PiecewiseLinearFuzzyNumber-class {FuzzyNumbers} | R Documentation |

## S4 Class Representing a Piecewise Linear Fuzzy Number

### Description

A piecewise linear fuzzy number (PLFN) has side functions and alpha-cut bounds that linearly interpolate a given set of points (at fixed alpha-cuts).

### Details

If `knot.n`

is equal to 0 or all left and right knots lie on common lines,
then a Piecewise Linear Fuzzy Number reduces to a
TrapezoidalFuzzyNumber.
Note that, however, the
`TrapezoidalFuzzyNumber`

does not inherit from
`PiecewiseLinearFuzzyNumber`

for efficiency reasons.
To convert the former to the latter, call `as.PiecewiseLinearFuzzyNumber`

.

### Slots

`a1`

,`a2`

,`a3`

,`a4`

,`lower`

,`upper`

,`left`

,`right`

:-
Inherited from the

`FuzzyNumber`

class. `knot.n`

:number of knots, a single integer value, 0 for a trapezoidal fuzzy number

`knot.alpha`

:alpha-cuts, increasingly sorted vector of length

`knot.n`

with elements in [0,1]`knot.left`

:nondecreasingly sorted vector of length

`knot.n`

; defines left alpha-cut bounds at knots`knot.right`

:nondecreasingly sorted vector of length

`knot.n`

; defines right alpha-cut bounds at knots

### Extends

Class `FuzzyNumber`

, directly.

### See Also

`PiecewiseLinearFuzzyNumber`

for a convenient constructor,
`as.PiecewiseLinearFuzzyNumber`

for conversion of objects to this class,
and `piecewiseLinearApproximation`

for approximation routines.

Other PiecewiseLinearFuzzyNumber-method: `Arithmetic`

,
`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`

### Examples

showClass("PiecewiseLinearFuzzyNumber") showMethods(classes="PiecewiseLinearFuzzyNumber")

*FuzzyNumbers*version 0.4-1 Index]