Abstract
In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise.In this paper, we redefine some concepts about fuzzy hypotheses testing, and then we give the sequential probability ratio test for fuzzy hypotheses testing with fuzzy observations. Finally, we give some applied examples.
Highlights
Fuzzy set theory is a powerful and known tool for formulation and analysis of imprecise and subjective situations where exact analysis is either difficult or impossible
Some methods in descriptive statistics with vague data and some aspects of statistical inference is proposed in Kruse and Meyer (1987)
Because of our main purpose, we only consider and discuss fuzzy random variables associated with an ordinary random variable
Summary
Fuzzy set theory is a powerful and known tool for formulation and analysis of imprecise and subjective situations where exact analysis is either difficult or impossible. Some methods in descriptive statistics with vague data and some aspects of statistical inference is proposed in Kruse and Meyer (1987). Because of our main purpose (statistical inference about a parametric population with fuzzy data), we only consider and discuss fuzzy random variables associated with an ordinary random variable. Kruse and Meyer (1987), Taheri and Behboodian (2002) considered the problem of testing vague hypotheses in the presence of vague hypothesis. Up to now testing hypotheses with fuzzy data was considered by Casals et al (1986), and Son et al (1992).
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