Civil Engineering Reference
In-Depth Information
Tabl e 9
Class 1 and Class 3—fuzzy mood median test
Type
Overall median
Chi-Square
DF
P
A
By the center value
c
of the fuzzy number
75.00
32.00
1
0.000
B
Used Formula 2.1 to defuzzification value
75.86
32.00
7
0.000
C
Used Formula 2.2 to defuzzification value
0.862
32.00
7
0.000
Tabl e 10
Classes 1, 2, and 3—fuzzy Kruskal-Wallis test
N
Median
Ave rank
Z
Overall all
Overall rank
H
DF
P
A
8
75.00
12.5
0.00
24
12.5
0.00
2
1.00
8
75.00
12.5
0.00
8
75.00
12.5
0.00
B
8
75.86
12.5
0.00
24
12.5
0.00
2
1.00
8
75.64
12.5
0.00
8
75.90
12.5
0.00
C
8
0.8617
11.5
−
0
.
49
24
12.5
18.24
2
0.00
8
0.7428
5.5
−
3
.
43
8
0.9054
20.5
3.92
value c of the fuzzy number and uses Formula 2.1 to transform the second-type test
using the defuzzification value of the fuzzy number value. If the first- and second-
type information is the same, Formula 2.2 must be used to calculate the third-type
test using the defuzzification value of the interval length. By comparing the three
types, subtle differences become apparent. Tables
4
-
10
show these results. The last
row of the tables shows significant differences when comparing the third-type test.
4.3
Fuzzy Wilcoxon Rank-Sum Test
4.3.1
Class 1 and Class 2
Row A shows the first-type test using center value
c
of the fuzzy number; the results
of median analysis do not show significant differences. 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 do not show significant
differences. 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 showed significant differences. Table
4
shows these results.
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