Abstract
This paper discusses the problem of testing fuzzy and statistical hypotheses of the observed data are from a symmetric fuzzy environment. In this approach, many fuzzy tests statistics are obtained based on fuzzy data with varied forms of membership functions of fuzzy sets. To accept or reject the hypothesis of interest, a decision rule based on a new distance function to find the distance between symmetric fuzzy numbers with many forms of membership functions is proposed. The proposed method is employed to test hypotheses for mean and variance, as well as the difference between the means of a normal distribution and two normal distributions, with both known and unknown variances.
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