tconorm_minimum {agop} | R Documentation |
t-conorms
Description
Various t-conorms. Each of these is a fuzzy logic generalization of the classical alternative operation.
Usage
tconorm_minimum(x, y)
tconorm_product(x, y)
tconorm_lukasiewicz(x, y)
tconorm_drastic(x, y)
tconorm_fodor(x, y)
Arguments
x |
numeric vector with elements in |
y |
numeric vector of the same length as |
Details
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.
Value
Numeric vector of the same length as x
and y
.
The i
th element of the resulting vector gives the result
of calculating S(x[i], y[i])
.
References
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
See Also
Other fuzzy_logic:
fimplication_minimal()
,
fnegation_yager()
,
tnorm_minimum()