Description Usage Arguments Details Value References See Also
Various t-conorms. Each of these is a fuzzy logic generalization of the classical alternative operation.
1 2 3 4 5 6 7 8 9 | tconorm_minimum(x, y)
tconorm_product(x, y)
tconorm_lukasiewicz(x, y)
tconorm_drastic(x, y)
tconorm_fodor(x, y)
|
x |
numeric vector with elements in [0,1] |
y |
numeric vector of the same length as |
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≤ z, then S(x,y)≤ 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 ≥ 1, and max(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 S(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
,
tnorm_minimum
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