A Rule-based Granular Model Design For Interval-valued Time Series

As one type of time series,interval-valued time series(ITS)is encountered frequently in many fields such as finance,environment,agriculture and so on since it can describe the uncertainty and variability of observed variables.The modeling of ITS is an ongoing issue that pursued by researchers.However,the conventional modeling methods of ITS mostly take numerical values as the center and focus on improving the prediction accuracy of the prediction results,which may ignore the linguistic information and leads to the lack of interpretability.It can also have some limitations when they are faced with incomplete and uncertain intervalvalued data or uncertain factors caused by the fuzziness of human language.Granular computing(Gr C)is generally regarded as a human-centric coherent conceptual and computational platform focusing on constructing,representing and handling information granules.As a new information processing method centered on people,it pays attention to the cognition of the overall trend and characteristics of data.In this paper,a novel rule-based granular ITS model is proposed by considering the interval-valued data as interval information granules in the framework of Gr C.The development of the proposed granular model consists of three components with progressive relationship,that is,the generation of granular prototypes,the formation of initial granular model and the refinement of the initial granular model.Further,the detail computation of reasoning of the corresponding granular model is also given.In the process of developing the granular model,ITS is first organized into a series of input-output pairs.Then interval fuzzy c-means(IFCM)clustering is directly invoked to group those input-output pairs,such that some granular prototypes are generated in the input-output space.These granular prototypes depict key characteristics of relationships of ITS between at the current time moment and the previous time moment.In a sequel,the resulting granular prototypes are projected into the input space and the output space,respectively.As a result,the linguistic information granules located in the input space and the output space are formed.Finally,the linguistic information granules in the input space are articulated with the linguistic information granules in the output space by using a series of“If-Then” rules,which results in the formation of initial granular model.Further the initial granular model is refined by introducing the interval-valued factors to augment its conclusion parts so that the refined granular model is emerged completely.The resulting granular models have not only accuracy,but also interpretability and an ability to process ITS containing linguistic variables.Numerical experiments on six real-world financial datasets reveal the impact of the parameter involved in the proposed method on the resulting granular model,and also illustrate the feasibility and effectiveness of the proposed method.