Testing statistical hypotheses for intuitionistic fuzzy data

Akbari, Mohammad Ghasem; Hesamian, Gholamreza

doi:10.1007/s00500-018-3590-2

Cited by 9 publications

(2 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They are generalizations of the classical tests, so that they are reduced to the classical tests if both the data and the parameters are crisp. Fuzzy hypothesis tests are also developed in [13][14][15] for cases in which the available data are fuzzy and in [16], where the authors propose fuzzy hypothesis testing for a proportion with crisp data as the exact generalized one-tailed hypergeometric test with fuzzy hypotheses. Fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion is presented in [17].…”

Section: Introductionmentioning

confidence: 99%

Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

Mylonas¹,

Papadopoulos²

2021

Algorithms

View full text Add to dashboard Cite

In this paper, we develop fuzzy, possibilistic hypothesis tests for testing crisp hypotheses for a distribution parameter from crisp data. In these tests, fuzzy statistics are used, which are produced by the possibility distribution of the estimated parameter, constructed by the known from crisp statistics confidence intervals. The results of these tests are in much better agreement with crisp statistics than the ones produced by the respective tests of a popular book on fuzzy statistics, which uses fuzzy critical values. We also present an error that we found in the implementation of the unbiased fuzzy estimator of the variance in this book, due to a poor interpretation of its mathematical content, which leads to disagreement of some fuzzy hypotheses tests with their respective crisp ones. Implementing correctly this estimator, we produce test statistics that achieve results in hypotheses tests that are in much better agreement with the results of the respective crisp ones.

show abstract

Section: Introductionmentioning

confidence: 99%

Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

Mylonas¹,

Papadopoulos²

2021

Algorithms

View full text Add to dashboard Cite

show abstract

“…Parchami et al [25] presented a minimax approach to the problem of fuzzy hypotheses while data are crisp. Akbari and Hesamian [26] suggested a degree-based criterion to compare the fuzzy p-value and a specific significance level for making the decision to accept the null hypothesis or not. Kahraman et al [27] developed intervalvalued intuitionistic fuzzy confidence intervals for population mean and differences in means of two populations.…”

Section: Introductionmentioning

confidence: 99%

Possibility Measure of Accepting Statistical Hypothesis

2020

View full text Add to dashboard Cite

Taking advantage of the possibility of fuzzy test statistic falling in the rejection region, a statistical hypothesis testing approach for fuzzy data is proposed in this study. In contrast to classical statistical testing, which yields a binary decision to reject or to accept a null hypothesis, the proposed approach is to determine the possibility of accepting a null hypothesis (or alternative hypothesis). When data are crisp, the proposed approach reduces to the classical hypothesis testing approach.

show abstract

Statistical inference on quantiles of two independent populations under uncertainty

Hesamian,

Chukhrova,

Johannssen

2023

Soft Comput

View full text Add to dashboard Cite

Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on $$\alpha $$ α -values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a specific significance level to decide whether the underlying fuzzy null hypothesis can be rejected or not. The effectiveness of the proposed two-sample test on quantiles is investigated via numerical examples.

show abstract

Testing statistical hypotheses for intuitionistic fuzzy data

Cited by 9 publications

References 46 publications

Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

Possibility Measure of Accepting Statistical Hypothesis

Statistical inference on quantiles of two independent populations under uncertainty

Contact Info

Product

Resources

About