# necessityUndervaluation: Necessity of undervaluation In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## 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

 ```1 2 3``` ```## S4 method for signature ## 'PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber' necessityUndervaluation(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.

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`; `necessityStrictUndervaluation`, `necessityStrictUndervaluation,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`; `necessityStrictUndervaluation`, `necessityStrictUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method`; `possibilityExceedance`, `possibilityExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method`; `possibilityStrictExceedance`, `possibilityStrictExceedance,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method`; `possibilityStrictUndervaluation`, `possibilityStrictUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method`; `possibilityUndervaluation`, `possibilityUndervaluation,PiecewiseLinearFuzzyNumber,PiecewiseLinearFuzzyNumber-method`
 ```1 2 3 4 5``` ```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) necessityUndervaluation(a,b) ```