fnegation_yager {agop} | R Documentation |
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)
x |
numeric vector with elements in [0,1] |
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≤ y, then N(x)≥ 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.
Numeric vector of the same length as x
.
The i
th element of the resulting vector gives the result
of calculating N(x[i])
.
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