tnorm_minimum {agop} | R Documentation |
Various t-norms. Each of these is a fuzzy logic generalization of the classical conjunction operation.
tnorm_minimum(x, y)
tnorm_product(x, y)
tnorm_lukasiewicz(x, y)
tnorm_drastic(x, y)
tnorm_fodor(x, y)
x |
numeric vector with elements in |
y |
numeric vector of the same length as |
A function T: [0,1]\times [0,1]\to [0,1]
is a t-norm if for all x,y,z\in [0,1]
it holds:
(a) T(x,y)=T(y,x)
;
(b) if y\le z
, then T(x,y)\le T(x,z)
;
(c) T(x,T(y,z))=T(T(x,y),z)
;
(d) T(x, 1)=x
.
The minimum t-norm is given by T_M(x,y)=min(x, y)
.
The product t-norm is given by T_P(x,y)=xy
.
The Lukasiewicz t-norm is given by T_L(x,y)=max(x+y-1,0)
.
The drastic t-norm is given by T_D(x,y)=0
iff
x,y\in [0,1)
, and min(x, y)
otherwise.
The Fodor t-norm is given by T_F(x,y)=0
iff x+y \le 1
, and min(x, y)
otherwise.
Numeric vector of the same length as x
and y
.
The i
th element of the resulting vector gives the result
of calculating T(x[i], y[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()
,
fnegation_yager()
,
tconorm_minimum()