Information Technology Reference
In-Depth Information
Two correlation matrices were developed for both weekday and weekend to define
the relationship between the input and output variables (Table 3) in the fuzzy infer
ence system.
It is to be noted that some of the correlation values is showing unexpected signs
(e.g. V/C ratio to 85
th
percentile speed shows positive relation). This is because of Site
2 (a local road), which has very low 85
th
percentile speed (low posted speed limit of
40 km/hr) and very low traffic volume. Including the data of this particular road seg-
ment in calculating the correlation values affects the overall results, particularly be-
cause of the limited data (only four segments). Site 2 data were kept for calculating
the correlation values to have representation of both road categories in the devised
FLM, keeping in mind that increasing the sample road segments may result in better
correlation values.
The used operator type for generating the fuzzy rules has been the 'MIN-MAX'.
The 'MIN-MAX' method tests the magnitude of each rule and selects the highest one.
The fuzzy composition eventually combines the different rules to one conclusion.
The 'BSUM' (Bounded Sum) method was used as it evaluates all rules. A total of 729
rules were generated for both weekday and weekend models. Table 4 shows six rules
as an example with the final adjusted DoS's after the neuro-fuzzy training. Detail of
the neuro-fuzzy training will be discussed later.
Table 4.
Examples of (IF-THEN) rules
IF
THEN
Length
IntLnks
PedCros
VCRat
PedVol
PostSp
DoS
SpEF
low
low
low
low
low
low
0.90
med.
low
low
low
low
med.
low
1.00
med.
low
low
low
low
high
low
1.00
med.
low
low
low
med.
low
low
1.00
low
low
low
low
med.
med.
low
0.90
med.
low
low
low
med.
high
low
0.90
med.
The bold row indicates that for a road segment with low length, low number of in-
tersecting links, low number of pedestrian crossings, medium hourly traffic volume,
medium hourly pedestrian volume and low posted speed limit, the estimated 85
th
per-
centile speed is medium and the strength for this rule (DoS) is 0.90.
3.1.3
Defuzzification
The results of the inference process are the linguistic terms describing the 85
th
percen-
tile speed. As mentioned above, five linguistic terms were used for the output results-
very low through very high 85
th
percentile speed). In the defuzzification process, all
output linguistic terms are transformed into crisp numeric values. This is done by
aggregating (combining) the results of the inference process and then by computing
the fuzzy centroid of the combined area. The 'Center-of-Maximum (CoM) method
[22] is used for estimating the output numeric value, Y, as follows:
