Sign Test for Fuzzy Random Variables

Abstract

This paper extends the sign test to the case where data are observations of fuzzy random variables, and the hypotheses are imprecise rather than crisp. In this approach, first a new notion of fuzzy random variables is introduced. Then, the $alpha$-level sets of the imprecise observations are transacted to extend the usual method of sign test. To do this, the concepts of fuzzy median and fuzzy sample median are defined.<br />We also develop a well-known large sample property of the classical sample median. In addition, the test statistic is extended for investigating fuzzy hypothesis. After that, applying an index called credibility degree, the degree that the observed fuzzy test statistics belongs to the critical region is evaluated. The result provides a fuzzy test function which leads to some degrees to accept or to reject the fuzzy null hypothesis.<br />A numerical example is provided to clarify the discussions made in this paper.