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The 'L-shape' membership function (MBF) was used for all variables. The MBFs
were generated using the “Compute MBF” fuzzification method. Figure 3 shows the
MBF for the Hourly Pedestrian Volume input variable for weekday. For this particu-
lar variable, the ranges of linguistic terms were set as (0, 92), (42.465, 138) and (92,
184) for the low, medium and high terms, respectively. The possibility that a numeric
level belongs to a linguistic term's range is denoted by the membership degree, µ (Y
axis in Figure 3). A µ of 0.0 indicates zero possibility, while µ of 1.0 indicates full
membership.
Fig. 3. Membership function for 'hourly pedestrian volume' input variable
3 . 1.2 Fuzzy Inference (Knowledge Base- 'IF-THEN' Logics)
The rules (IF-THEN logics) were generated to describe the logical relationship be-
tween the input variables (IF part) and the output variable (THEN part). The degree of
support (DoS) was used to weigh each rule according to its importance. A 'DoS' val-
ue of '0' means non-valid rules. Initially, all the DoS's were set to a fixed value of
'1'. The IF-THEN rules were formed exhaustively based on the correlation of the
input and output variables considering all possible combinations of input and output
terms. The neuro-fuzzy training capability was activated in later stage to eliminate
non-valid rules (the ones with DoS approaching zero value).
Table 3. Correlation values between input and output variables for both weekday and weekend
85 th percentile speed
Weekday
Weekend
Length
0.87
0.82
Number
of
access
0.15
0.11
points/intersecting links
Number of pedestrian crossings
-0.64
-0.35
Volume to capacity (V/C) ratio
0.27
0.08
Hourly pedestrian volume
-0.84
-0.57
Posted speed limit
0.77
0.53
 
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