Description Usage Arguments Value References Examples

Several linear functions are constructed in this package for easily inspiration to the fuzzy concepts *\ll approximately smaller \gg* , *\ll approximately bigger \gg* and *\ll approximately equal \gg*.
For example, function *Tr* is one of them which users can use it to construct the fuzzy concept *\ll approximately equal \gg* for fuzzy statistics or fuzzy hypotheses.
As presented bellow, the membership function of fuzzy set `Tr`

has four parameters *a*, *b*, *c* and *d*:

* Tr(a,b,c,d)(x)=≤ft\{
\begin{array}{lcc}
\frac{x-a}{b-a} &\ \ if & \ \ a < x ≤q b
\\
1 &\ \ if & \ \ b < x ≤q c
\\
\frac{x-d}{c-d} &\ \ if & \ \ c < x ≤q d
\\
0 &\ \ if & \ \ elsewhere
\end{array}
\right. *

1 |

`a` |
Considering the introduced above membership function, the first parameter is the first point of the support of trapezoidal fuzzy number. |

`b` |
The second parameter is the first point of the core of trapezoidal fuzzy number. |

`c` |
The third parameter is the end point of the core of trapezoidal fuzzy number. |

`d` |
The fourth parameter is the end point of the support of trapezoidal fuzzy number. |

This function easily introduce the membership function of a trapezoidal fuzzy number.

Parchami, A., Taheri, S. M., and Mashinchi, M. (2010). Fuzzy p-value in testing fuzzy hypotheses with crisp data. Statistical Papers 51: 209-226.

Parchami, A., Taheri, S. M., and Mashinchi, M. (2012). Testing fuzzy hypotheses based on vague observations: a p-value approach. Statistical Papers 53: 469-484.

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