PIFTSF model is demonstrated with sixteen diversified time series datasets and seven existing FTS models. A sensitivity analysis is carried out with respect to different design strategies to ensure the robustness of the proposed model. Extensive statistical analyses on obtained results confirm the superiority of the proposed model over other existing models. Further, Wilcoxon signed rank test, and Friedman and Nemenyi hypothesis test ensures the accuracy, robustness and reliability of the proposed model against its counterparts.