Calculator.LR.FNs (version 1.3)

L: Introducing the form of L fuzzy number

Description

Considering the definition of LR fuzzy number in LR, if the left and the right shape functions of a LR fuzzy number are be equal (i.e., \( L(.) = R(.) \)), then LR fuzzy number is a L fuzzy number which denoted by \( (n, \alpha, \beta)L \). Function L introduce a total form for L fuzzy number to computer.

Usage

L(m, m_l, m_r)

Arguments

m

The core of L fuzzy number

m_l

The left spread of L fuzzy number

m_r

The right spread of L fuzzy number

Value

This function help to users to define any L fuzzy number after introducing the left shape function L. This function consider L fuzzy number L(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 0.5 for distinguish L fuzzy number from LR and RL 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 the left shape function of L fuzzy number
Left.fun  = function(x)  { (1-x^2)*(x>=0)}
A = L(20, 12, 10)
LRFN.plot(A, xlim=c(0,60), col=2, lwd=2)

## The function is currently defined as
function (m, m_l, m_r) 
{
    c(m, m_l, m_r, 0.5)
  }
# }