a. parchami

An approach is proposed to construct fuzzy confidence intervals for unknown parameters in statistical models. In this approach, a family of confidence intervals of the unknown crisp parameter has been considered. Such confidence intervals are used to obtain a fuzzy confidence interval for the parameter of interest. ‎The proposed approach benefits a wide range of confidence intervals to obtain a trapezoidal shaped fuzzy set of the parameter space as the fuzzy confidence interval for the parameter of interest. By using the resolution identity, it is shown that the constructed fuzzy confidence intervals are really fuzzy sets of the parameter space.Some numerical examples are provided to explain the approach in one-sided and two-sided fuzzy confidence intervals. ‎‎Moreover, ‎an‎‎‎ application in health sciences ‎‎‎is provided about the ‎‎‎‎recovery time of olfactory and gustatory dysfunctions for COVID-19 patients.

This paper presents two approaches for testing quality to make adecision based on the extended process capability indices. Common methodsin measuring quality of the manufactured product have widely focused on theprecise specification limits, but in this study the lower and upper specificationlimits are considered as non-precise/fuzzy sets. Based on  a general statistical approach using an extended process capability index, the purpose of this study is  estimating a critical value  to determine whether the process meets the customer requirements. Moreover, a simulation approach to analyze the manufacturing process capability has been suggested for testing quality based on fuzzy specifications by normal data. Meanwhile, this paper discusses howwell the Monte Carlo simulation approach can be used for non-normal data.Finally, the real application of the proposed methods is investigated in a realcase study.

Testing the capability of a productive process on the basis of the flexible fuzzy quality  using Yongting's index is proposed in this paper by the Monte Carlo simulation.The theoretical approach and detailed steps of an algorithm are given to simulate the critical-value-based and also p-value-based approaches to statistical testing fuzzy quality. Also, the probability of type textit{II} error of the quality test simulated by Monte Carlo  approach. Moreover, a real-world case study is provided to show the performance of the proposed algorithm for triangular and trapezoidal fuzzy qualities.

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis when explanatory variables are discrete and response variables are continues and independent from each other. The simplest type of ANOVA is one-way analysis of variance for comparison among means of several populations. In this paper, we extend one-way analysis of variance to a case where observed data are non-symmetric triangular or normal fuzzy observations rather than real numbers. Meanwhile, a case study on the car battery length-life is provided on the basis on the proposed method.

In testing hypotheses, we may confront with cases where data are recorded as non-precise (fuzzy) rather than crisp. In such situations, the classical methods of testing hypotheses are not capable and need to be generalized. In solving the problem of testing hypotheses based on fuzzy data, the fuzziness of the observed data leads to the fuzzy p-value. This paper has been focused to calculate fuzzy p-value based on fuzzy data using the extension principle. Also, considering that p-value method is the most widely used / popular approach for testing hypotheses among different sciences users, two fuzzy $p$-value-based case studies have been provided in this paper. The first case study is discussed on ″the fuzzy data from a speedometer camera" and the second is deliberate about ″the lifetime of produced batteries in a factory" and both of them have been solved by a novel approach considering other studies found in the literature.

This paper reviews and compares two R packages ``FPV" and ``Fuzzy.p.value".These packages are designed for testing hypotheses in a fuzzy environment using a fuzzy $p$-value based approach.In fact, the packages ``FPV" and ``Fuzzy.p.value" propose some useful functions for testing hypotheses when the data / hypotheses are fuzzy rather than crisp.The proposed methods and functions have been presented together with illustrative practical examples.