Various t-conorms. Each of these is a fuzzy logic generalization of the classical alternative operation.
tconorm_minimum(x, y)tconorm_product(x, y)
tconorm_lukasiewicz(x, y)
tconorm_drastic(x, y)
tconorm_fodor(x, y)
Numeric vector of the same length as x and y.
The ith element of the resulting vector gives the result
of calculating S(x[i], y[i]).
numeric vector with elements in \([0,1]\)
numeric vector of the same length as x,
with elements in \([0,1]\)
A function \(S: [0,1]\times [0,1]\to [0,1]\) is a t-conorm if for all \(x,y,z\in [0,1]\) it holds: (a) \(S(x,y)=S(y,x)\); (b) if \(y\le z\), then \(S(x,y)\le S(x,z)\); (c) \(S(x,S(y,z))=S(S(x,y),z)\); (d) \(S(x, 0)=x\).
The minimum t-conorm is given by \(S_M(x,y)=max(x, y)\).
The product t-conorm is given by \(S_P(x,y)=x+y-xy\).
The Lukasiewicz t-conorm is given by \(S_L(x,y)=min(x+y,1)\).
The drastic t-conorm is given by \(S_D(x,y)=1\) iff \(x,y\in (0,1]\), and \(max(x, y)\) otherwise.
The Fodor t-conorm is given by \(S_F(x,y)=1\) iff \(x+y \ge 1\), and \(max(x, y)\) otherwise.
Klir G.J, Yuan B., Fuzzy sets and fuzzy logic. Theory and applications, Prentice Hall PTR, New Jersey, 1995.
Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7
Other fuzzy_logic:
fimplication_minimal(),
fnegation_yager(),
tnorm_minimum()