fuz_and.m

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

function f = fuz_and(method,ua,ub)

% f=fuz_and(method,ua,ub)
%
% Intersection (logical AND) of two fuzzy sets ua and ub.
%
% 'method' determines the operator types:
% 'min'    : Minimum operator.                  uc=min(ua;ub).
% 'max'    : Bounded-difference t1.             uc=max(0;ua+ub-1).
% 'pro'    : Produkt op. / Algebraic-produkt t2.uc=ua*ub.
% 
% The Minimum operator has the following characteristics:
%
% -Commutativity : op(ua,ub) = op(ub,ua).
% -Associativity : op(ua,ub,uc) = op(op(ua,ub),uc)
% -A smaller value of ua can not be compensated by a larger value of ub.
% -It is "pessimistic", it chooses always the smaller value.
% -It is a member of the triangular-norm class (t-norms), which are used for
%  the modelling of the intersection between two Fuzzy-sets.
%  
% For both sets ua,ub the same universe of discourse x is assumed.
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% 24-Feb-1994
 
[m,resx]=size(ua);
if m==4                        % Sets in compact trapeziodal form.
  resx=200;                    % Convert them in the appripriate form.
  [ua,ub]=fuz_conv(ua,ub,resx);
end;
% Determine 'method'. Check first three letters.
if all(method=='min')          % Minimum operator
  f=min(ua,ub);
elseif all(method=='max')      % Bounded difference t1.
  f=max(zeros(1,resx),(ua+ub-ones(1,resx)));
elseif all(method=='pro')      % Product operator / Algebraic-product t2.
  f=ua.*ub;
end;