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Testing fuzzy hypotheses with crisp data

Authors
Journal
Fuzzy Sets and Systems
0165-0114
Publisher
Elsevier
Publication Date
Volume
94
Issue
3
Identifiers
DOI: 10.1016/s0165-0114(96)00258-8
Keywords
  • Fuzzy Hypotheses
  • Gauß Tests
  • Sample Size

Abstract

Abstract In this paper an approach is presented how statistical tests originally constructed to examine crisp hypotheses can also be applied to fuzzily formulated hypotheses. In particular, criterions α and β are proposed generalizing the probabilities of the errors of type I and type II, respectively. The general approach is applied to one- and two-sided Gauß tests. Here, diagrams are given to determine the critical values in the most popular cases of α = 0.01 and α = 0.05. If, in addition, the value of β is fixed in advance the sample size of a one- or two-sided Gauß test can be obtained using supplementary graphs.

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