SYSTEM MODELING WITH FUZZY MODELS: FUNDAMENTAL DEVELOPMENTS AND PERSPECTIVES

In this study, we offer a general view at the area of fuzzy modeling and fuzzymodels, identify the visible development phases and elaborate on a new and promisingdirections of system modeling by introducing a concept of granular models. Granularmodels, especially granular fuzzy models constitute an important generalization of existingfuzzy models and, in contrast to the existing models, generate results in the form ofinformation granules (such as intervals, fuzzy sets, rough sets and others). We present arationale and deliver some key motivating arguments behind the emergence of granularmodels and discuss their underlying design process. Central to the development of granularmodels are granular spaces, namely a granular space of parameters of the models and agranular input space. The development of the granular model is completed through anoptimal allocation of information granularity, which optimizes criteria of coverage andspecificity 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 thatachieving a sound coverage-specificity tradeoff (compromise) is of paramount relevance inthe realization of the granular models.