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In this paper, we study some properties of condition for fuzzy data, agrement index by ratio of area and the uniformly most powerful fuzzy test of hypothesis. Also, we suggest a confidence bound for uniformly most powerful fuzzy test. For illustration, we take the most powerful critical fuzzy region from exponential distribution by likelihood ratio and test the hypothesis of   distribution by agreement index.

We furnished some properties of fuzzy testing of independence for correlation in a bivariate normal distribution by agreement index. First we present some restriction of the fuzzy data, define fuzzy sample correlation coefficient and agreement index for testing hypothesis with acceptance or rejection degree. Also, we show that UMP unbiased fuzzy test and drawing conclusions the fuzzy test.

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