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Usually, the statistical estimators (or mathematical functions) are the base of scientific decision making. In applied situations, at least one of the parameters or variables of the decision function may be fuzzy valued, instead of real valued. In such vague situations, one way to perform the calculations is using extension principle approach which has a complex form. Recently, two software packages have been freely available to perform some facilities in calculation and computation based on fuzzy numbers. In other words, these two software packages have the role of the first calculator on fuzzy numbers. This paper discussed and compared two software packages “FuzzyNumbers” and “Calculator.LR.FNs” which were recently published on CRAN by Gagolewski and Parchami, respectively. These packages have the ability of installation on R software, and in fact they propose some useful instruments and functions to the users for drawing and easily using arithmetic operators on the set of fuzzy numbers. For the convenience of the readers, the proposed methods and functions have been presented with several numerical examples to help in better understanding.

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which the hypotheses of interest are imprecise. In this paper, we recall and redefine some concepts about testing fuzzy hypotheses and then we provide a minimax approach to the problem of testing fuzzy hypotheses by using crisp (non-fuzzy) data. We give some illustrative/numerical examples, by which we study the effect of fuzziness by using the power functions of minimax tests.

Testing one-way analysis of variance (ANOVA) is used for experimental data analysis in which there is a continuous response variable and a single independent classification variable. In this paper, we extend one-way ANOVA to a case where observed data are imprecise numbers rather than real numbers. Several fast computable formulas are calculated for symmetric triangular and normal fuzzy data. Similar to the classical testing ANOVA, the total observed variation in the response variable is explained as the sum of observed variation due to the effects of the classification variable and the observed variation due to random error. A real case is given to clarify the proposed method.

This paper deals with the problem of testing statistical hypotheses when both the hypotheses and data are fuzzy. To this end, we first introduce the concept of fuzzy p-value and then develop an approach for testing fuzzy hypotheses by comparing a fuzzy p-value and a fuzzy significance level. Numerical examples are provided to illustrate the approach for different cases.

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first introduce the notion of fuzzy p-value, by applying the extension principle and then present an approach for testing fuzzy hypotheses by comparing a fuzzy p-value and a fuzzy significance level, based on a comparison of two fuzzy sets. Numerical examples are also provided to illustrate the approach.