This paper is concerned with fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion. Moreover, we differentiate between a test of significance and an alternative test to control the type I error or both error types simultaneously. In contrast to classical (non-)randomized hypothesis testing, fuzzy hypothesis testing provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. In particular, various types of hypotheses with user-specified membership functions can be formulated. Additionally, the proposed test methods are compared via a comprehensive case study, which demonstrates the high flexibility of fuzzy hypothesis testing in practical applications.

中文翻译：

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随机与非随机超几何假设检验与清晰和模糊的假设

本文在随机和非随机超几何检验的框架内对比例进行模糊假设检验。此外，我们区分显着性检验和替代检验以同时控制 I 类错误或两种错误类型。与经典（非）随机假设检验相比，模糊假设检验根据专家意见或用户优先级提供了对无差异区的额外渐进考虑。特别是，可以制定具有用户指定隶属函数的各种类型的假设。此外，通过综合案例研究对所提出的测试方法进行了比较，这证明了模糊假设检验在实际应用中的高度灵活性。