LR {Calculator.LR.FNs} | R Documentation |

## Introducing the form of LR fuzzy number

### Description

Function `LR`

introduce a total form for LR fuzzy number.
Note that, if the membership function of fuzzy number `N`

is

```
N(x)=\left\{
\begin{array}{lcc}
L \left( \frac{n-x}{\alpha} \right) &\ \ if & \ \ x \leq n
\\
R \left( \frac{x-n}{\beta} \right) &\ \ if & \ \ x > n
\end{array}
\right.
```

where `L`

and `R`

are two non-increasing functions from ` R^+ \cup \{0\} `

to `[0,1]`

(say left and right shape function) and `L(0)=R(0)=1`

and also `\alpha,\beta>0`

;
then `N`

is named a LR fuzzy number and we denote it by ` N=(n, \alpha, \beta)LR `

in which `n`

is core and `\alpha`

and `\beta`

are left and right spreads of `N`

, respectively.

### Usage

```
LR(m, m_l, m_r)
```

### Arguments

`m` |
The core of LR fuzzy number |

`m_l` |
The left spread of LR fuzzy number |

`m_r` |
The right spread of LR fuzzy number |

### Value

This function help to users to define any LR fuzzy number after introducing the left shape and the right shape functions L and R. This function consider LR fuzzy number LR(m, m_l, m_r) as a vector with 4 elements. The first three elements are m, m_l and m_r respectively; and the fourth element is considerd equal to 0 for distinguish LR fuzzy number from RL and L fuzzy numbers.

### Author(s)

Abbas Parchami

### References

Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications. Academic Press (1980).

Taheri, S.M, Mashinchi, M., Introduction to Fuzzy Probability and Statistics. Shahid Bahonar University of Kerman Publications, In Persian (2009).

### Examples

```
# First introduce left and right shape functions of LR fuzzy number
Left.fun = function(x) { (1-x^2)*(x>=0)}
Right.fun = function(x) { (exp(-x))*(x>=0)}
A = LR(20, 12, 10)
LRFN.plot(A, xlim=c(0,60), col=1)
## The function is currently defined as
function (m, m_l, m_r)
{
c(m, m_l, m_r, 0)
}
```

*Calculator.LR.FNs*version 1.3 Index]