Testing Hypothesis Concerning Correlation Coefficient with Fuzzy Data

Testing hypothesis of correlation coefficient is important in inference statistics. The extension of the idea of correlation to fuzzy environments is of great interesting. The aim of this work is to elucidate the test of hypothesis concerning correlation coefficient with fuzzy data. The alpha-cuts of fuzzy sample correlation coefficient are first derived at various alpha-values. The membership function of the fuzzy test statistic is then constructed based on these alpha-cuts. The fuzzy probability of rejecting the null hypothesis is then determined using this membership function. For crisp data, this method reduces to the corresponding classical statistical method. Tests of correlation coefficient between interview scores and academic scores from a sample of 30 applicants for admission to a college are considered to demonstrate the interpretation of test of correlation coefficient with fuzzy data in real-world situations.