Arithmetic Operations on Fuzzy Numbers
Applies arithmetic operations using the extension principle and interval-based calculations.
## S4 method for signature 'numeric,FuzzyNumber' e1 + e2 # e2 + e1 ## S4 method for signature 'TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber' e1 + e2 ## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' e1 + e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,numeric' e1 + e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,FuzzyNumber' e1 + e2 # calls as.PiecewiseLinearFuzzyNumber() ## S4 method for signature 'numeric,FuzzyNumber' e1 - e2 # e2*(-1) + e1 ## S4 method for signature 'TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber' e1 - e2 ## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' e1 - e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,numeric' e1 - e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,FuzzyNumber' e1 - e2 # calls as.PiecewiseLinearFuzzyNumber() ## S4 method for signature 'FuzzyNumber,ANY' e1 - e2 # -e1 ## S4 method for signature 'numeric,FuzzyNumber' e1 * e2 # e2 * e1 ## S4 method for signature 'TrapezoidalFuzzyNumber,numeric' e1 * e2 ## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' e1 * e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,FuzzyNumber' e1 * e2 # calls as.PiecewiseLinearFuzzyNumber() ## S4 method for signature 'PiecewiseLinearFuzzyNumber,numeric' e1 * e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,numeric' e1 / e2 ## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' e1 / e2 ## S4 method for signature 'PiecewiseLinearFuzzyNumber,FuzzyNumber' e1 / e2 # calls as.PiecewiseLinearFuzzyNumber()
e1 |
a fuzzy number or single numeric value |
e2 |
a fuzzy number or single numeric value |
Implemented operators: +, -, *, /
for piecewise linear fuzzy numbers.
Also some versions may be applied on numeric values and
trapezoidal fuzzy numbers.
Note that according to the theory the class of PLFNs is not closed under the operations * and /. However, if you operate on a large number of knots, the results should be satisfactory.
Thanks to Jan Caha for suggestions on PLFN operations.
Returns a fuzzy number of the class PiecewiseLinearFuzzyNumber or TrapezoidalFuzzyNumber.
Other FuzzyNumber-method: FuzzyNumber-class,
FuzzyNumber, alphaInterval,
alphacut, ambiguity,
as.FuzzyNumber,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character, core,
distance, evaluate,
expectedInterval,
expectedValue,
integrateAlpha,
piecewiseLinearApproximation,
plot, show,
supp,
trapezoidalApproximation,
value, weightedExpectedValue,
width
Other PiecewiseLinearFuzzyNumber-method: PiecewiseLinearFuzzyNumber-class,
PiecewiseLinearFuzzyNumber,
^,PiecewiseLinearFuzzyNumber,numeric-method,
alphaInterval, arctan2,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
as.character,
expectedInterval, fapply,
maximum, minimum,
necessityExceedance,
necessityStrictExceedance,
necessityStrictUndervaluation,
necessityUndervaluation,
plot, possibilityExceedance,
possibilityStrictExceedance,
possibilityStrictUndervaluation,
possibilityUndervaluation
Other TrapezoidalFuzzyNumber-method: TrapezoidalFuzzyNumber-class,
TrapezoidalFuzzyNumber,
TriangularFuzzyNumber,
alphaInterval,
as.PiecewiseLinearFuzzyNumber,
as.PowerFuzzyNumber,
as.TrapezoidalFuzzyNumber,
expectedInterval, plot
Other extension_principle: ^,PiecewiseLinearFuzzyNumber,numeric-method,
fapply
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