## 3 Results  
### Assessing the Strength of Association Rules with 7-Score  
Considering the three basic ratios describing the rules, i.e., confidence, support, and lift, the most powerful is confidence. If a certain type of predecessor appears, a certain type of a consequent appears too every time. The confidence of this kind of rule is 100%. This kind of information gathered by a user of association analysis is very strong. The collected data provide the user with a high likelihood of a certain result if the same type of predecessor appears again. However, not every rule of 100% confidence gives the same level of certainty of appearing to be a specified consequent. The three examples of phenomena that can be described with 100% confidence are presented in Figure 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Line of Code** & **Code** \\ \hline
1 & sBest = s0 \\
2 & bestCandidate = s0 \\
3 & tabuList = [] \\
4 & tabuList.push(s0) \\
5 & repeat (loop) \\
6 & sNeighborod \(\leftarrow\) getNeighbors(bestCandidate) \\
7 & for (sCandidate in Neighborhood) \\
8 & if ((not tabuList.contains(sCandidate)) and \\  & (fitness(sCandidate) > fitness(bestCandidate))) \\
9 & bestCandidate = sCandidate \\
10 & end \\
11 & end \\
12 & if (fitness(bestCandidate) > fitness(sBest)) \\
13 & sBest = bestCandidate \\
14 & end \\
15 & tabuList.push(bestCandidate) \\
16 & if (tabubitList.size > maxTabuSize) \\
17 & tabuList.removeFirst() \\
18 & end \\
19 & until stopping-criteria satisfied \\
20 & return sBest \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simplified tabu search pseudocode. As presented in Figure 3b, predicting the effect--dark green--based on this dataset seems more powerful than in the case presented in Figure 3a. There, the rule is based on one case only. It is unknown if the case is caused by the nature of the analyzed phenomenon, or if it has happened by chance. The rule seems to be the most powerful in the case presented in Figure 3c. Support calculated for the rule, for cases (a), (b), and (c), is 1/6, 3/6, and 5/6, respectively. It can be concluded that, for the rules of the same confidence, the more powerful (meaningful) is the rule with higher support. Then, the following question can be asked: which rule is stronger of the following two: rule 1: conf = 100% and sup = 33.3%, rule 2: conf = 75% and sup = 66.7%? To answer this, the large database should be considered. Then, if the rule of 100% confidence is supported by 33.3% of cases, it still a large number of cases where the appearance of a light green body always makes the head dark green. For much smaller databases being analyzed, it seems sufficient if support is higher than its minimum value, i.e., \(1/N\) (where \(N\) is a total value of cases in the database). Minimum support means that the rule is based on one case meeting the conditions of the rule. It can be stated that, for the rules with support higher than the minimum of one, confidence is more meaningful than support. The rules of sup = \(1/N\) should be excluded from the analysis. The influence of lift on the strength of the rule should also be considered, as two rules of identical confidence and support can have different lifts (as presented in Figure 4). Aiming at predicting a dark green head, based on a light green appearance, the rule for the dataset presented in Figure 4a seems to be a bit stronger, as the dark green head appears only if the light green body has appeared earlier. In case (b), dark green heads can also appear for bodies other than light green ones, but in case (a), the rule gives the full explanation for the appearance of the dark green bodies. For both cases, conf = 100% and sup = 33.3%; however, lift = 3 for (a) and lift = 1.2 for (b). It can be concluded that, for two rules of the same confidence and the same support, the stronger is the rule with the higher lift. When comparing the rules of different confidences and different supports, considering a lift seems unreasonable as--as discussed earlier--the meaning of confidence is higher than the meaning of support.