As seen in Table 2, the mean values of J and the cluster validity indices computed for all the hybrid algorithms for over the range are more desirable than that of arFCM (lower values of J and VPE, and VK measures, and higher values of VPC). These results can show the efficiency of the hybrid approach to improve the performance of the FCM algorithm.

Table 2

Mean values of J and cluster validity indices computed for all the examined clustering algorithms for c = 2, 3, … , 7 over the range m ∈ [1.1, 2.5]

AlgorithmObjective function (J)VPCVPEVXB,mVK
arFCM 39.175 0.710 0.575 0.294 19.359 
SLFCM 39.111 0.722 0.554 0.225 15.405 
CLFCM 38.636 0.720 0.557 0.230 15.894 
ALFCM 38.707 0.721 0.556 0.226 15.510 
WFCM 37.939 0.716 0.563 0.258 17.256 
SOFMFCM 38.821 0.714 0.568 0.269 17.360 
AlgorithmObjective function (J)VPCVPEVXB,mVK
arFCM 39.175 0.710 0.575 0.294 19.359 
SLFCM 39.111 0.722 0.554 0.225 15.405 
CLFCM 38.636 0.720 0.557 0.230 15.894 
ALFCM 38.707 0.721 0.556 0.226 15.510 
WFCM 37.939 0.716 0.563 0.258 17.256 
SOFMFCM 38.821 0.714 0.568 0.269 17.360 
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