Fuzzy p value pdf

Buckley JJ Fuzzy statistics: hypothesis testing. Soft Comput 9: — Casals MR Bayesian testing of fuzzy parametric hypotheses from fuzzy information. Oper Res — Fuzzy Sets Syst 1— Dubois D, Prade H Possibility theory. Plenum Press, New York. Filzmoser P, Viertl R Testing hypotheses with fuzzy data: the fuzzy p -value. Metrika 21— Stat Sci 20 4 : — Holena M A fuzzy logic generalization of a data mining approach.

Neural Netw World — Google Scholar. Holena M Fuzzy hypotheses testing in a framework of fuzzy logic. Knight K Mathematical statistics. Lehmann EL Testing statistical hypotheses, 2nd edn. Wiley, London. Neyman J, Pearson ES The theory of statistical hypotheses in relation to probabilities a priori. Proc Camb Phil Soc — Article Google Scholar.

Metrika 3— Fuzzy Sets Syst 39— In Examples 4 and 6 we consider one-sided tests, and in Examples 5 and 7 we consider two-sided tests. Also, in Example 6 the test statistic has a discrete distribution, but others have continuous distributions. Note that all the calculations and plots in this section have been carried out using Maple software.

The programs are available upon request. Also one can see the results of Example 4 for several fuzzy hypotheses in Table 1, see Fig. The results for several fuzzy hypotheses are shown in Table 2. This is similar to the behavior of the ordinary p-value for testing crisp hypotheses see Berger and Sellke Remark 8 With increasing fuzziness of the null hypothesis in case c , the no-decision region increases.

On the other hand, this region is deleted in usual crisp hypotheses testing. Example 6 The manager of a factory has reinstalled a new system to upgrade the security of his personnel. A study shows that there occurred 27 accidents during the past year.

After installation of the new system the manager wants to test if the average of the monthly accidents is at least approximately 3. The 12 family of joint p. We test the above fuzzy hypotheses at the fuzzy significance levels approximately 0. In this case, we accept H level 0. The fam- ily of joint p.

One can see the results of Example 7 in Table 4, for several fuzzy hypotheses. Hence, we reject H degree of rejection one, at significance level 0. In such a case, we can express the terms: approximately equal to, away from, … by fuzzy sets, and then try to solve the related problem of testing. On the other hand, in testing hypotheses problems when the hypotheses are fuzzy rather than crisp, the p -value should be a fuzzy set as well. This fuzzification is done by extension principle approach.

If the p-value is fuzzy, it is natural to introduce a fuzzy significance level. Therefore, the comparison of the fuzzy p-value and the fuzzy significance level are discussed. Numerical examples are given to illustrate the performance of the method. Further research is needed to cover the situation where both hypotheses and observations are fuzzy.

We hope to discuss this topic in the future. Acknowledgments The authors thank the referees and Professor M. Tata for their constructive sugges- tions and comments. The first and third authors are partially supported by the grant No. References Arnold BF An approach to fuzzy hypothesis testing. Metrika — Arnold BF Testing fuzzy hypotheses with crisp data.

Stat Sci 20 4 — Holena M A fuzzy logic generalization of a data mining approach. In: Gupta MM et al. Inf Control — Related Papers. Testing Statistical Hypotheses in Fuzzy Environment. By Adel Mohammadpour. Filzmoser, P. Testing hypotheses with fuzzy data: The fuzzy p -value. Metrika 59, 21—29 Download citation. Issue Date : February Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article.

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