Causalities-multiplicity oriented joint interval-trend fuzzy information granulation for interval-valued time series multi-step forecasting

Interval-valued time series (ITSs) multi-step forecasting research is still in its infancy. Two cruces here lie in counterintuitive or conservative nature of semantic descriptors for ITSs, and disregard for multiplicity of causalities resulting from uncertainty in causalities between data or between trends within a set of interval-valued data. In this paper, we put forth a type of joint interval-trend fuzzy information granules, which takes non-loss of within-interval information as the main design criterion. A modified fuzzy information granulation method carries originality in portraying intuitive and accurate interval-trends, directly linked with inherent relational constraints such as lower bound data should not be greater than upper bound data. Furthermore, we formulate a legible format of multi-factor fuzzy IF-THEN rules, which exhibits interesting interpretations to causalities between interval-trends at a higher level of multiplicity. The forecasting process is fuzzy rules-based, resulting in wise results by calculating rule firing weights. Thus, we develop a well construct of accuracy and interpretability for multi-step forecasting of ITSs, manifested in: (a) reducing cumulative errors by operating at the granular level, and (b) perceiving interval-trends in an intelligible manner and emphasizing multiple causalities via transparent fuzzy logic inference. Experimental results convincingly confirm the validity of the model.