Mahalanobis fuzzy  Davies-Bouldin index

Input: data set 𝒜 ⊂ (ℝ^n), centers (Subscript[z, 1]),⃛,(Subscript[z, k]) ∈ (ℝ^n), membership matrix U, covariance matrices (∑_j)∈(ℝ^(n×n)), j=1⃛k;
Output: MFDB index;
Submodules: dM[]

Clear[MFDB]
MFDB[A_,cen_,U_,cov_]:=Module[{m=Length[A],k=Length[cen],VV,max,sum=0},
VV=Table[0,{j,k}];
Do[
VV[[j]]=Sum[U[[i,j]]^q dM[cen[[j]],A[[i]],cov[[j]]],{i,m}]/Sum[U[[i,j]]^q,{i,m}]
   ,{j,k}];
Do[
max={};
Do[
If[i≠j,max=Append[max,(VV[[i]]+VV[[j]])/dM[cen[[i]],cen[[j]],cov[[i]]+cov[[j]]] ]]
,{i,k}];
sum=sum+Max[max]
,{j,k}];
sum/k
            ]