Tests of fuzzy hypotheses based on linear correlation using small sample data with membership grades are presented which are tests of characteristics or attributes. The t-test statistic with respect to a fuzzy set / fuzzy sets are defined using the membership grades. Also, the rules for making decisions about the fuzzy hypotheses are provided. Further, the linguistic data examples are given for understanding the proposed testing procedures. The proposed tests of hypotheses can help decision makers to analyze a linear relation between two attributes on a population or between two populations on an attribute. © Research India Publications.