Description Usage Arguments Value Author(s) References Examples

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.

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`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 |

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).

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