frpos2pro.m

FISMAT accommodates different arithmetic operators, fuzzification and defuzzification algorithm, imp

function l = frPos2Pro(lvec)

% l = frPos2Pro(lvec)
%
% From Possibility to Probability conversion using a bijective transformation.
% Reference:
% Dubois and Prade: 'Unfair coins and neccessity measures'
% Fuzzy Sets and Systems 10 (1983) 15-20
%
% The elements in lvec represent a possibility distribution.
% The result in l will be a corresponding probability distribution.
% lvec has to be a row vector. 
% If max(lvec) ~= 1 (normalisation condition for poss. distr.) the set is 
% normalized by a mulitplying each element with 1/(max(lvec)).
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% 13-Oct-1995
% Last change: 13 Oct 1995

n=length(lvec);
l=zeros(1,n);
% Normalisation if necessary: 
if (max(lvec) > 1.00001) | (max(lvec) < 0.99),
  lvec = (1./max(lvec)) .* lvec;
end;

% It is necessary to rank the elements in lvec in decreasing order so that
% lvec(1)=1 :
[lvec,index] = sort(lvec); % gives the elements in ascending order.
lvec = fliplr(lvec);       % now in decreasing order.
index = fliplr(index);
lvec=[lvec,0]; % extension for the loop where lvec(n+1) is used.

for i=1:n,
  for k=i:n,
    l(i) = l(i) +  (1./k .* (lvec(k)-lvec(k+1)));
  end;
end;

l(index) = l; % restoring the order according to the original.