frpro2nes.m

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

function l = frPro2Nes(lvec)

% l = frPro2Nes(lvec)
%
% From Probability to Necessity 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 probability distribution.
% The result in l will be a corresponding neccessity distribution.
% lvec has to be a row vector. 
% We assume that for N(A) - the neccessity of A, A is equal to a singleton or
% elementary event v_i. Therefor l(k) = N(v_i).
%
% 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);

%if (sum(lvec) > 1) | (sum(lvec) < 0.99), 
%  error('Sum(lvec) not equal to zero !') 
%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,
  dummy = lvec; % a vector with all elements except v(i)
  dummy(i) = 0;
  dummy = dummy(find(dummy));
  l(i) =  max((lvec(i) - max(dummy)),0);;
end;

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