Abstract
In this paper an approach is presented how to test fuzzily formulated hypotheses with crisp data. The quantitiesα andβ, the probabilities of the errors of type I and of type II, are suitably generalized and the concept of a best test is introduced. Within the framework of a one-parameter exponential distribution family the search for a best test is considerably reduced. Furthermore, it is shown under very weak conditions thatα andβ can simultaneously be diminished by increasing the sample size even in the case of testingH 0 against the omnibus alternativeH 1: notH 0, a result completely different from the case of crisp setsH 0 andH 1: notH 0.
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Arnold, B.F. An approach to fuzzy hypothesis testing. Metrika 44, 119–126 (1996). https://doi.org/10.1007/BF02614060
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DOI: https://doi.org/10.1007/BF02614060