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Show that any $\lambda$ - cut relation of a fuzzy tolerance relation results in a crisp tolerance relation.
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teamques10
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Solution: Consider the fuzzy relation:
R = $ \left[ \begin{array} & 1& 0.8 & 0 & 0.1 & 0.2\\ 0.8&1&0.4&0&0.9\\ 0&0.4&1&0&0\\ 01&0&0&1&0.5\\ 0.2&0.9&0&0.5&1\\ \end{array} \right]$
Fuzzy tolerance relation is having the property of reflexivity, symmetry but not transitivity.
$M_R (x_1, x_2) = 0.8$ $M_R (x_2, x_3) = 0.4$
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