Calculator.LR.FNs (version 1.3)

LR: 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.

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

# NOT RUN {
# 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)
  }
# }