# A Multiple Criteria Decision Analysis Framework for Dispersed Group Decision-Making Contexts
## 3 The Multiple Criteria Decision Analysis Framework
### Recommending Alternatives to Reject and as Solution
#### 3.3.1 Recommending based on the Alternatives/Criteria Predicted Importance
```
1:foreach \((\mathrm{a}_{i}\in\mathrm{A})\)
2:foreach \(\left(\mathrm{d}_{c_{\mathrm{a}_{i}}}\in\mathrm{D}\prime\right)\)
3:\(\mathrm{imp}\gets 1\)
4:while\(\left(\left(\mathrm{d}\;\epsilon_{c_{\mathrm{a}_{i}}}\leq\left(\max\left( \mathrm{d}\;\epsilon_{c_{\mathrm{a}_{i}}}\right)-\mathrm{imp}\times\frac{F_{ \mathrm{Mod}_{\mathrm{diam}_{\mathrm{A}}}}\left(\mathrm{d}\;\epsilon_{c_{ \mathrm{a}_{i}}}\right)}{1}\right)\right)\right)\wedge\mathrm{imp}<5\)do
5:\(\mathrm{imp}\leftarrow\mathrm{imp}+1\)
6:endwhile
7:\(\mathrm{imp}_{\mathrm{d}_{\mathrm{a}_{i}}}\gets 6-\mathrm{imp}\)
8:endforeach
9:endforeach
```  
**Algorithm 4** The relevance that the value of each criterion \(c_{j}\) has in alternative \(a_{i}\) based on an overall appreciation of the criterion value in all alternatives. The next step consists of applying to \(D\prime\) a process like the one applied to the definition of the alternatives and criteria importance to each decision-maker. For that, for each criterion, we calculate the difference between the instance of \(c_{j}\) with the highest value and the instance of \(c_{j}\) with the lowest value. For example, \(F_{Di_{\ell_{\ell_{\ell_{\ell_{\ell_{\ell_{\ell_{\ell_{\ell_{\ell}}}}}}}}} }=0.910912919-0.109129194\). Then, we use Table 3 to find the \(l\) value, followed by the Algorithm 4 to define the importance levels. **Definition 19**. : _Let \(Clmp_{a_{i}}\) be the set of importance values of all the criteria to alternative \(a_{i}\), where:_  
* \(Clmp_{a_{i}}=\left\{imp_{c_{\mathrm{a}_{i}}},imp_{c_{\mathrm{a}_{i}}},\ldots, imp_{c_{\mathrm{a}_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{   }}}}}}}}}}}}}}}}} \right\),p>1\)_;
* \(\left\langle Clmp_{a_{i}}\right\rangle=\left\langle\mathrm{C}\right\rangle\)_._  
After defining the criteria importance for all the alternatives, we can now proceed to the definition of the consistency method. \begin{table \begin{tabular}{c c c c} \hline \hline
**Criteria/Alternatives** & **Zingara** & **ThaiPalace** & **Nosh** \\ \hline distance & 0.554564597 & 0.109129194 & 0.910912919 \\ transportExpenses & 1 & 0 & 1 \\ speedOfService & 0.175836616 & 0.450557744 & 0.862639436 \\ qualityOfTheFood & 0.688247202 & 0.688247202 & 0.229415734 \\ mealPrice & 0.166203318 & 0.499721991 & 0.766536929 \\ atmosphere & 0.707106781 & 0.707106781 & 0 \\ wine & 0.707106781 & 0.707106781 & 0 \\ cuisineStyle & 0.577350269 & 0.577350269 & 0.577350269 \\ healthy & 0.707106781 & 0.707106781 & 0 \\ \hline \hline \end{tabular} 
\end{table}
Table 7: Normalized values for each criterion in each alternative on the given example. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria/Alternatives** & **Zingara** & **ThaiPalace** & **Nosh** \\ \hline distance & 3 & 1 & 5 \\ transportExpenses & 5 & 1 & 5 \\ speedOfService & 1 & 3 & 5 \\ qualityOfTheFood & 5 & 5 & 2 \\ mealPrice & 1 & 4 & 5 \\ atmosphere & 5 & 5 & 1 \\ wine & 5 & 5 & 1 \\ cuisineStyle & 1 & 1 & 1 \\ healthy & 5 & 5 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The importance of each criterion to the existing alternatives. **Definition 20**. : _Let \(F_{CriterionConsistency}\Big{(}dm_{k},c_{j},a_{i}\Big{)}\) be a function that returns the difference between the importance of a criterion \(c_{j}\in C\) to an alternative \(a_{i}\in A\) and the importance of the same criterion \(c_{j}\in C\) to a decision-maker \(dm_{k}\in DM\):_  
\[F_{CriterionConsistency}\Big{(}dm_{k},c_{j},a_{i}\Big{)}=\left\{ \begin{array}{ c}0,if\text{ great}_{c_{j}}=Subjective\\ imp_{d_{c_{j_{i}}}}-imp_{dm_{k_{j}}},if\text{ imp}_{dm_{k_{j}}}>3\\ 0,if\text{ imp}_{dm_{k_{j}}}\leq 3\end{array} \right. \tag{5}\]  
As previously referred, the consistency method only considers the differences when \(imp_{dm_{k_{j}}}>3\). After calculating the criteria consistency for each decision-maker, we are now in conditions of defining a consistency matrix for each decision-maker. **Definition 21**.