Paper:

# A Granular Unified Min-Max Fuzzy-Neuro Framework for Learning Fuzzy Systems

## Mokhtar Beldjehem

Sainte Anne University, 1589 Walnut Street Halifax, Nova Scotia, B3H 3S1, Canada

We propose a novel computational granular unified framework that is cognitively motivated for learning if-then fuzzy weighted rules by using a hybrid neuro-fuzzy or fuzzy-neuro possibilistic model appropriately crafted as a means to automatically extract or learn fuzzy rules from only input-output examples by integrating some useful concepts from the human cognitive 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 (both input and output) and proceed progressively toward fine-grained partitions until finding the appropriate partitions that fit the data. According to the complexity of the problem at hand, it learns the whole structure of the fuzzy system, i.e. conjointly appropriate fuzzy partitions, appropriate fuzzy rules, their number and their associated membership functions.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.13, No.5, pp. 520-528, 2009.

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