Fuzzy Covering-Based Three-Way Clustering

Algorithm 2

kNN-FRFCM algorithm-based three-way clustering.

	Input: the valid fuzzy covering of universe , the cluster centers , and the initial fuzzy membership degrees ;
	Output: the positive, boundary, and negative regions of each cluster, respectively.
	: compute the optimal partition thresholds and for each cluster using formula (13);
	: according to formula (14), determine the positive region , boundary region , and for each cluster by , , and fuzzy partition matrix ;
	: update each clustering region by Algorithm 1;
	: update the membership partition matrix by formula (6);
	: update the cluster center with formula (8);
	repeat Step 1 to Step 5 until convergence is reached;
	: the results of fuzzy covering clustering are replaced by the corresponding objects in the universe.