| minimum {FuzzyNumbers} | R Documentation |
Minimum of fuzzy nubmers
Description
Determines minimum fuzzy number based on two inputs.
Usage
## S4 method for signature
## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber'
minimum(e1, e2)
Arguments
e1 |
a PiecewiseLinearFuzzyNumber |
e2 |
a PiecewiseLinearFuzzyNumber |
Details
The resulting PiecewiseLinearFuzzyNumber is only an approximation of the result it might not be very precise for small number of knots (see examples).
Value
Returns a PiecewiseLinearFuzzyNumber representing maximal value of the inputs.
References
KAUFMANN, A., GUPTA, M. M. (1985) Introduction to Fuzzy Arithmetic. New York : Van Nostrand Reinhold Company. ISBN 044230079.
See Also
Other min_max-operators:
maximum()
Other PiecewiseLinearFuzzyNumber-method:
Arithmetic,
Extract,
PiecewiseLinearFuzzyNumber-class,
PiecewiseLinearFuzzyNumber,
^,PiecewiseLinearFuzzyNumber,numeric-method,
alphaInterval(),
arctan2(),
as.PiecewiseLinearFuzzyNumber(),
as.PowerFuzzyNumber(),
as.TrapezoidalFuzzyNumber(),
as.character(),
expectedInterval(),
fapply(),
maximum(),
necessityExceedance(),
necessityStrictExceedance(),
necessityStrictUndervaluation(),
necessityUndervaluation(),
plot(),
possibilityExceedance(),
possibilityStrictExceedance(),
possibilityStrictUndervaluation(),
possibilityUndervaluation()
Examples
# example with low number of knots, showing the approximate nature
# of the result
x = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-4.8, -3 , -1.5))
y = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-5.5, -2.5, -1.1))
minFN = minimum(x,y)
min = min(alphacut(x,0)[1],alphacut(y,0)[1])
max = max(alphacut(x,0)[2],alphacut(y,0)[2])
plot(x, col="red", xlim=c(min,max))
plot(y, col="blue", add=TRUE)
plot(minFN, col="green", add=TRUE)
# example with high number of knots, that does not suffer
# from the approximate nature of the result
x = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-4.8, -3 , -1.5), knot.n = 9)
y = as.PiecewiseLinearFuzzyNumber(TriangularFuzzyNumber(-5.5, -2.5, -1.1), knot.n = 9)
minFN = minimum(x,y)
min = min(alphacut(x,0)[1],alphacut(y,0)[1])
max = max(alphacut(x,0)[2],alphacut(y,0)[2])
plot(x, col="red", xlim=c(min,max))
plot(y, col="blue", add=TRUE)
plot(minFN, col="green", add=TRUE)