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 |
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.
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()