Minimum of fuzzy nubmers
Determines minimum fuzzy number based on two inputs.
## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' minimum(e1, e2)
e1 |
a PiecewiseLinearFuzzyNumber |
e2 |
a PiecewiseLinearFuzzyNumber |
The resulting PiecewiseLinearFuzzyNumber is only an approximation of the result it might not be very precise for small number of knots (see examples).
Returns a PiecewiseLinearFuzzyNumber representing maximal value of the inputs.
KAUFMANN, A., GUPTA, M. M. (1985) Introduction to Fuzzy Arithmetic. New York : Van Nostrand Reinhold Company. ISBN 044230079.
Other min_max-operators: maximum
Other PiecewiseLinearFuzzyNumber-method: Arithmetic,
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
# 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)
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