SYSTEM MODELING WITH FUZZY MODELS: FUNDAMENTAL DEVELOPMENTS AND PERSPECTIVES

Abstract

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