# Fuzzy Case-Based Reasoning System
## 4 Experiments and Discussion  
**Data collection:** Weather data (May 2010-October 2010, May 2011-October 2011, May 2012-October 2012, May 2014-October 2014) were collected from the meteorological department of Shanxi, China, Asia. The day's wind speed, dry wet bulb temperature, relative humidity, and pressure at 20 o'clock are taken as inputs while the cumulative precipitation quantity for the next 24 h is taken as outputs for our weather prediction model.  
Atmospheric pressure falls into four fuzzy sets in Table 3; relative humidity falls into four fuzzy sets shown in Table 4; dry and wet bulb temperature falls into six fuzzy sets shown in Table 5; wind force falls into 5 levels (fuzzy sets) shown in Table 6; precipitation falls into five fuzzy sets shown in Table 7. In order to test, numbers from 0 to 4 inclusively is given to represent Light rain, Moderate rain, Heavy rain, Rainstorm and Heavy rainstorm respectively. In Section 4.2, we keep the original fuzzy classification of fuzzy outputs unchanged. Thus, we maintain the precision and show a change in prediction accuracy with the change in fuzzy classification of fuzzy inputs.  
**Working sample:** We give a simple example to show how to work with a fuzzy case-based reasoning system. Assume the original case base contains four cases with four inputs and one output as shown below:  
\begin{tabular}{c c c c c c}
927.1 & 12. & 35 & 0.9 & 0 & (old case 1) \\
919.7 & 18.5 & 30 & 2 & 0 & (old case 2) \\
920.3 & 20.6 & 49 & 1.4 & 1.2 & (old case 3) \\
917 & 17.1 & 75 & 1.8 & 0 & (old case 4) \\
915.9 & 18.0 & 37 & 2.6 &? & (New coming case) \\ \end{tabular} and we check the Tables 3-7 to fuzzify them into  
\begin{tabular}{c c c c c}
3 & 2 & 2 & 2 & 0 & (old case 1) \\
1 & 2 & 1 & 3 & 0 & (old case 2) \\
3 & 2 & 2 & 2 & 0 & (old case 3) \\
1 & 2 & 4 & 3 & 1 & (old case 4) \\
1 & 2 & 2 & 3 &? & (New coming case) \\ \end{tabular}  
Then, the system finds the nearest case is number 2, and generates output according to it, which should be \"0\".  
\begin{table}
\begin{tabular}{c c c c c}
**Atmospheric Pressure Rating** & **Moderate** & **Slightly Lower** & **Lower** & **Lowest** \\ \hline hPa & \(\geq\)940 & [930, 940] & [920, 930) & \textless{}920 \\ \end{tabular}
\end{table}
Table 3: Fuzzy classification of atmospheric pressure.  
Both CBR and FCBR (Fuzzy case-based reasoning system) are machine learning prediction methods: CBR works with crisp cases and FCBR works with fuzzy ones. The fuzzy expert system differs from the two above largely since it is not a machine learning prediction method but a mathematical one. Experimental results (Figures 5 and 6) show that FCBR has a higher hitting rate than its relatives CBR and the fuzzy expert system, and the fuzzy expert system shows its worst performance among these three. The main reason is shown below.  
Practical weather prediction is very complicated and the fuzzy expert system is a comparatively simpler and linear mathematical prediction model, so it cannot predict future states very well. To solve this, a lot of work has been put into improving the fuzzy expert system, such as combining it with neural networks since machine learning models are non-linear and can predict complex relationships.