A Granular Unified Framework for Learning Fuzzy Systems

We propose a novel computational granular unified framework that is cognitively motivated for learning if-then fuzzy weighted rules by using a hybrid fuzzy-neuro possibilistic model appropriately crafted as a learning device of fuzzy rules from only raw input-output examples by integrating some useful concepts from the human cognition processes and adding some interesting granular functionalities. This learning scheme uses an exhaustive search over the fuzzy partitions of involved variables, automatic fuzzy hypotheses generation, formulation and testing, and approximation procedure of min-max relational equations. The main idea is to start learning from coarse fuzzy partitions of the involved variables and proceed progressively toward fine-grained partitions until finding the appropriate partition that fits the data. It learns conjointly appropriate fuzzy partitions, appropriate fuzzy rules and appropriate membership functions for the problem at hand.