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An operator set in XFL3 is an object containing the mathematical functions that
are assigned to each fuzzy operator. Fuzzy operators can be binary (like the
T-norms and S-norms employed to represent linguistic variable connections,
implication, or rule aggregations), unary (like the C-norms or the operators
related with linguistic hedges), or can be associated with defuzzification
methods.
XFL3 defines the operator sets with the following format:
operatorset identifier {
operator assigned_function(parameter_list);
operator assigned_function(parameter_list);
........... }
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It is not required to specify all the operators. When one of them is not
defined, its default function is assumed. The following table shows the
operators (and their default functions) currently used in XFL3.
| Operator |
Type |
Default function |
| and |
binary |
xfl.min(a,b) |
| or |
binary |
xfl.max(a,b) |
| implication, imp |
binary |
xfl.min(a,b) |
| also |
binary |
xfl.max(a,b) |
| not |
unary |
xfl.not(a) |
| very, strongly |
unary |
xfl.square(a) |
| moreorless |
unary |
xfl.sqrt(a) |
| slightly |
unary |
xfl.parabola(a) |
| defuzzification, defuz |
defuzzification |
xfl.CenterOfArea |
The assigned functions are defined in external files which we name as packages.
The format to identify a function is "package.function".
operatorset systemop {
and xfl.min();
or xfl.max();
imp xfl.min();
strongly xfl.pow(3);
moreorless xfl.pow(0.4);
} |
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