Abstract
Testing the parameters of two populations is important in inference statistics. This study extends this topic to fuzzy environments to widen the application, especially in manufacturing environments. The aim of this study is to implement tests of central tendency of two dependent populations with paired fuzzy sample differences. When the distribution of the population of differences is normal, the membership function of the fuzzy test statistic is constructed, and the fuzzy probability is calculated based on this membership function. Unlike classical tests, which provide only binary decisions, fuzzy probabilities can provide a degree of rejection of the null hypothesis. The proposed method reduces to the classical test method when crisp data are used. 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. Two examples are presented to elucidate the proposed methods. We can conclude that the proposed method can not only apply a randomized test to obtain the paired t test in the fuzzy sense, but can also use the signed distance ranking of fuzzy numbers to derive a sign test problem in the fuzzy sense.
Published Version
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