Abstract
In statistical inference hypotheses related to different kinds of phenomena are formulated, and then data are collected and analyzed, which either confirm or falsify these hypotheses. Considering traditional statistics, in the underlying models hypotheses and sample data should be well defined. However, these models are often inadequate with regard to real-life problems, as theoretical specifications and observed information are frequently imprecise, vague, incomplete, qualitative, linguistic or noisy. To relax this rigidity, numerous researchers have proposed modifications and extensions of statistical inference approaches with the help of concepts of fuzzy statistics. In the meantime there are many papers on the topic of hypothesis testing in fuzzy environments, especially based on fuzzy hypotheses and/or by using fuzzy data. In order to structure this variety of contributions, proposals and applications, we give a comprehensive systematic review in this paper and offer a bibliography on fuzzy hypothesis testing. The paper seeks to consolidate the topic of fuzzy hypothesis testing with the purpose of supporting new researchers in this field and highlighting potential directions for future research.
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