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Fuzzy logic was developed by Professor Zadeh at U.C. Berkeley (Zadeh, 1965). The Fuzzy logic algorithm can utilize imprecise or incomplete information to balance interests and maximize freeway throughput.

It can use incomplete or inaccurate data
Data collected from loop detectors can be misreported or inaccurate because of communication, hardware failures, or poor calibration. The fuzzy logic algorithm preprocesses the data rather than directly calculating the meter rate from the raw data – this method is better suited for imprecise data handling.

It can balance conflicting objectives
During periods of heavy congestion there are two conflicting objectives: reducing mainline congestion by restricting the passage of vehicles and reducing ramp queuing by increasing meter rates. Previous control algorithms fluctuated between these objectives because they use threshold activation. This means that they responded to existing problems instead of preventing them. Fuzzy logic provides various degrees of activation for more efficient control.

Does not require extensive system modeling
Many algorithms are overly dependent on the accuracy of a system model, which is highly susceptible to changing conditions, such as poor weather. By using congestion indicators the fuzzy logic algorithm can handle poor data, special events, construction, and inclement weather.

Maintenance and adjustment of control variables is simple
The ability to easily tune the fuzzy logic algorithm is valuable because performance objectives vary by location. Some ramps may require more aggressive metering to prevent secondary queuing, while other ramps may have the capacity to store vehicles.

How it works
The fuzzy logic algorithm involves three main steps:
 * 1) Fuzzification to convert quantitative inputs into natural language variables
 * 2) Rule evaluation to implement the control heuristics
 * 3) Defuzzification to map the qualitative rule outcomes to a numerical output.

Data Inputs
The Fuzzy Meter Equations supply the algorithm with information about:
 * Local occupancy
 * Local speed
 * Downstream occupancy
 * Downstream speed
 * Upstream occupancy (when local occupancy is unavailable)
 * Upstream speed (when local speed is unavailable)
 * Queue occupancy
 * Advanced queue occupancy

Fuzzification
The first step in the fuzzy logic algorithm is fuzzification which translates each numerical input into a set of fuzzy classes. In many algorithms values are classified on a trust/false basis, i.e. an input satisfies a condition or it does not. Fuzzy logic is able to determine a degree of trueness ranging between a value of 0 and 1.

In order to establish a degree of trueness input data is translated into a set of fuzzy classes, also known as linguistic variables. The fuzzy classes used are very small (VS), small (S), medium (M), big (B), and very big (VB). The trueness of each class can be thought of as a degree of likelihood or probability.

Rule Evaluation
After fuzzification the rule base is evaluated. The rules are a set of if-then statements that include which fuzzy class or metering is specified. The outcome is equal to the degree of activation of the rule. Each rule has a weight that reflects its relative importance within the rule base. Rule weights can be adjusted to balance performance objectives.

Defuzzification
The last step in the fuzzy logic algorithm is to produce a numerical meter rate given all of the rule outcomes. Just as the numerical inputs were translated into linguistic variables, so is the meter rate represented by the translation of fuzzy class linguistic variables to a numerical metering rate.

$$ \mbox{Meter Rate} = \frac{C_{VS}VS+C_SS+C_MM+C_BB+C_{VB}VB}{VS+S+M+B+VB}$$

$$C_{VS} =$$ Centroid of Very Small Meter Rate Fuzzy Class

$$C_S =$$ Centroid of Small Meter Rate Fuzzy Class

$$C_M =$$ Centroid of Medium Meter Rate Fuzzy Class

$$C_B =$$ Centroid of Big Meter Rate Fuzzy Class

$$V_{VB} =$$ Centroid of Very Big Meter Rate Fuzzy Class

$$VS, S, M, B, VB = $$ Meter Rate Fuzzy Class Weights

HOV Adjustment
The HOV adjustment is made to the metering rate to account of HOVs and violators. The HOV adjustment is the HOV passage volume scaled by the percentage adjustment that is specified for that lane.

Biblography

 * C. Taylor and D. Meldrum, 2000. "Evaluation of a Fuzzy Logic Ramp Metering Algorithm: A Comparative Study Between Three Ramp Metering Algorithms used in theGreater Seattle Area," WA-RD Technical Report to be published, Washington State Department of Transportation, National Technical Information Service.


 * C. Taylor and D. Meldrum, 2000. "A Programmer’s Guide to the Fuzzy Logic Ramp Metering Algorithm: Software Design, Integration, Testing, and Evaluation," WARD Technical Report to be published, Washington State Department of Transportation, National Technical Information Service.


 * C. Taylor and D. Meldrum, 1995. "Simulation Testing of a Fuzzy Neural Ramp Metering Algorithm," Final Technical Report.  Washington State Department of Transportation, National Technical Information Service, WA-RD 395.1.


 * L. Zadeh, 1965. "Fuzzy Sets," Information and Control 8, pp. 338-353.