FuzzyNumbers (version 0.4-7)

Arithmetic: Arithmetic Operations on Fuzzy Numbers

Description

Applies arithmetic operations using the extension principle and interval-based calculations.

Usage

# S4 method for numeric,FuzzyNumber
+(e1, e2) # e2 + e1
# S4 method for TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber
+(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber
+(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,numeric
+(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,FuzzyNumber
+(e1, e2) # calls as.PiecewiseLinearFuzzyNumber()
# S4 method for numeric,FuzzyNumber
-(e1, e2) # e2*(-1) + e1
# S4 method for TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber
-(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber
-(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,numeric
-(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,FuzzyNumber
-(e1, e2) # calls as.PiecewiseLinearFuzzyNumber()
# S4 method for FuzzyNumber,ANY
-(e1, e2) # -e1
# S4 method for numeric,FuzzyNumber
*(e1, e2) # e2 * e1
# S4 method for TrapezoidalFuzzyNumber,numeric
*(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber
*(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,FuzzyNumber
*(e1, e2) # calls as.PiecewiseLinearFuzzyNumber()
# S4 method for PiecewiseLinearFuzzyNumber,numeric
*(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,numeric
/(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber
/(e1, e2)
# S4 method for PiecewiseLinearFuzzyNumber,FuzzyNumber
/(e1, e2) # calls as.PiecewiseLinearFuzzyNumber()

Arguments

e1

a fuzzy number or single numeric value

e2

a fuzzy number or single numeric value

Value

Returns a fuzzy number of the class '>PiecewiseLinearFuzzyNumber or '>TrapezoidalFuzzyNumber.

Details

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.

See Also

Other FuzzyNumber-method: Extract, 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: Extract, 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()