Various fuzzy negations. Each of these is a fuzzy logic generalization of the classical negation operation.
fnegation_yager(x)fnegation_classic(x)
fnegation_minimal(x)
fnegation_maximal(x)
numeric vector with elements in \([0,1]\)
Numeric vector of the same length as x.
The ith element of the resulting vector gives the result
of calculating N(x[i]).
A function \(N: [0,1]\to [0,1]\) is a fuzzy implication if for all \(x,y\in [0,1]\) it holds: (a) if \(x\le y\), then \(N(x)\ge N(y)\); (b) \(N(1)=0\); (c) \(N(0)=1\).
The classic fuzzy negation is given by \(N_C(x)=1-x\).
The Yager fuzzy negation is given by \(N_Y(x)=sqrt(1-x^2)\).
The minimal fuzzy negation is given by \(N_0(x,y)=1\) iff \(x=0\), and \(0\) otherwise.
The maximal fuzzy negation is given by \(N_1(x,y)=1\) iff \(x<1\), and \(0\) 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,
tconorm_minimum,
tnorm_minimum