
## 2.4 The Proposed Procedure

Developed algorithms use four basic axioms upon the balancing of the successive granules assumption: - Step (1): dividing the monitored data into groups of training and testing data 
- Step (2): first granulation (crisp) by SOM or other crisp granulation methods Step (2-1): selecting the level of granularity randomly or depend on the obtained error from the NFIS or RST (regular neuron growth) 
Step (2-2): construction of the granules (crisp). 

- Step (3): second granulation (fuzzy or rough granules) by NFIS or RST 
Step (3-1): crisp granules as a new data. Step (3-2): selecting the level of granularity; (Error level, number of rules, strength threshold...) 
Step (3-3): checking the suitability. (Close-open iteration: referring to the real data and reinspect closed world) 
Step (3-4): construction of fuzzy/rough granules. 

- Step (4): extraction of knowledge rules Selection of initial crisp granules can be supposed as "Close World Assumption (CWA)" .But in many applications, the assumption of complete information is not feasible, and only cannot be used. In such cases, an "Open World Assumption (OWA)', where information not known by an agent is assumed to be unknown, is often accepted [14]. 

![0_image_0.png](0_image_0.png)

Balancing assumption is satisfied by the close-open iterations: this process is a guideline to balancing of crisp and sub fuzzy/rough granules by some random/regular selection of initial granules or other optimal structures and increment of supporting rules (fuzzy partitions or increasing of lower /upper approximations ), gradually. The overall schematic of Self Organizing Neuro-Fuzzy Inference System -Random: SONFIS-R has been shown in Fig.2. In first granulation step, we use a linear relation is given by: 