Table 1 The results of five different tests in Example 4
From: A Simple but Efficient Approach for Testing Fuzzy Hypotheses
Test | H 0(μ) | H 1(μ) | p 01 | p 10 | Accepted | CF |
|---|---|---|---|---|---|---|
number | hypothesis | |||||
1 | \(\left \{ \begin {array}{lr} \mu -3 \ \ & \ \ 3<\mu \leq 4 \\ 5-\mu \ \ & \ \ 4<\mu \leq 5 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | \(\left \{ \begin {array}{lr} \mu \ \ & \ \ 0<\mu \leq 1 \\ 2-\mu \ \ & \ \ 1<\mu \leq 2 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | 0.019 | 0.244 | \(\tilde {H}_{1}\) | 0.927 |
2 | \(\left \{ \begin {array}{lr} \mu -3 \ \ & \ \ 3<\mu \leq 4 \\ 5-\mu \ \ & \ \ 4<\mu \leq 5 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | \(\left \{ \begin {array}{lr} \mu +5 \ \ & \ \ -5<\mu \leq -4 \\ -3-\mu \ \ & \ \ -4<\mu \leq -3 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | 0.019 | ≃0 | \(\tilde {H}_{0}\) | 0.99 |
3 | \(\left \{ \begin {array}{lr} \mu -3 \ \ & \ \ 3<\mu \leq 4 \\ 5-\mu \ \ & \ \ 4<\mu \leq 5 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | \(\left \{ \begin {array}{lr} \frac {\mu +1}{2} \ \ & \ \ -1<\mu \leq 1 \\ \frac {3-\mu }{2} \ \ & \ \ 1<\mu \leq 3 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | 0.019 | 0.283 | \(\tilde {H}_{1}\) | 0.937 |
4 | \(\left \{ \begin {array}{lr} \frac {\mu -2}{2} \ \ & \ \ 2<\mu \leq 4 \\ \frac {6-\mu }{2} \ \ & \ \ 4<\mu \leq 6 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | \(\left \{ \begin {array}{lr} \frac {\mu +1}{2} \ \ & \ \ -1<\mu \leq 1 \\ \frac {3-\mu }{2} \ \ & \ \ 1<\mu \leq 3 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | 0.041 | 0.283 | \(\tilde {H}_{1}\) | 0.873 |
5 | \(\left \{ \begin {array}{lr} \frac {\mu +4}{8} \ \ & \ \ -4<\mu \leq 4 \\ 5-\mu \ \ & \ \ 4<\mu \leq 5 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | \(\left \{ \begin {array}{lr} \mu \ \ & \ \ -1<\mu \leq 1 \\ \frac {5-\mu }{4} \ \ & \ \ 1<\mu \leq 3 \\ 0 \ \ &\ \ o.w. \end {array} \right.\) | 0.527 | 0.452 | \(\tilde {H}_{0}\) | 0.538 |