## 4 Materials and Methods
### Diagnostic Methods
#### 4.3.3 Method of Weights (WM)  
This method uses some kinds of weights given by experts. After the symptoms related to each disease were determined and the decision trees were produced, the experts were asked to assign a value to each parameter/symptom, except those of the 1 st decision level, showing how important the presence of the symptom is considered for the diagnosis of the corresponding disease, which is called the _symptom significance factor_ (_SSF_). Those values were then normalized with the min-max technique so that their sum equals '1' at each decision level. Based on SSFs, a _level significance factor_ (_LSF\({}_{x}\)_) at each decision level \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Symptoms** & **Photo-Bacteriosis** & **Myxo-Bacteriosis** & **Myxo-Bacteriosis** & **Ceratothoa** \\ \hline Weight loss & & & X & \\ Mortality (deaths) & nomass, mass & & & \\ Anorexia & X & X & & X \\ Lethargic fish & & X & & \\ Swimming Behavior & normal, alien & & & \\ Color Darkening & X & X & & \\ Skin discoloration & & X & & \\ Mouth Lower & & & & \\ Jav Deformity & & & & X \\ Fins and tail corrosion & & X & & \\ Scales Loss & & & X & \\ Stomatitis & & X & & \\ Skin ulcers & & X & & \\ Gill mucous & & & & X \\ Anemic gills & & & X & \\ Granulomatosis & & & X & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Table of correlations of parameters/symptoms and diseases (part). \(x\) (\(x\) = 2, 3) is determined as the sum of the _SSF_s of the common (let say \(k\)) symptoms between those given by the user and those related to the disease:  
\[LSF_{x}=\sum_{i=1}^{k}SSF_{i}\]  
The \(LSF_{x}\) shows how important the given symptoms of level \(x\) are in diagnosing the disease. So, with this metric, not just how many common symptoms there are matters, but also how important they are. As it is obvious, additional symptoms not related to the disease do not contribute to the \(LSF_{x}\). We indicatively present the \"ceratothoa\" disease with its _SF_s:  
\"DISEASE\": \"ceratothoa\",  
\"symptoms\": {  
\"anorexia\": \"0.09\",  
\"mouthDeformity\": \"0.73\",  
\"gillMucous\": \"0.18\"  
In this case, we have the following input from the user at decision level 3:  
'deaths:no',  
'anorexia',  
'lethargy',  
'swimActivity:normal',  
'swimBladderControlLoss',  
'colorDarkening',  
'gillMucous'  
the \(LSF_{3(ceratothoa)}\) is calculated as \(LSF_{3(ceratothoa)}\) = 0.09 + 0.18 = 0.27, given that 'anorexia' and 'gillMucous' are the common symptoms and have as _SSF_s '0.09' and '0.18' respectively. For each level \(x\), for each disease, a _level certainty factor_ (\(LCF_{x}\)) has also been determined by the expert, showing how certain a decision about the disease is at that level if based only on the symptoms up to that level. If we have a \(LSF_{3(ceratothoa)}\) at level 3, calculated as above, and \(LCF_{3(ceratothoa)}\) is the corresponding level certainty factor, then we define the _decision certainty factor_ for ceratothoa at level 3 (\(DCF_{3(ceratothoa)}\)), which is calculated as follows:  
\[DCF_{3(ceratothoa)}=LSF_{3(ceratothoa)}\times LCF_{3(ceratothoa)}\]  
If \(LCF_{3(ceratothoa)}\) = 0.8 was given by the expert, then \(DCF_{3(ceratothoa)}\) = 0.27 * 0.8 = 0.216. Also, this is a novel method of reasoning using a combination of different significance or certainty factors. Existing expert systems [23; 30; 31; 32] use the method of CFs based on MYCINs approach. To implement that approach, they ask the experts to assign a CF factor to each symptom, and the final CF is calculated based on those values. This approach has two problems: (a) the values assigned to each symptom by the expert(s) represent the significance of the symptom in diagnosing a disease, not the certainty of the observed value, which is the normal semantics of the CFs, and (b) each symptom is assigned one value independent of the disease, which is not valid.