For fuzzy numbers the equality of X*X == X^2 does not hold.
X*X == X^2
# S4 method for PiecewiseLinearFuzzyNumber,numeric ^(e1, e2)
a PiecewiseLinearFuzzyNumber
numeric (if it is not integer it will be converted by function as.integer())
Returns a fuzzy number of the class '>PiecewiseLinearFuzzyNumber indicating e1^e2.
e1^e2
This function calculates integer power of a PiecewiseLinearFuzzyNumber according to the reference below.
KAUFMANN, A., GUPTA, M. M. (1985) Introduction to Fuzzy Arithmetic. New York : Van Nostrand Reinhold Company. ISBN 044230079.
Other extension_principle: Arithmetic, fapply
Arithmetic
fapply
Other PiecewiseLinearFuzzyNumber-method: Arithmetic, PiecewiseLinearFuzzyNumber-class, PiecewiseLinearFuzzyNumber, alphaInterval, arctan2, as.PiecewiseLinearFuzzyNumber, as.PowerFuzzyNumber, as.TrapezoidalFuzzyNumber, as.character, expectedInterval, fapply, maximum, minimum, necessityExceedance, necessityStrictExceedance, necessityStrictUndervaluation, necessityUndervaluation, plot, possibilityExceedance, possibilityStrictExceedance, possibilityStrictUndervaluation, possibilityUndervaluation
PiecewiseLinearFuzzyNumber-class
PiecewiseLinearFuzzyNumber
alphaInterval
arctan2
as.PiecewiseLinearFuzzyNumber
as.PowerFuzzyNumber
as.TrapezoidalFuzzyNumber
as.character
expectedInterval
maximum
minimum
necessityExceedance
necessityStrictExceedance
necessityStrictUndervaluation
necessityUndervaluation
plot
possibilityExceedance
possibilityStrictExceedance
possibilityStrictUndervaluation
possibilityUndervaluation
# NOT RUN { x = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-2, 1, 9), knot.n = 2) x^2 x^3 # }
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