New Evolving Fuzzy System Algorithms Using Dynamic Constraint - Ahme, Md. Manjur (2016)
An information granule has to be translated into significant frameworks of granular computing to realize interpretability-accuracy tradeoff. These two objectives are in conflict and constitute an open problem. Evolving information granules is a significant concept of granular computing which consider coarser partition (or lower granule i.e. higher error) to fine partition (or higher granule i.e. lower error). While this error reducing granular framework is considered, interpretability constraint is the factor to improve the tradeoff between interpretability and accuracy. Furthermore, overfitting and underfitting criteria are noteworthy to be considered while evolving process continues. In addition, the stability-plasticity tradeoff is another significant consideration to design a granular framework in order to find a consistent and up-to-date fuzzy information granule method. A new operational framework namely evolving fuzzy system (EFS) is developed in this research work, which ensures a compromise between interpretability and reasonable accuracy. Three models are designed based on EFS namely, evolving structural fuzzy system (ESFS), evolving output-context fuzzy system (EOCFS) and evolving information granule (EIG). The evolving information granule is initiated with the first information granule by translating the knowledge of the entire output domain. The initial information granule is considered as an underfitting state with a high approximation error. Then, the EFS starts evolving in the information granule by partitioning the output (or input) domain and uses a dynamic constraint to maintain semantic interpretability in the output (or input) contexts. The outcome on the synthetic and real-world data using the EFS shows the effectiveness of the proposed system, which outperforms state-of-the-art methods. The EFS needs less number of rules (i.e. high interpretable) and low error (i.e. high accuracy) with respect to the existing methods. For example, if the proposed EIG method is applied to the Nakanishi‘s nonlinear system then four fuzzy rules and 0.142 mean square error (MSE) are found. Furthermore, the EIG outperforms if compared with the existing methods. The important criterion in the EFS is to determine the prominent distinction (output or input context) and realize the distinct information granule that depicts the semantics at the fuzzy partition level. The EFS tends to evolve toward the lower error region and realizes the effective rule base by avoiding overfitting. Furthermore, the evolving overfitting index and uncertainty controller of the self-adaptive process are dynamically attained from past and current knowledge. Therefore, effective rule base is the balanced fuzzy model of the approximated system. Within the proposed three models (ESFS, EOCFS and EIG), EIG has the significant ability to tradeoff between interpretability and accuracy, while the proposed ESFS method shows the highly interpretable granular framework which also realizes the interpretability-accuracy tradeoff.