Interval Granular Fuzzy Models: Concepts and Development

In this paper, we present a concept of interval granular fuzzy models and elaborate on their detailed development scheme and performance evaluation. The crux of the underlying design is that the information granules and information granularity which play a pivotal role in human cognitive and decision-making activities are incorporated into existing fuzzy modeling methods to realize system modeling at the level of information granules. The overall development process of interval granular fuzzy model includes two stages. At the first stage, we form input-error data by computing residual error resulting from the well-established numeric model and then establish granular structures positioned in the input space by clustering input-error data and invoking the principle of justifiable information granularity for weighted data. These granular structures discovered in the input space become condition parts of the rules of the developed interval granular fuzzy model. At the second stage, the interval information granules positioned in the error space are directly induced with the aid of granular structures discovered in the input space. These interval information granules describe the range of residual error produced by the numeric model and are exploited to form the conclusion part of the corresponding rules of the developed interval granular fuzzy model. So far, the interval granular fuzzy model is completely constructed, whose rules help compensate the discrepancies of the numeric model. The output of the developed model is an interval information granule showing a range of possible residual error produced by the numeric model. The several performance indices are presented to evaluate the developed interval granular fuzzy model. A series of numeric experiments completed for synthetic data and real-world data coming from the machine learning repository provide a useful insight into the effectiveness of the presented development scheme, reveal the impact of some parameters on the performance of the developed model and demonstrate its advantages.