Abstract
Buckley’s approach (Buckley (2004), (2005), (2006)) uses sets of confidence intervals by taking into consideration both of the uncertainty and impreciseness of concepts that produce triangular shaped fuzzy numbers for the estimator. This approach produces fuzzy test statistics and fuzzy critical values in hypothesis testing. In addition, the sample size is fixed for this test. When data comes sequentially, however, it is not suitable to study with a fixed sample size test. In such cases, sequential and group sequential tests are recommended. Unlike a sequential test, a group of sequential test provides substantial savings in sample and enables us to make decisions as early as possible. This intends paper to combine the benefits of group sequential test and Buckley's approach usingα-cuts. It attempts to show that usingα-cuts can be used within the group sequential tests. To illustrate the test more explicitly a numerical example is also given.
Highlights
Estimation of unknown parameters of statistical models or testing of statistical hypothesis in fuzzy environments are interesting subjects for different approaches
In Buckley’s approach, fuzzy test statistic is obtained by using more than one confidence interval as the α-cut of triangular shaped fuzzy number
Compared with each stage based on the critical value and test statistic, H0 is rejected in third stage
Summary
Estimation of unknown parameters of statistical models or testing of statistical hypothesis in fuzzy environments are interesting subjects for different approaches. Fixed sample size test is not useful where subjects enter the study sequentially. Wald [11] introduced a sequential probability ratio test (SPRT) which requires substantially fewer observations than a fixed sample size test. Several authors such as Torabi and Behboodian [12] have proposed fuzzy sequential probability ratio test. Torabi and Mirhosseini [14] introduced the SPRT for fuzzy hypotheses testing. Jamkhaneh and Gildeh [15] presented a new approach for SPRT based on fuzzy hypothesis
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