Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures

Table 13

Estimated parameters of A 4-component GMM using the EM algorithm (load).

Cluster or rule no. (𝑚)	Weight of the rule 𝑝(𝑐𝑚)	Mean (𝐳^𝑚)	Covariance (∑𝑚)
Cluster or rule no. 1	𝑝(𝑐1)=0.2646	𝐳^1=^0.47200.45000.46940.38200.5007	∑1=^0.0031−0.0000−0.00107−0.00160.0026−0.00000.03060.0160−0.00510.0010−0.00170.01600.02460.0050−0.0005−0.0016−0.00510.00500.0227−0.00150.00260.0010−0.0005−0.00150.0029
Cluster or rule no. 2	𝑝(𝑐2)=0.2225	𝐳^2=^0.52260.74300.55640.45980.5269	∑2=^0.0188−0.00070.0031−0.00040.0122−0.00070.00810.0031−0.0044−0.00010.00310.00310.00520.00340.0024−0.0004−0.00440.00340.03080.00090.01220.0001−0.00240.00090.0084
Cluster or rule no. 3	𝑝(𝑐3)=0.2474	𝐳^3=^0.29020.30000.68440.43930.3771	∑3=^0.0228−0.0014−0.0035−0.00120.0137−0.00140.01540.00180.0003−0.0044−0.00350.00180.00650.0018−0.0025−0.00120.00030.00180.0054−0.00200.0137−0.0044−0.0025−0.00200.0142
Cluster or rule no. 4	𝑝(𝑐4)=0.2655	𝐳^4=^0.64740.57380.73720.49400.6013	∑4=^0.01020.00110.0009−0.00230.00680.00110.0093−0.00040.00300.00370.0009−0.00040.0108−0.00330.0002−0.00230.0030−0.00330.01890.00240.00680.00370.00020.00240.0073