| Summary: | 博士 === 國立成功大學 === 工業與資訊管理學系碩博士班 === 93 === Statistical hypotheses testing has been widely applied to different areas for establishing a set of statistical rules to reject or accept a hypothesis. The existing statistical testing models are limited to crisp data. This research proposes a fuzzy data statistical testing model to proceed statistical tests with fuzzy data.
The idea is based on the α-cuts and extension principle to a fuzzy data statistical testing model to a family of crisp statistical testing model, which can be described by a pair of parametric programs, to find the lower and upper bounds of the efficiency measures at α level. From different levels α, the membership function of fuzzy test statistic can be constructed correspondingly. Based on these membership functions, we can derive the probability of rejecting null hypothesis or an alternative p-value, which is used to compare with the significant level to make a statistical decision. Since the value of fuzzy test statistic expressed by membership function is in the form of interval, more information is provided for management.
This research develops two approaches, a randomized test approach and an alternative p-value approach, to proceed statistical tests of mean for normal population with known and unknown population variance. The tests of central tendency of two dependent populations concerning paired fuzzy sample differences using the randomized test approach is also discussed in this thesis. Unlike classical tests, which provide only binary decisions, fuzzy decision, proposed by this research, can be used to show the possibility of rejecting or accepting the null hypothesis. When the distribution is non-normal, a signed distance method is used to determine the distance between two fuzzy numbers and to define ranking. After the fuzzy problem is defuzzified, the classical sign test is applied to determine whether the medians of two populations are equal. When the data are crisp, the proposed method reduces to the classical testing methods.
When data is in the form of linguistic and incomplete, tests of correlation coefficient between interview scores and academic scores from of candidates for admission to a college in Taiwan is to demonstrate the interpretation of test of correlation coefficient with fuzzy data. The correlation between those two scores does not exceed 80% and is insignificant. Finally, the tests of fuzzy data process capability index using the randomized test approach is discussed to judge whether a process meets the present quality requirement and runs under the desired quality condition. It is shown that the fuzzy data statistical testing model is an effective approach to analysis data and make decision under fuzzy environment.
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