Description Usage Arguments Details Value References See Also Examples
This method finds a piecewise linear approximation P(A)
of a given fuzzy number A by using the algorithm specified by the
method
parameter.
1 2 3 4 5 6 |
object |
a fuzzy number |
... |
further arguments passed to |
method |
character; one of: |
knot.n |
desired number of knots (if missing, then calculated from given
|
knot.alpha |
alpha-cuts at which knots will be positioned (defaults to equally distributed knots) |
verbose |
logical; should some technical details on the computations being performed be printed?
[only |
'method
' may be one of:
NearestEuclidean
: see (Coroianu, Gagolewski, Grzegorzewski, 2013 and 2014a);
uses numerical integration, see integrateAlpha
.
Slow for large knot.n
.
SupportCorePreserving
:
This method was proposed in (Coroianu et al., 2014b)
and is currently only available for knot.n==1
.
It is the L2-nearest piecewise linear approximation with constraints
core(A)==core(P(A)) and supp(A)==supp(P(A));
uses numerical integration.
Naive
:
We have core(A)==core(P(A)) and supp(A)==supp(P(A)) and the knots are
taken directly from the specified alpha cuts (linear interpolation).
Returns a PiecewiseLinearFuzzyNumber
object.
Coroianu L., Gagolewski M., Grzegorzewski P. (2013), Nearest Piecewise Linear Approximation of Fuzzy Numbers, Fuzzy Sets and Systems 233, pp. 26-51.
Coroianu L., Gagolewski M., Grzegorzewski P., Adabitabar Firozja M., Houlari T. (2014a), Piecewise linear approximation of fuzzy numbers preserving the support and core, In: Laurent A. et al. (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems, Part II (CCIS 443), Springer, pp. 244-254.
Coroianu L., Gagolewski M., Grzegorzewski P. (2014b), Nearest Piecewise Linear Approximation of Fuzzy Numbers - General Case, submitted for publication.
Other approximation:
trapezoidalApproximation()
Other FuzzyNumber-method:
Arithmetic
,
Extract
,
FuzzyNumber-class
,
FuzzyNumber
,
alphaInterval()
,
alphacut()
,
ambiguity()
,
as.FuzzyNumber()
,
as.PiecewiseLinearFuzzyNumber()
,
as.PowerFuzzyNumber()
,
as.TrapezoidalFuzzyNumber()
,
as.character()
,
core()
,
distance()
,
evaluate()
,
expectedInterval()
,
expectedValue()
,
integrateAlpha()
,
plot()
,
show()
,
supp()
,
trapezoidalApproximation()
,
value()
,
weightedExpectedValue()
,
width()
1 2 3 4 | (A <- FuzzyNumber(-1, 0, 1, 3,
lower=function(x) sqrt(x),upper=function(x) 1-sqrt(x)))
(PA <- piecewiseLinearApproximation(A, "NearestEuclidean",
knot.n=1, knot.alpha=0.2))
|
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