From Fuzzy Models to Granular Fuzzy Models

Fuzzy models occupy one of the dominant positions on the research agenda of fuzzy sets exhibiting a wealth of conceptual developments and algorithmic pursuits as well as a plethora of applications. Granular fuzzy modeling dwelling on the principles of fuzzy modeling opens new horizons of investigations and augments the existing design methodology exploited in fuzzy modeling. In a nutshell, granular fuzzy models are constructs built upon fuzzy models or a family of fuzzy models. We elaborate on a number of compelling reasons behind the emergence of granular fuzzy modelling, and granular modeling, in general. Information granularity present in such models plays an important role. Given a fuzzy model M, the associated granular model incorporates granular information to quantify a performance of the original model, facilitate collaborative pursuits of knowledge management and knowledge transfer. We discuss several main categories of granular fuzzy models where such categories depend upon the formalism of information granularity giving rise to interval-valued fuzzy models, fuzzy fuzzy model (fuzzy

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models, for short), and rough -fuzzy models. The design of granular fuzzy models builds upon two fundamental concepts of Granular Computing: the principle of justifiable granularity and an optimal allocation (distribution) of information granularity. The first one supports a construction of information granules of a granular fuzzy model. The second one emphasizes the role of information granularity being treated as an important design asset. The underlying performance indexes guiding the design of granular fuzzy models are discussed and a multiobjective nature of the construction of these models is stressed.