Granular fuzzy models as a new paradigm of system modeling

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We introduce and thoroughly investigate a novel category of granular system modeling and concepts of granular fuzzy models. Granular fuzzy models build upon fuzzy models. Fuzzy models develop relationships between input and output variables described in terms of fuzzy sets regarded as the essential building functional components of the models. This makes fuzzy models transparent, helps establish a suitable level of specificity (detail) of the models and enhance their development (learning) mechanisms. Granular fuzzy models augment existing fuzzy models by introducing important and practically sound abilities to quantify their performance. Granular fuzzy models can directly result from fuzzy models where their parameters are made granular (say, characterized by fuzzy sets, interval, rough sets and alike) that help describe and quantify the performance of the model. Granular fuzzy models can also emerge at a higher level of hierarchy as constructs capturing the diversity of fuzzy models present at the lower level and describing the same system (process) from different points of view. We form a sound, well rounded, and coherent methodology supporting the analysis of granular fuzzy models. The underling fundaments of granular modeling dwell upon the key ideas and constructs of Granular Computing (GrC) regarded as a unified processing framework of sets (intervals), fuzzy sets, and rough sets. We build a comprehensive design platform with clearly delineated categories of key construction problems of such models, especially a class of estimation problems and inverse problems. A suite of estimation problems are concerned with a realization of the granular fuzzy models with a focus on main categories of fuzzy rule-based models, fuzzy neural networks and fuzzy cognitive maps. The principle of justifiable granularity and an allocation of information granularity are the two concepts of GrC supporting a variety of design practices developed in the project. We also exploit the applied facets of the granular models by applying them to problems of time series prediction, pattern classification, and spatiotemporal data analysis.