TY - JOUR ID - 70450 TI - Sign Test for Fuzzy Random Variables JO - Journal of Algorithms and Computation JA - JAC LA - en SN - 2476-2776 AU - Shams, Mehdi AU - Hesamian, Gholamreza AD - Department of Mathematical Sciences, University of Kashan, Isfahan, Iran. AD - Department of Statistics, Payame Noor University, Tehran, 19395-3697, Iran. Y1 - 2018 PY - 2018 VL - 50 IS - issue 2 SP - 121 EP - 139 KW - Sign test KW - fuzzy median KW - fuzzy sample median KW - fuzzy test statistic KW - credibility index KW - optimistic value KW - degree of belonging DO - 10.22059/jac.2018.70450 N2 - 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.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.A numerical example is provided to clarify the discussions made in this paper. UR - https://jac.ut.ac.ir/article_70450.html L1 - https://jac.ut.ac.ir/article_70450_0a2fe9c34dd4bab68198b0dde50a274c.pdf ER -