This paper deals with the problem of testing hypothesis when both the hypotheses and the available data are fuzzy. First, four different kinds of fuzzy hypotheses are defined. Then, a procedure is developed for constructing the fuzzy point estimation based on fuzzy data. Also, the concept of fuzzy test statistic is defined based on the α-cuts of the fuzzy null hypothesis and the α-cuts of the c...

Statistical hypothesis testing is very important for finding decisions in practical problems. Usually, the underlying data are assumed to be precise numbers, but it is much more realistic in general to consider fuzzy values which are non-precise numbers. In this case the test statistic will also yield a non-precise number. This article presents an approach for statistical testing at the basis o...

In this article, we propose totally new grey clustering method and fuzzy comprehensive evaluation method and accordingly, a Matlab toolbox for grey clustering statistic and fuzzy comprehensive evaluation is developed. As an illustrative example, we use the toolbox developed for carrying on an analysis of the test scores of the Grade 3 at the National Changhua Girls’ Senior High School, Taiwan. ...

In this paper, we consider a nonparametric Shewhart chart for fuzzy data. We utilize the fuzzy data without transforming them into a real-valued scalar (a representative value). Usually fuzzy data (described by fuzzy random variables) do not have a distributional model available, and also the size of the fuzzy sample data is small. Based on the bootstrap methodology, we design a nonparametric S...

Hypothesis testing is one of the most significant facets of statistical inference, which like other situations in the real world is definitely affected by uncertain conditions. The aim of this paper is to develop hypothesis testing based on likelihood ratio test in fuzzy environment, where it is supposed that both hypotheses under study and sample data are fuzzy. The main idea is to employ Zade...

For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized li...