Fuzzy Sets Based Granular Logics for Granular Computing

Granular computing become a new label of theories, methodologies, and tools that make use of granules in the process of problem solving. The infrastructure of granular computing is granular logic. However, much work about granular computing is built on classical set theory. In this research, we extend the granular logic from classical set to fuzzy sets and further intuitionistic fuzzy sets. A fuzzy sets based decision logic language is proposed for granular computing. It is an extended predication logic language in the Tarski's style through the notions of a model and satisfiability. The model is a generalized information system based on intuitionistic fuzzy sets. An intuitionistic fuzzy sets based truth degree function is proposed, where objects satisfying a formula at a given threshold is defined in term of the truth degree function. The fuzzy decision logic languages are generalization of traditional decision logic language . Information granulation is accurately interpreted with fuzzy decision logic language. Moreover, formal concept analysis and rule extraction are also analyzed with the extended decision logic based granular computing model.