Overcome the Sort Problem of Low Discrimination by Interval Fuzzy Number - Innovative Management in Information and Production - page 26

4.5 Fuzzy Kruskal-Wallis Test

Row A shows the first-type test using center value c of the fuzzy number; the results
of median analysis are not significantly different. Row B shows the results of using
Formula 2.1 to calculate the second-type test using the defuzzification value of the
fuzzy number value; the results of median analysis are not significantly different.
Row C shows the results of using Formula 2.2 to calculate the third-type test using
the defuzzification value of the interval length; the results of median analysis are
significantly different. Table 10 shows these results.

5 Conclusions

This study solved two research problems. The first is the problem of sorting scores
when discrimination is low or means are equal. The second is the problem of testing
nonparametric analysis using interval fuzzy scores. The defuzzification value of
the interval fuzzy scores solves these research problems. The novel interval fuzzy
score definition, Definition 2.1 , defines the interval fuzzy score as

.Defini-
tion 2.2 is used to conduct three-type defuzzification-sorting analysis. Therefore,
the results could solve the problem of sorting identical scores or scores with low
discrimination. The results could also solve admission-sorting problems for 12-year
compulsory education in Taiwan. The results could improve the efficiency of sorting
student scores.

( a , b )

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