Fuzzy Calinski–Harabasz index for spherical clustering

Input: data set 𝒜 ⊂ (ℝ^n), centers (Subscript[c, 1]),⃛,(Subscript[c, k]) ∈ (ℝ^n), membership matrix U;
Output: FCH index;
Submodules: none needed

Clear[FCH]
FCH[A_,cen_,U_]:=Module[{m,k},m=Length[A];k=Length[cen];
cc=Mean[A];
kappa=Table[Sum[U[[ii,j]]^q,{ii,m}] ,{j,k}];
Return[(Sum[kappa[[j]]*Norm[cc-cen[[j]] ]^2,{j,k}]/(k-1))/(Sum[U[[i,j]]^q Norm[cen[[j]]-A[[i]]]^2,{i,m},{j,k}]/(m-k))]
]