Hypotheses Tests Using Non-asymptotic Fuzzy Estimators and Fuzzy Critical Values

Abstract

In fuzzy hypothesis testing we use fuzzy test statistics produced by fuzzy estimators and fuzzy critical values. In this paper we use the non-asymptotic fuzzy estimators in fuzzy hypothesis testing. These are triangular shaped fuzzy numbers that generalize the fuzzy estimators based on confidence intervals in such a way that eliminates discontinuities and ensures compact support. Our approach is particularly useful in critical situations, where subtle fuzzy comparisons between almost equal statistical quantities have to be made. In such cases the hypotheses tests that use non-asymptotic fuzzy estimators give better results than the previous approaches, since they give us the possibility of partial rejection or not of.