LR {Calculator.LR.FNs}R Documentation

Introducing the form of LR fuzzy number


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.


LR(m, m_l, m_r)



The core of LR fuzzy number


The left spread of LR fuzzy number


The right spread of LR fuzzy number


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


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).


# First introduce left and right shape functions of LR fuzzy number  = function(x)  { (1-x^2)*(x>=0)} = 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)

[Package Calculator.LR.FNs version 1.3 Index]