PiecewiseLinearFuzzyNumber-class: S4 Class Representing a Piecewise Linear Fuzzy Number In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

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.

`PiecewiseLinearFuzzyNumber` for a convenient constructor, `as.PiecewiseLinearFuzzyNumber` for conversion of objects to this class, and `piecewiseLinearApproximation` for approximation routines.

Other PiecewiseLinearFuzzyNumber-method: `Arithmetic`, `Extract`, `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

 ```1 2``` ```showClass("PiecewiseLinearFuzzyNumber") showMethods(classes="PiecewiseLinearFuzzyNumber") ```

Example output

```Class "PiecewiseLinearFuzzyNumber" [package "FuzzyNumbers"]

Slots:

Name:      knot.n knot.alpha  knot.left knot.right         a1         a2
Class:    numeric    numeric    numeric    numeric    numeric    numeric

Name:          a3         a4      lower      upper       left      right
Class:    numeric    numeric   function   function   function   function

Extends: "FuzzyNumber"
Function: * (package base)
e1="PiecewiseLinearFuzzyNumber", e2="FuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="numeric"

Function: + (package base)
e1="PiecewiseLinearFuzzyNumber", e2="FuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="numeric"

Function: - (package base)
e1="PiecewiseLinearFuzzyNumber", e2="FuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="numeric"

Function: / (package base)
e1="PiecewiseLinearFuzzyNumber", e2="FuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"
e1="PiecewiseLinearFuzzyNumber", e2="numeric"

Function: [ (package base)
x="PiecewiseLinearFuzzyNumber", i="character"

Function: ^ (package base)
e1="PiecewiseLinearFuzzyNumber", e2="numeric"

Function: alphaInterval (package FuzzyNumbers)
object="PiecewiseLinearFuzzyNumber"

Function: arctan2 (package FuzzyNumbers)
y="PiecewiseLinearFuzzyNumber", x="PiecewiseLinearFuzzyNumber"

Function "arctan2e":
<not an S4 generic function>

Function "arctan2m":
<not an S4 generic function>
Function: as.PiecewiseLinearFuzzyNumber (package FuzzyNumbers)
object="PiecewiseLinearFuzzyNumber"

Function: as.PowerFuzzyNumber (package FuzzyNumbers)
object="PiecewiseLinearFuzzyNumber"

Function: as.TrapezoidalFuzzyNumber (package FuzzyNumbers)
object="PiecewiseLinearFuzzyNumber"

Function: as.character (package base)
x="PiecewiseLinearFuzzyNumber"

Function: expectedInterval (package FuzzyNumbers)
object="PiecewiseLinearFuzzyNumber"

Function: fapply (package FuzzyNumbers)
object="PiecewiseLinearFuzzyNumber", fun="function"

Function "fuzzyNumberUnification":
<not an S4 generic function>
Function: initialize (package methods)
.Object="PiecewiseLinearFuzzyNumber"

Function "intersectionY":
<not an S4 generic function>
Function: maximum (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: minimum (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: necessityExceedance (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: necessityStrictExceedance (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: necessityStrictUndervaluation (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: necessityUndervaluation (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: plot (package graphics)
x="PiecewiseLinearFuzzyNumber", y="missing"

Function: possibilityExceedance (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: possibilityStrictExceedance (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: possibilityStrictUndervaluation (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"

Function: possibilityUndervaluation (package FuzzyNumbers)
e1="PiecewiseLinearFuzzyNumber", e2="PiecewiseLinearFuzzyNumber"
```

FuzzyNumbers documentation built on Nov. 15, 2021, 5:09 p.m.