Fuzzy.p.value (version 1.1)

Tr: Class of trapezoidal fuzzy numbers

Description

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 \(d\): $$ Tr(a,b,c,d)(x)=\left\{ \begin{array}{lcc} \frac{x-a}{b-a} &\ \ if & \ \ a < x \leq b \\ 1 &\ \ if & \ \ b < x \leq c \\ \frac{x-d}{c-d} &\ \ if & \ \ c < x \leq d \\ 0 &\ \ if & \ \ elsewhere \end{array} \right. $$

Usage

Tr(a, b, c, d)

Arguments

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.

Value

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

References

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.

Examples

# NOT RUN {
# Introducing the membership function of trapezoidal fuzzy number (for test statistics t)
t = Tr(2,4,6,9)

## The function is currently defined as
function (a, b, c, d) 
(TrapezoidalFuzzyNumber(a, b, c, d))
# }