Algorithm 1 FCM

1:C: number of clusters 2:m: the degree of fuzziness $(m>1)$ 3:$ϵ$: the error 4:Initalize randomly the centers of clusters ${\mathbf{c}}_i^{\left(0\right)}$ 5:Begin at iteration $k=1$. 6:repeat 7:     Calculate the membership $u_{ij}^{\left(k\right)}$ using the centers ${\mathbf{c}}_i^{(k-1)}$: 8:     $u_{ij}=\frac{1}{{\sum }_{k=1}^c{\left(\frac{d_{ij}}{d_{kj}}\right)}^{\frac{2}{m-1}}}$ 9:  Calculate the membership matrix $U^{\left(k\right)}={\left[u_{ij}\right]}_{c\times n}$ using the membership $u_{ij}^{\left(k\right)}$. 10:   Update the centers ${\mathbf{c}}_i^{\left(k\right)}$ using $u_{ij}^{\left(k\right)}$ 11: ${\mathbf{c}}_i=\frac{{\sum }_{j=1}^n{u}_{ij}^m{\mathit{x}}_j}{{\sum }_{j=1}^n{u}_{ij}^m}$ 12:until $\parallel U^{(k+1)}-U^{\left(k\right)}\parallel <ϵ$ 13:Return ${\mathbf{c}}_i^{\left(k\right)}$