A Statistical Hypothesis Testing of Analysis of Variance for Two Way Classification in Fuzzy Environments

The Analysis of Variance (ANOVA) is the most popular technique for testing of significance. ANOVA for one way classification model is a series of observations distributed over the different levels at single factor and the two-way classification model is the set of observations distributed over different levels of two simultaneous factors. In real-life situations, most of the observations cannot be recorded or collected precisely. A fuzzy environment is the decision-making process in which the goals and the constraints, but not necessarily the system under control, are fuzzy in nature. The two-way classification model is the collection of observations of two simultaneous variables distributed over challenging levels without the h -level concept of Trapezoidal Fuzzy Numbers (TZFNs). In this paper a statistical hypothesis testing of ANOVA two way classification with fuzzy environments through an numerical examples.