Overcome the Sort Problem of Low Discrimination by Interval Fuzzy Number - Innovative Management in Information and Production - page 20

3 Research Method

3.1 Study Flow Chart

Figure 1 is a flow chart of the steps followed by the study.

3.2 Software

MINITAB16.0 software was used to statistically analyze the questionnaire using
nonparametric analysis. Nonparametric analysis was used because the sample was
not normally distributed. Because sample 8 was small, nonparametric analysis was
better suited to this situation ( Harloff 2011 ; Sun and Wu 2007 ).

4 Empirical Study

Example 4.1. A 12-year compulsory education exists in Taiwan. Students apply for
high school using their junior high school accounting math scores. Several students
achieve the same math scores, which presents sorting problems.

4.1 Comparing Three Classes with the Same Means

For example, if there are three classes (1, 2, and 3) with first and second mean math
scores of 75, how can we compare the three class scores? This study uses the novel
model to compare the scores to produce an effective distribution analysis for the
three classes. This solves the comparative difficulty of identical means. Tables 1 - 3
show the results for classes 1, 2, and 3, respectively.

4.2 Fuzzy Nonparametric Analysis

This section focuses on nonparametric analysis. The interval fuzzy number was
transformed to the defuzzification value. A fuzzy Wilcoxon rank-sum test was
conducted to compare class-medians. Tables 4 - 6 show these results. A fuzzy mood
median test was conducted to compare variance between classes. These results are
showninTables 7 - 9 . A fuzzy Kruskal-Wallis test was conducted to calculate and
compare variance among the three classes. Table 10 shows these results. Conducting
a nonparametric fuzzy test produces three types of data. The first-type tests center