TwoStage Fuzzy Traffic Congestion Detector
4.1. First Step: ShortTerm Average Speed Prediction
To represent the wide range of data, we set n_{x}_{1} = n_{x}_{2} = n_{x}_{3} = 5 linguistic terms as:
$\mathrm{F}=\left\{FF,RFF,AF,CF,VCF\right\}$ and K =$\left\{VLD,LD,MD,HD,VHD\right\}$
The output variable is also classified as: V = $\left\{VS,S,A,F,VF\right\}$
Explanation of variables:

FF: Free Flow, RFF: Reasonably Free Flow, AF: Average Flow, CF: Congested Flow and VCF: Very Congested Flow

VLD: Very Low Density, LD: Low Density, MD: Medium Density, HD: High Density and VHD: Very High Density

VS: Very Slow, S: Slow, A: Average, F: Fast and VF: Very Fast
$$\mu LD(k)=\left\{\begin{array}{l}\frac{k7}{187},7\le k<18\\ \frac{30k}{3018},18\le k<30\\ 0,k<7ork\ge 30\end{array}\right.$$
$$\left(F\u2022F\left(f\right)\right)\Theta min\left(K\u2022K\left(k\right)\right)\to \left(A\u2022A(f,k)\right),$$
where the symbol $\u2022$ states the linguistic term IS, the symbol $\Theta min$ states the logic operator AND.

If density is ‘Very Low’ then average speed is ‘Average’.

If density is ‘Very Low’ then average speed is ‘Fast’.

If density is ‘Very Low’ then average speed is ‘Very Fast’.

If density is ‘High’ then average speed is ‘Slow’.

If density is ‘Very High’ then average speed is ‘Very Slow’.

If flow is ‘Free’ then average speed is ‘Average’.

If flow is ‘Free’ then average speed is ‘Fast’.

If flow is ‘Free’ then average speed is ‘Very Fast’.

If flow is ‘Reasonably Free’ then average speed is ‘Average’.

If flow is ‘Reasonably Free’ then average speed is ‘Fast’.

If flow is ‘Congested’ then average speed is ‘Fast’.

If flow is ‘Congested’ then average speed is ‘Average’.

If flow is ‘Congested’ then average speed is ‘Slow’.

If flow is ‘Very Congested’ then average speed is ‘Average’.

If density is ‘Very High’ then average speed is ‘Slow’.

If density is ‘Very High’ then average speed is ‘Average’.

If density is ‘High’ then average speed is ‘Very Slow’.

If density is ‘High’ then average speed is ‘Average’.

If flow is ‘Average’ then average speed is ‘Very Fast’.

If flow is ‘Average’ then average speed is ‘Fast’.

If flow is ‘Reasonably Free’ and density is ‘Very Low’ then average speed is ‘Very Fast’.

If flow is ‘Reasonably Free’ and density is ‘Low’ then average speed is ‘Fast’.

If flow is ‘Average’ and density is ‘Low’ then average speed is ‘Fast’.

If density is ‘Average’ and density is ‘Very Low’ then average speed is ‘Very Fast’.
µ_{F∩K} = MIN (µ(F), µ(K))
At this point, each IF–THEN rule refers to a fuzzy set with the corresponding belonging membership values, which must be accumulated into a single fuzzy set. The MAX operator is one of the most widely used operators for this process. After this aggregation operation, the fuzzy set must be defuzzified. In this study, we used the centroid method, since it is the most widely applied.
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