Bad Weather Driving

The following fuzzy cognitive map is taken from the book Fuzzy Thinking by Bart Kosko (Flamingo, 1994). According to the author, the fuzzy map shows how bad weather can affect how fast you drive on a California freeway in the daytime.

The fuzzy conginitive map for this system is represented in the figure below.

In this fuzzy map the causal relationships between factors have word weights like "usually" and "a little". The type of relationship is indicated with the symbols "+" and "-".

1. Loading the fuzzy cognitive map in the applet

The Bad Weather Driving fuzzy cognitive map has been stored in the applet. To load it, click the Load System button, select the system in the list of the popup window and click OK.

The factors of the system appear in the list of factors in the main window of the applet. The levels of all the factors have been set at 50. The causal relationships between factors are as indicated in the figure above. The intensities of effect reflect the word weights that Bart Kosko has included in his fuzzy cognitive map. I had to translate the word weights to numerical values from 0 to 100. I have used the following correspondences:

The meaning of words is rather subjective. Therefore, another person (or I in a different day or a different mood) may come up with a different set of correspondences. If you wish to use different values you can edit the factors by selecting them in the list of the applet and then clicking the Edit button.

2. Effect of weather on driving speed

We want to use the fuzzy cognitive map to see how bad or good weather affects the driving speed, the patrol frequency, etc. First we run simulations for low values of bad weather (that is, good weather). We can try bad weather levels of 20, 30 and 40. The simulations reach convergence after 10, 12 and 13 steps, respectively. The final states reached are reported in the following table.

The results indicate that with good weather the freeway tends not to be congested, the car accidents are few and the driving speed is high (too high perhaps!). These results are reasonable. But the final states also indicate that the risk aversion is high (people are less prepared to take risks) and that the patrol frequency is very high. This does not seem very reasonable. I would expect that with good weather (i.e. good driving conditions) drivers are more prepared to take risks (low risk aversion) and that the patrol frequency is low because there are fewer accidents.

To see the effect of bad weather I have run simulations for bad weather levels of 60, 70 and 80. The simulations reach convergece after 12, 12 and 10 cycles. The final states are in the table below.

Again, the results obtained for freeway congestion (high), car accidents (high) and driving speed (low) are reasonable for bad weather conditions, except for the fact that the driving speed has a value too low. The results for the risk aversion and patrol frequency are unexpected. These results indicate that in bad weather drivers are prepared to take risks (low risk aversion) and that the patrol frequency is low.

3. Modifications to the fuzzy cognitive map

The partially unexpected results that we have obtained suggest that there must be something wrong in the fuzzy cognitive map as shown in the figure above. In the fuzzy map there is a negative causality relationship between the car accidents and the patrol frequency. This means that the more car accidents occur, the lower the patrol frequency. This does not seem right. In fact, we could expect that when more accidents happen, more police are patrolling the freeway. Therefore we have to change the causality relationship from negative to positive. The modified fuzzy cognitive map is shown in the figure below.

To apply this modification in the applet we have to select the patrol frequency factor in the list of factors in the applet and then click the Edit button. The Factor Editor dialog box for the patrol frequency pops up. The potential causes of the patrol frequency are listed in the popup window. We select the car accidents factor and then change the effect factor from Negative to Positive. To accept the changes we click the OK button.

4. Effect of weather on driving speed revised

After applying the modification to the fuzzy cognitive map we run the same simulations as above to see the effect of the weather. The tables below show the results of the simulations for bad weather levels of 20, 30 and 40 (i.e. good weather) and bad weather levels of 50, 60 and 70. Convergence is reached after 11 or 12 cycles in all cases.

These results seem more reasonable than those shown in Section 2. When the weather is good there is little freeway congestion, few car accidents and low patrol frequency, and drivers speed and are prepared to risk more (low risk aversion). On the other hand, when the weather is bad there is traffic congestion, more car accidents, more patrols, more risk aversion and less speed.

The final values for the driving speed, although qualitatively correct, are rather extreme (either 0 or 100). It would be necessary to refine further the fuzzy cognitive map to avoid these extreme results. However it is not clear how to achieve this. I have tried modifying the intensity of effect of the causality relationship between freeway congestion and own driving speed from 80 to 50, but this does not prevent extreme final values for the driving speed.

5. Conclusion

We have seen that a very simple fuzzy cognitive map with only six factors can provide reasonable predictions of how the weather affects traffic congestion, patrol frequency, risk aversion and driving speed.

We have also seen in this example that the type ("+" or "-") of a single causality relationship in the fuzzy cognitive map can have very significant effects on the results of the simulations. Therefore, it is important to review a fuzzy cognitive map thoroughly and ensure that all the relationships are complete and correct before we run simulations on it.