Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables

摘要: In this paper, a new method is proposed for developing two-sample Kolmogorov–Smirnov test the case when data are observations of fuzzy random variables, and hypotheses imprecise rather than crisp. approach, first notion variables introduced. Then, \(\alpha \)-pessimistic values transacted to extend usual test. To do this, concepts cumulative distribution function empirical defined. We also develop well-known large sample property classical function. addition, statistic extended variables. After that, computing so-called \(p\) value introduced evaluate interest. regard, applying an index called credibility degree, obtained crisp significance level compared. The result provides which leads some degrees accept or reject null hypothesis. Some numerical examples provided throughout paper clarifying discussions made in paper.