Necessity of strict undervaluation

Description

Determines value of necessity of e1<e2, the result is from range [0,1]. Value 0 indicates no fulfilment of the operator and 1 indicates complete fulfilment.

Usage

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## S4 method for signature 
## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber'
necessityStrictUndervaluation(e1, e2)

Arguments

e1

a PiecewiseLinearFuzzyNumber

e2

a PiecewiseLinearFuzzyNumber

Details

The detailed description of the operator and its definition is provided in article referenced below.

Value

Returns a value from range [0,1] indicating the necessity of exceedance of e2 by e1.

References

DUBOIS, Didier and PRADE, Henri, 1983, Ranking Fuzzy Numbers in the Setting of Possibility Theory. Information Sciences. 1983. Vol. 30, no. 3, p. 183–224.

See Also

Other PiecewiseLinearFuzzyNumber-method: *,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, *,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, *,PiecewiseLinearFuzzyNumber,numeric-method, *,TrapezoidalFuzzyNumber,numeric-method, *,numeric,FuzzyNumber-method, +,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, +,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, +,PiecewiseLinearFuzzyNumber,numeric-method, +,TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, +,numeric,FuzzyNumber-method, -,FuzzyNumber,ANY-method, -,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, -,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, -,PiecewiseLinearFuzzyNumber,numeric-method, -,TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, -,numeric,FuzzyNumber-method, /,PiecewiseLinearFuzzyNumber,FuzzyNumber-method, /,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, /,PiecewiseLinearFuzzyNumber,numeric-method, Arithmetic; PiecewiseLinearFuzzyNumber-class; PiecewiseLinearFuzzyNumber; ^,PiecewiseLinearFuzzyNumber,numeric-method; alphaInterval, alphaInterval,FuzzyNumber-method, alphaInterval,PiecewiseLinearFuzzyNumber-method, alphaInterval,PowerFuzzyNumber-method, alphaInterval,TrapezoidalFuzzyNumber-method; arctan2, arctan2,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; as.PiecewiseLinearFuzzyNumber, as.PiecewiseLinearFuzzyNumber,FuzzyNumber-method, as.PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.PiecewiseLinearFuzzyNumber,TrapezoidalFuzzyNumber-method, as.PiecewiseLinearFuzzyNumber,numeric-method; as.PowerFuzzyNumber, as.PowerFuzzyNumber,FuzzyNumber-method, as.PowerFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.PowerFuzzyNumber,PowerFuzzyNumber-method, as.PowerFuzzyNumber,TrapezoidalFuzzyNumber-method, as.PowerFuzzyNumber,numeric-method; as.TrapezoidalFuzzyNumber, as.TrapezoidalFuzzyNumber,FuzzyNumber-method, as.TrapezoidalFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.TrapezoidalFuzzyNumber,PowerFuzzyNumber-method, as.TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, as.TrapezoidalFuzzyNumber,numeric-method; as.character, as.character,FuzzyNumber-method, as.character,PiecewiseLinearFuzzyNumber-method, as.character,PowerFuzzyNumber-method, as.character,TrapezoidalFuzzyNumber-method; expectedInterval, expectedInterval,FuzzyNumber-method, expectedInterval,PiecewiseLinearFuzzyNumber-method, expectedInterval,PowerFuzzyNumber-method, expectedInterval,TrapezoidalFuzzyNumber-method; fapply, fapply,PiecewiseLinearFuzzyNumber,function-method; maximum, maximum,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; minimum, minimum,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; necessityExceedance, necessityExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; necessityStrictExceedance, necessityStrictExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; necessityUndervaluation, necessityUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; plot, plot,DiscontinuousFuzzyNumber,missing-method, plot,FuzzyNumber,missing-method, plot,PiecewiseLinearFuzzyNumber,missing-method, plot,TrapezoidalFuzzyNumber,missing-method; possibilityExceedance, possibilityExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityStrictExceedance, possibilityStrictExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityStrictUndervaluation, possibilityStrictUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityUndervaluation, possibilityUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method

Other comparison-operators: necessityExceedance, necessityExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; necessityStrictExceedance, necessityStrictExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; necessityUndervaluation, necessityUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityExceedance, possibilityExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityStrictExceedance, possibilityStrictExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityStrictUndervaluation, possibilityStrictUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method; possibilityUndervaluation, possibilityUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method

Examples

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a <- TriangularFuzzyNumber(0.2, 1.0, 2.8)
b <- TriangularFuzzyNumber(0, 1.8, 2.2)
a <- as.PiecewiseLinearFuzzyNumber(a, knot.n = 9)
b <- as.PiecewiseLinearFuzzyNumber(b, knot.n = 9)
necessityStrictUndervaluation(a,b)

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