electre3.rar

function [ORD, hnp] = electre3 (A,q,p,v,w,s1,s2) %ELECTRE3 performs the multi attribute analysis according to the ELECTRE III method % % Syntax: [ORD, hnp] = electre3 (A,q,p,v,w,s1,s2) % % INPUT ARGUMENTS % - A n X m Environmental Impact matrix where m are alternatives considered and n the indicators. % - q n X 1 "indifference threshold vector" % - p n X 1 "strict preference vector" % - v n X 1 "veto vector" % - w n X 1 weights vector % - s1,s2 parameters of the discrimination threshold (slamb), according to the following expression: % % slamb = s1 +lamb*s2 % % where lamb is a value depending on the "MATRICE DI CREDIBILITA' DEI SURCLASSAMENTI". % % OUTPUT ARGUMENTS % - ORD n X n array. The ith row contains information about the ith alternative. A 1 in the position i,j % means that the ith alternative out competes the jth one; NaN otherwise. % - hnp handle to the figure created % Author: Francesco di Pierro Dep. of Electronics and Computer Science (DEI), % Politecnico di Milano % f_dipierro@yahoo.com %%%%%%%%%%%%%%%% INPUT ARGUMENTS CHECKING %%%%%%%%%%%%%%%% error(nargchk(7,7,nargin)); if size(A,1)~=size(q,1) | size(A,1)~=size(p,1) | size(A,1)~=size(v,1) | size(A,1)~=size(w,1) error(['Size(vec,2) must be equal to size(',inputname(1),'2) where vec represents vectors ',inputname(2),',',inputname(3),',',inputname(4),',',inputname(5),' !!!']); end if any(isnan(A(:))) | any(isnan(q)) | any(isnan(p)) | any(isnan(v)) | any(isnan(w)) | any(isnan(s1)) | any(isnan(s2)) error('NaN detected: NaNs are not allowed within this routine!'); end if prod([size(s1),size(s2)])~=1 error([inputname(6),' and ',inputname(7),' must be scalar numeric valid values!']); end %%%%%%%%%%%%%%%% EVALUATE AGREEMENT-DESAGREEMENT MATRICES %%%%%%%%%%%%% %initialize agreement-disagreement matrices C = zeros(size(A,2),size(A,2),size(A,1)); D = zeros(size(A,2),size(A,2),size(A,1)); for ind=1:size(A,1) %for every indicator %initialize the performance matrix perf = []; for i=1:size(A,2) for j=1:size(A,2) perf(i,j) = A(ind,j)-A(ind,i); if perf(i,j) < q(ind) C(i,j,ind) = 1; elseif perf(i,j) > p(ind) C(i,j,ind) = 0; else C(i,j,ind) = 1-(q(ind)-perf(i,j))/(q(ind)-p(ind)); end if perf(i,j) < p(ind) D(i,j,ind) = 0; elseif perf(i,j) > v(ind) D(i,j,ind) = 1; else D(i,j,ind) = (perf(i,j)-p(ind))/(v(ind)-p(ind)); end end end end W = shiftdim(repmat(w,[1,size(A,2),size(A,2)]),1); CW = sum(C.*W,3)./100; DW = sum(D.*W,3)./100; %%%%%%%%%%%%%%%%%%% "MATRICE DI CREDIBILITA' DEI SURCLASSAMENTI" %%%%%%%%%%%%%%%%%%%%%% CS = []; for i=1:size(A,2) for j=1:size(A,2) if i==j CS(i,j) = NaN; continue end CS(i,j) = CW(i,j); for k=1:size(A,1) if D(i,j,k) > CW(i,j) CS(i,j) = CS(i,j)*(1-D(i,j,k))/(1-CW(i,j)); end end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%% DESCENDING ORDER %%%%%%%%%%%%%%%%%%%% TMP = CS; OD = NaN*ones(size(A,2)); for i=1:size(A,2) [worst,TMP] = calc_Alpha(TMP,'dis',s1,s2); OD(i,:) = [worst', NaN*(1:length(A)-length(worst))]; if all(isnan(TMP)) alt_no = 1:length(TMP); miss_alt_dis = setdiff(alt_no,OD(~isnan(OD(:)))); if ~isempty(miss_alt_dis) OD(i+1,:) = [miss_alt_dis,NaN*(1:length(A)-length(miss_alt_dis))]; end break end end %%%%%%%%%%%%%%%%%%%%%%%%%%%% ASCENDING ORDER %%%%%%%%%%%%%%%%%%%% TMP = CS; OA = NaN*ones(size(A,2)); for i=1:size(A,2) [best,TMP] = calc_Alpha(TMP,'asc',s1,s2); OA(i,:) = [best', NaN*(1:length(A)-length(best))]; if all(isnan(TMP)) alt_no = 1:length(TMP); miss_alt_as = setdiff(alt_no,OA(~isnan(OA(:)))); if ~isempty(miss_alt_as) OA(i+1,:) = [miss_alt_as,NaN*(1:length(A)-length(miss_alt_as))]; end break end end %%%%%%%%%%%%%%%%%%%%%%%%%%%% FINAL ORDER %%%%%%%%%%%%%%%%%%% OA = flipdim(OA,1); MREL = 0*ones(size(A,2)); for i=1:size(A,2) [rOD,cOD] = find(OD==i); saOD = OD(rOD+1:end,:); saOD = saOD(find(~isnan(saOD(:)))); spOD = OD(1:rOD-1,:); spOD = spOD(find(~isnan(spOD(:)))); nsOD = OD(rOD,:); nsOD = nsOD(find(~isnan(nsOD(:)) & nsOD(:)~=i)); [rOA,cOA] = find(OA==i); saOA = OA(rOA+1:end,:); saOA = saOA(find(~isnan(saOA(:)))); spOA = OA(1:rOA-1,:); spOA = spOA(find(~isnan(spOA(:)))); nsOA = OA(rOA,:); nsOA = nsOA(find(~isnan(nsOA(:)) & nsOA(:)~=i)); sur_att = union(intersect(saOD,saOA),union(intersect(nsOD,saOA),intersect(saOD,nsOA))); sur_pas = union(intersect(spOD,spOA),union(intersect(nsOD,spOA),intersect(spOD,nsOA))); MREL(i,sur_att) = 1; MREL(i,sur_pas) = -1; end LN = NaN*ones(size(A,2),size(A,2)+1); MTOP = NaN*ones(size(A,2)); altbeg = find(max(MREL')==0); ALL = 1:size(A,2); ln = find(MREL(altbeg(1),:)==0); LN(1:length(ln),1) = ln'; for i=1:length(ln) LN(i,3:2+length(find(MREL(ln(i),:)==-1))) = find(MREL(ln(i),:)==-1); LN(i,2) = length(find(MREL(ln(i),:)==-1)); end ALLTMP = setdiff(ALL,LN(:,1)); ORD = calcord(MTOP,MREL,ALL,ALLTMP,LN); for i=1:length(ORD) remc = find(ORD(i,:)==1); for j=1:length(remc) rm = intersect(remc,find(ORD(remc(j),:)==1)); if any(rm) ORD(i,rm) = NaN; end if all(isnan(ORD(i,remc+1:end))) break end end end hnp = plotorder(ORD,mfilename); %%%%%%%%%%%%%%%%%%%%%%%%%%% SUBFUNCTION %%%%%%%%%%%%%%%%%%%%%%%%% % Recursive subfunction to compute ascending and descending ordering vectors function [worst, TMP] = calc_Alpha(TMP,ord,s1,s2,it) global LAMBDA_IT if strcmp(ord,'asc') method = 'min'; else method = 'max'; end if nargin == 4 LAMBDA_IT = 0; lamb = max(max(TMP)); slamb = s1+lamb*s2; treshold = lamb-slamb; else lamb_vec = flipdim(sort(TMP(:)),1); lamb_vec(isnan(lamb_vec)) = []; lamb = lamb_vec(it+1); slamb = s1+lamb*s2; treshold = lamb-slamb; end Alpha = zeros(length(TMP),1); [row,col] = find(TMP>treshold); survec = []; for i=1:length(row) if TMP(row(i),col(i))-TMP(col(i),row(i))>slamb survec(i) = 1; else survec(i) = 0; end end if strcmp(ord,'dis') testvec = unique(row); else testvec = unique(col); end for i=1:length(testvec) if ~isempty(find(row==testvec(i))) Alpha(testvec(i)) = sum(survec(find(row==testvec(i)))); end if ~isempty(find(col==testvec(i))) Alpha(testvec(i)) = Alpha(testvec(i))-sum(survec(find(col==testvec(i)))); end end altdel = find(all(isnan(TMP')).*all(isnan(TMP))); if ~isempty(altdel) Alpha(altdel) = NaN; end val = feval(method,Alpha); worst = find(Alpha==val); switch length(worst) case 1 TMP(worst,:) = NaN; TMP(:,worst) = NaN; case length(find(~isnan(Alpha))) if lamb==min(min(TMP)) TMP(worst,:) = NaN; TMP(:,worst) = NaN; else if isempty(LAMBDA_IT) LAMBDA_IT = 1; else LAMBDA_IT = LAMBDA_IT+1; end it = LAMBDA_IT; [worst, TMP] = calc_Alpha(TMP,ord,s1,s2,it); end otherwise TMP_it = TMP; ind = 1:size(TMP,1); ind(worst) = []; TMP_it(ind,:) = NaN; TMP_it(:,ind)