# LR: Introducing the form of LR fuzzy number In Calculator.LR.FNs: Calculator for LR Fuzzy Numbers

## Description

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

N(x)=≤ft\{ \begin{array}{lcc} L ≤ft( \frac{n-x}{α} \right) &\ \ if & \ \ x ≤q n \\ R ≤ft( \frac{x-n}{β} \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 α,β>0; then N is named a LR fuzzy number and we denote it by N=(n, α, β)LR in which n is core and α and β are left and right spreads of N, respectively.

## Usage

 1 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.

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

  1 2 3 4 5 6 7 8 9 10 11 # 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) } 

### Example output

Attaching package: 'Calculator.LR.FNs'

The following object is masked from 'package:base':

sign

function (m, m_l, m_r)
{
c(m, m_l, m_r, 0)
}


Calculator.LR.FNs documentation built on May 2, 2019, 8:25 a.m.