Boosted Fuzzy Granular Regression Trees

Algorithm 2

Fuzzy granular regression tree.

Input: instance set , regression value set
Output: fuzzy granular tree
(1)	Remove the instances missing some attribute values.
(2)	Normalize each attribute value.
(3)	Calculate the cluster center set (Algorithm 1).
(4)	and . // Parallel distributed fuzzy granulation.
(5)	//This is parallel process. Here, take as example.
FOR to
FOR to
, sample is fuzzy granulated as
END FOR
Build a fuzzy granular vector ;
Get label of , ;
A fuzzy granular rule can be built. ;
END FOR
(6)	Select the optimal segmentation variable (i.e., the attribute ) and segmentation point (i.e., ) by solving equation
That is, traverse variable to find the pair that minimizes the loss function by fixing the segmentation variable and scanning segmentation point .
(7)	Divide the area with the selected pair and decide output value as follows:
(8)	Continue to call Step 6 and Step 7 for the two subregions until the number of split nodes is .
(9)	Divide the input fuzzy granular space into regions and generate a fuzzy granular regression tree