Granular fuzzy rule-based architectures: Pursuing analysis and design in the framework of granular computing

In this study, we propose a new concept of granular rule-based models whose rules assume a format ``if G(A i ) then G(f i )'' where G$(.)s are granular generalizations of the numeric conditions and conclusions of the rules. Those generalizations can be expressed e.g., in terms of interval-valued, type-2 or probabilistic fuzzy sets. We discuss several classes of fuzzy models depending upon available information granules and offer a motivation present behind their emergence. The design of these granular architectures exploits the essentials of Granular Computing such as a principle of justifiable granularity and an optimal allocation of information granularity. Detailed investigations of the performance indexes (objective functions) along with the related optimization schemes are covered as well.