A Combined Approach of Fuzzy Cognitive Maps and Fuzzy RuleBased Inference Supporting Freeway Traffic Control Strategies^{ †}
Abstract
:1. Introduction
2. Traffic Control Strategies
3. Fuzzy SystemBased Controllers in Transportation
3.1. The Case Study
3.2. The Fuzzy Inference System
 Identifying the acceptable numerical interval for involved linguistic parameters (Table 1 and Table 2). The input parameters are as follows:
 Flow, rate expressed in terms of vehicles per minute,$$q=\frac{n}{T}=\frac{n}{{\sum}_{i=0}^{n}i}$$
 Length of each segment of freeway in kilometers.
 Lane, the number of lanes of the given segment.
 2.
 Given that they capture and express the characteristics of the fuzzy set employed in the case study, triangular and trapezoidal membership functions are utilized to assess how directly the input and output parameters match. Equations (2) and (3) explain triangular and trapezoidal membership functions, respectively:
 3.
 Input–output links are constrained by ifthen fuzzy rules. A total of 75 rules were implemented, mainly founded on the percentile distribution of the data, and expert evaluation. These rules were applied via the MATLAB Fuzzy Rule Editor in order to create the inference and nonlinear surface model.
 4.
 Centroid of Area (COA) was utilized as the defuzzification operator to determine the corresponding action (i.e., in this study congestion level) to be conducted. The following denotes COA:$${Z}_{COA}=\frac{{\int}_{Z}{\mu}_{A}\left(z\right)zdz}{{\int}_{Z}{\mu}_{A}\left(z\right)dz}$$
3.3. The Fuzzy Cognitive Map
 Calculating the value of concept Ci at time t, wherein the value of Ci may represent the calculated density in the given segment [38]:
 Calculating the value of concept Ci at time t, wherein the value of Ci may represent the calculated density in the given segment [30]:
4. Results and Discussion
4.1. FIS in Congestion Level Prediction
4.2. FCM in Traffic Flow Simulation
5. Conclusions and Future Direction
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Input Variables  Numerical Ranges  Linguistic Term  Effect on Traffic Congestion 

Flow  1< F ≤ 300 vehicles  Very low  Very small impact 
200 ≤ F ≤600 vehicles  Low  Small impact  
500 ≤ F ≤ 1000 vehicles  Average  Steady state  
800 ≤ F ≤ 1400 vehicles  High  High increasing impact  
1200 ≤ F ≤ 2000 vehicles  Very High  Very high increasing impact  
Length  0.1 < Le ≤ 2 KM  Very Short  Very high impact 
1 ≤ Le≤ 6 KM  Short  High impact  
4≤ Le ≤ 12 KM  Average  Steady state  
8 ≤ Le ≤ 17 KM  Long  Reducing impact  
15 ≤ Le < 19 KM  Very Long  High reducing impact  
Lane  1 < La ≤ 2  Narrow  High increasing impact 
2 ≤ La ≤ 3  Average  Reducing impact  
3 ≤ La < 4  Wide  High reducing impact 
Output Variable  Numerical Ranges  Linguistic Term  Equivalence 

LOC  1< LOC ≤ 280 vehicles  Completely congestion free 

186 ≤ LOC ≤ 580 vehicles  Congestion free 
 
470 ≤ LOC ≤ 940 vehicles  Low 
 
750 ≤ LOC ≤ 1200 vehicles  Stable 
 
1130≤ LOC ≤ 1500 vehicles  Near Congestion 
 
1400 ≤ LOC ≤ 1650 vehicles  Congestion 
 
1600 ≤ LOC < 2000 vehicles  Severe Congestion 

Step  S3  S3a  S3b  S3c  S3d  S3e  S3f  S3g  S3h  S3i  S3j  S3k  S3l  S3m  S3n 

0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
1  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50  0.50 
2  0.67  0.71  0.73  0.65  0.71  0.74  0.73  0.74  0.64  0.68  0.80  0.70  0.76  0.66  0.67 
3  0.67  0.72  0.76  0.63  0.72  0.77  0.76  0.78  0.63  0.68  0.85  0.72  0.79  0.66  0.66 
4  0.67  0.72  0.77  0.63  0.72  0.78  0.77  0.79  0.63  0.67  0.85  0.73  0.80  0.67  0.65 
5  0.67  0.72  0.77  0.62  0.72  0.78  0.77  0.79  0.63  0.66  0.85  0.73  0.80  0.67  0.65 
6  0.67  0.72  0.77  0.62  0.72  0.78  0.77  0.79  0.63  0.66  0.85  0.73  0.80  0.67  0.65 
7  0.67  0.72  0.77  0.62  0.72  0.78  0.77  0.79  0.63  0.66  0.85  0.73  0.80  0.67  0.65 
Step  S3  S3a  S3b  S3c  S3d  S3e  S3f  S3g  S3h  S3i  S3j  S3k  S3l  S3m  S3n 

0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
1  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5  0.5 
2  0.67  0.71  0.73  0.65  0.71  0.74  0.74  0.74  0.62  0.68  0.80  0.70  0.76  0.66  0.67 
3  0.67  0.72  0.76  0.63  0.72  0.77  0.78  0.78  0.61  0.68  0.85  0.72  0.79  0.66  0.66 
4  0.67  0.72  0.77  0.63  0.72  0.77  0.79  0.79  0.61  0.67  0.83  0.73  0.80  0.67  0.65 
5  0.67  0.72  0.77  0.62  0.72  0.79  0.84  0.84  0.61  0.64  0.83  0.73  0.80  0.67  0.65 
6  0.67  0.72  0.77  0.62  0.72  0.79  0.84  0.94  0.63  0.62  0.82  0.73  0.80  0.67  0.65 
7  0.67  0.72  0.77  0.62  0.72  0.79  0.84  0.94  0.63  0.59  0.82  0.73  0.80  0.67  0.65 
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Amini, M.; Hatwagner, M.F.; Koczy, L.T. A Combined Approach of Fuzzy Cognitive Maps and Fuzzy RuleBased Inference Supporting Freeway Traffic Control Strategies. Mathematics 2022, 10, 4139. https://doi.org/10.3390/math10214139
Amini M, Hatwagner MF, Koczy LT. A Combined Approach of Fuzzy Cognitive Maps and Fuzzy RuleBased Inference Supporting Freeway Traffic Control Strategies. Mathematics. 2022; 10(21):4139. https://doi.org/10.3390/math10214139
Chicago/Turabian StyleAmini, Mehran, Miklos F. Hatwagner, and Laszlo T. Koczy. 2022. "A Combined Approach of Fuzzy Cognitive Maps and Fuzzy RuleBased Inference Supporting Freeway Traffic Control Strategies" Mathematics 10, no. 21: 4139. https://doi.org/10.3390/math10214139