Fuzzy sets approaches to statistical parametric and nonparametric tests

The parametric tests often require that the population distributions be normal or approximately so. Statistical methods that do not require the knowledge of the population distribution or its parameters are called nonparametric tests. In this article, first we review some industrial applications of fuzzy parametric tests. Then we present some new algorithms for fuzzy nonparametric tests, namely a fuzzy sign test and a fuzzy Wilcoxon signed-ranks test. Later, we further give fuzzy parametric tests, fuzzy nonparametric tests, and their numerical applications, and also provide a comparison study on crisp and fuzzy nonparametric tests. When the data are vague, the result of the fuzzy nonparametric tests may be different from that of the crisp nonparametric tests.