From Fuzzy Models to Granular Fuzzy Models

In this study, we offer a general view at the area of fuzzy modeling and elaborate on a new direction of system modeling by introducing a concept of granular models. Those models constitute a generalization of existing fuzzy models and, in contrast to existing models, generate results in the form of information granules (such as intervals, fuzzy sets, rough sets and others). We present a rationale and some key motivating arguments behind the emergence of granular models and discuss their underlying design process. Central to the development of granular models are granular spaces, namely a granular space of parameters of the models and a granular input space. The development of the granular model is completed through an optimal allocation of information granularity, which optimizes criteria of coverage and specificity of granular information. The emergence of granular models of type-2 and type-n, in general, is discussed along with an elaboration on their formation. It is shown that achieving a sound coverage-specificity tradeoff (compromise) is of essential relevance in the realization of the granular models.