From granulation-degranulation mechanisms to fuzzy rule-based models: Augmentation of granular-based models with a double fuzzy clustering

Abstract

In this study, we develop a novel clustering with double fuzzy factors to enhance the performance of the granulation-degranulation mechanism, with which a fuzzy rule-based model is designed and demonstrated to be an enhanced one. The essence of the developed scheme is to optimize the construction of the information granules so as to eventually improve the performance of the fuzzy rule-based models. In the design process, a prototype matrix is defined to express the Fuzzy C-Means based granulation-degranulation mechanism in a clear manner. We assume that the dataset degranulated from the formed information granules is equal to the original numerical dataset. Then, a clustering method with double fuzzy factors is derived. We also present a detailed mathematical proof for the proposed approach. Subsequently, on the basis of the enhanced version of the granulation-degranulation mechanism, we design a granular fuzzy model. The whole design is mainly focused on an efficient application of the fuzzy clustering to build information granules used in fuzzy rule-based models. Comprehensive experimental studies demonstrate the performance of the proposed scheme.