The granular extension of Sugeno-type fuzzy models based on optimal allocation of information granularity and its application to forecasting of time series.

Graphical abstractThe schematic diagram of the design process for extending the Sugeno-type fuzzy model to its granular model (granular counterpart) by an optimal allocation of information granularity. Display Omitted HighlightsWe proposed a novel Sugeno-type granular model in which the output is an information granular, which facilitates further interpretation..Information granularity, which is regarded as an important and practically useful design asset, is fully exploited for designing Sugeno-type granular model.The proposed approach of constructing the Sugeno-type granular model is of general nature as it could be applied to various fuzzy models and realized by invoking different formalisms of information granules.The proposed Sugeno-type granular model can provide much more flexibility than the Sugeno-type numeric fuzzy model. The Sugeno-type fuzzy models are used frequently in system modeling. The idea of information granulation inherently arises in the design process of Sugeno-type fuzzy model, whereas information granulation is closely related with the developed information granules. In this paper, the design method of Sugeno-type granular model is proposed on a basis of an optimal allocation of information granularity. The overall design process initiates with a well-established Sugeno-type numeric fuzzy model (the original Sugeno-type model). Through assigning soundly information granularity to the related parameters of the antecedents and the conclusions of fuzzy rules of the original Sugeno-type model (i.e. granulate these parameters in the way of optimal allocation of information granularity becomes realized), the original Sugeno-type model is extended to its granular counterpart (granular model). Several protocols of optimal allocation of information granularity are also discussed. The obtained granular model is applied to forecast three real-world time series. The experimental results show that the method of designing Sugeno-type granular model offers some advantages yielding models of good prediction capabilities. Furthermore, those also show merits of the Sugeno-type granular model: (1) the output of the model is an information granule (interval granule) rather than the specific numeric entity, which facilitates further interpretation; (2) the model can provide much more flexibility than the original Sugeno-type model; (3) the constructing approach of the model is of general nature as it could be applied to various fuzzy models and realized by invoking different formalisms of information granules.