# A Multiple Criteria Decision Analysis Framework for Dispersed Group Decision-Making Contexts

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. The Multiple Criteria Decision Analysis Framework

#### 3.1. Definition of the Entities and How They Relate

**Definition**

**1.**

- $C$is the set of criteria$C=\left\{{c}_{1},{c}_{2},\dots ,{c}_{p}\right\},p1$;
- $A$is the set of alternatives$A=\left\{{a}_{1},{a}_{2},\dots ,{a}_{m}\right\},m>1$.

**Rule**

**1.**

**Definition**

**2.**

- $\forall {c}_{j}\in C,j\in \left\{1,2,\dots ,p\right\}$;
- $i{d}_{{c}_{j}}$ is the identification of a particular criterion;
- $typ{e}_{{c}_{j}}$ is the type of a particular criterion (Numeric, Boolean or Classificatory);
- $grea{t}_{{c}_{j}}$ is the greatness associated with the criterion (Maximization, Minimization or Subjective).

- $distance=\left\{{c}_{1},Numeric,Minimization\right\}$; //minutes
- $transportExpenses=\left\{{c}_{2},Numeric,Minimization\right\}$; //dollars
- $speedOfService=\left\{{c}_{3},Numeric,Minimization\right\}$; //minutes
- $qualityOfTheFood=\left\{{c}_{4},Classificatory,Maximization\right\}$; //good, ok or poor
- $mealPrice=\left\{{c}_{5},Numeric,Minimization\right\}$; //dollars
- $atmosphere=\left\{{c}_{6},Boolean,Maximization\right\}$; //true or false
- $wine=\left\{{c}_{7},Boolean,Maximization\right\}$; //true or false
- $cuisineStyle=\left\{{c}_{8},Classificatory,Subjective\right\}$; //thai, italian or american
- $healthy=\left\{{c}_{9},Boolean,Maximization\right\}$. //true or false

**Definition**

**3.**

- $\forall {a}_{i}\in A,i\in \left\{1,2,\dots ,m\right\}$;
- $i{d}_{{a}_{i}}$ is the identification of a particular alternative.

- $zingara=\left\{{a}_{1}\right\}$;
- $thaiPalace=\left\{{a}_{2}\right\}$;
- $nosh=\left\{{a}_{3}\right\}$.

**Definition**

**4.**

- $DM=\left\{d{m}_{1},d{m}_{2},\dots ,d{m}_{n}\right\},n>1$.

**Definition**

**5.**

**Rule**

**2.**

- $W{a}_{d{m}_{k}}=\left\{w{a}_{d{m}_{{k}_{{a}_{1}}}},w{a}_{d{m}_{{k}_{{a}_{2}}}},\dots ,w{a}_{d{m}_{{k}_{{a}_{m}}}}\right\},m1$;
- $0\le w{a}_{d{m}_{{k}_{{a}_{i}}}}\le 1,\forall i\in \left\{1,2,\dots ,m\right\}$;
- $\langle W{a}_{d{m}_{k}}\rangle =\langle A\rangle $.

**Definition**

**6.**

**Rule**

**3.**

- $W{c}_{d{m}_{k}}=\left\{w{c}_{d{m}_{{k}_{{c}_{1}}}},w{c}_{d{m}_{{k}_{{c}_{2}}}},\dots ,w{c}_{d{m}_{{k}_{{c}_{p}}}}\right\},p1$;
- $0\le w{c}_{d{m}_{{k}_{{c}_{j}}}}\le 1,\forall j\in \left\{1,2,\dots ,p\right\}$;
- $\langle W{c}_{d{m}_{k}}\rangle =\langle C\rangle $.

**Definition**

**7.**

- $i{d}_{d{m}_{k}}$ is the identification of a particular decision-maker;
- $DMcredibl{e}_{d{m}_{k}}$ is the set of decision-makers that decision-maker $d{m}_{k}$ considers as credible, $DMcredibl{e}_{d{m}_{k}}\in DM$;$C{S}_{d{m}_{k}}$ is the value of the Concern for Self of decision-maker $d{m}_{k}$ chosen style of behavior;
- $C{O}_{d{m}_{k}}$ is the value of the Concern for Others of decision-maker $d{m}_{k}$ chosen style of behavior;
- ${e}_{d{m}_{k}}$ is the expertise level of decision-maker $d{m}_{k}$.

- $harry=\left\{d{m}_{1},\left[0.75,0.90,0.25\right],\left[0.5,0.25,0.25,0.75,0.5,0.75,0.75,0.9,0.75\right],\left[george,jane\right],0.548,0.616,0.5\right\}$;
- $george=\{d{m}_{2},\left[0.5,0.5,0.75\right],\left[0.75,0.9,0.25,0.5,0.9,0.75,0.75,0.25,0.25\right],\left[harry,jane\right],0.548,0.616,0.5$;
- $jane=\left\{d{m}_{3},\left[0.90,0.75,0.25\right],\left[0.5,0.25,0.25,0.9,0.25,0.75,0.75,0.75,0.75\right],\left[harry,george\right],0.548,0.616,0.5\right\}$.

**Definition**

**8.**

- $W{a}_{DM}=\left\{W{a}_{d{m}_{1}},W{a}_{d{m}_{2}},\dots ,W{a}_{d{m}_{n}}\right\},n>1$.

**Definition**

**9.**

- $W{c}_{DM}=\left\{W{c}_{d{m}_{1}},W{c}_{d{m}_{2}},\dots ,W{c}_{d{m}_{n}}\right\},n>1$.

**Definition**

**10.**

- $A{P}_{DM}=A\times W{a}_{DM}=\left[\begin{array}{cccc}W{a}_{{dm}_{{1}_{a1}}}& W{a}_{{dm}_{{2}_{a1}}}& \cdots & W{a}_{{dm}_{{n}_{a1}}}\\ W{a}_{{dm}_{{1}_{a2}}}& W{a}_{{dm}_{{2}_{a2}}}& \cdots & W{a}_{{dm}_{{n}_{a2}}}\\ \vdots & \vdots & \ddots & \vdots \\ W{a}_{{dm}_{{1}_{am}}}& W{a}_{{dm}_{{2}_{am}}}& \cdots & W{a}_{{dm}_{{n}_{am}}}\end{array}\right]$

**Definition**

**11.**

- $C{P}_{DM}=C\times W{c}_{DM}=\left[\begin{array}{cccc}W{c}_{{dm}_{{1}_{c1}}}& W{c}_{{dm}_{{2}_{c1}}}& \cdots & W{c}_{{dm}_{{n}_{c1}}}\\ W{c}_{{dm}_{{1}_{c2}}}& W{a}_{{dm}_{{2}_{c2}}}& \cdots & W{c}_{{dm}_{{n}_{c2}}}\\ \vdots & \vdots & \ddots & \vdots \\ W{c}_{{dm}_{{1}_{cp}}}& W{c}_{{dm}_{{2}_{cp}}}& \cdots & W{c}_{{dm}_{{n}_{ap}}}\end{array}\right]$

#### 3.2. Forecasting the Importance of Each Alternative/Criterion from the Perspective of Each Decision-Maker

**Definition**

**12.**

- $TP$ is the sum of the weights given to alternative ${a}_{i}$ by each of the credible decision-makers in $DMcredibl{e}_{d{m}_{k}}$, $TP={\displaystyle \sum}_{x=1}^{ND}w{a}_{d{m}_{{x}_{{a}_{i}}}}$;
- $ND$ is the number of credible decision-makers to $d{m}_{k}$ such that $ND=DMcredibl{e}_{d{m}_{k}}$;
- $e{\prime}_{d{m}_{k}}$ is the inverse of expertise level of decision-maker $d{m}_{k}$ (calculated as $1-{e}_{d{m}_{k}}$).

**Definition**

**13.**

**Definition**

**14.**

Algorithm 1. Alternatives’ importance classification algorithm. |

1: foreach $\left({\mathrm{dm}}_{\mathrm{k}}\in \mathrm{DM}\right)$ |

2: foreach $\left({\mathrm{a}}_{\mathrm{i}}\in \mathrm{A}\right)$ |

3: $\mathrm{imp}\leftarrow 1$ |

4: while $\left(\left({\mathrm{wa}}_{{\mathrm{dm}}_{{\mathrm{k}}_{{\mathrm{a}}_{\mathrm{i}}}}}\le \left(\mathrm{max}\left({\mathrm{Wa}}_{{\mathrm{dm}}_{\mathrm{k}}}\right)-\mathrm{imp}\times \frac{{\mathrm{F}}_{\mathrm{Dif}}\left({\mathrm{Wa}}_{{\mathrm{dm}}_{\mathrm{k}}}\right)}{\mathrm{l}}\right)\right)\wedge \mathrm{imp}<5\right)$ do |

5: $\mathrm{imp}\leftarrow \mathrm{imp}+1$ |

6: end while |

7: ${\mathrm{imp}}_{{\mathrm{dm}}_{{\mathrm{k}}_{{\mathrm{a}}_{\mathrm{i}}}}}\leftarrow 6-\mathrm{imp}$ |

8: end foreach |

9: end foreach |

#### 3.3. Recommending Alternatives to Reject and as Solution

#### 3.3.1. Recommending based on the Alternatives/Criteria Predicted Importance

**Definition**

**15.**

- $AIm{p}_{d{m}_{k}}=\left\{im{p}_{d{m}_{{k}_{{a}_{1}}}},im{p}_{d{m}_{{k}_{{a}_{2}}}},\dots ,im{p}_{d{m}_{{k}_{{a}_{m}}}}\right\},m>1$;
- $\langle AIm{p}_{d{m}_{k}}\rangle =\langle A\rangle $.

**Definition**

**16.**

- $CIm{p}_{d{m}_{k}}=\left\{im{p}_{d{m}_{{k}_{{c}_{1}}}},im{p}_{d{m}_{{k}_{{c}_{2}}}},\dots ,im{p}_{d{m}_{{k}_{{c}_{p}}}}\right\},p>1$;
- $\langle CIm{p}_{d{m}_{k}}\rangle =\langle C\rangle $.

**Definition**

**17.**

- $A{E}_{DM}=A\times W{AImp}_{DM}=\left[\begin{array}{cccc}{imp}_{{dm}_{{1}_{a1}}}& {imp}_{{dm}_{{2}_{a1}}}& \cdots & W{imp}_{{dm}_{{k}_{a1}}}\\ {imp}_{{dm}_{{1}_{a2}}}& {imp}_{{dm}_{{2}_{a2}}}& \cdots & {imp}_{{dm}_{{k}_{a2}}}\\ \vdots & \vdots & \ddots & \vdots \\ {imp}_{{dm}_{{1}_{am}}}& {imp}_{{dm}_{{2}_{am}}}& \cdots & {imp}_{{dm}_{{k}_{am}}}\end{array}\right]$

Algorithm 2. Algorithm for selecting the alternatives candidate to rejection. |

1: $\mathrm{value}\leftarrow 1$ |

2: while $\left(\mathrm{selectedAltsToReject}.\mathrm{size}()==0\wedge \mathrm{value}\le 5\right)$ do |

3: foreach $\left({\mathrm{a}}_{\mathrm{i}}\in \mathrm{A}\right)$ |

4: $\mathrm{flag}\leftarrow \mathrm{true}$ |

5: foreach $\left({\mathrm{dm}}_{\mathrm{k}}\in \mathrm{DM}\right)$ |

6: if $({\mathrm{AE}}_{\mathrm{DM}}\left[{\mathrm{a}}_{\mathrm{i}}][{\mathrm{dm}}_{\mathrm{k}}\right]>\mathrm{value})$ then $\mathrm{flag}\leftarrow \mathrm{false}$ |

7: end foreach |

8: if $\left(\mathrm{flag}==\mathrm{true}\right)$ then insert ${\mathrm{a}}_{\mathrm{i}}$ into $\mathrm{selectedAltsToReject}$ |

9: end foreach |

10: $\mathrm{value}\leftarrow \mathrm{value}+1$ |

11: end while |

Algorithm 3. Algorithm for selecting the alternatives as candidate solutions. |

1: $\mathrm{value}\leftarrow 5$ |

2: while $\left(\mathrm{selectedAltsToPropose}.\mathrm{size}()==0\wedge \mathrm{value}\ge 1\right)$ do |

3: foreach $\left({\mathrm{a}}_{\mathrm{i}}\in \mathrm{A}\right)$ |

4: $\mathrm{flag}\leftarrow \mathrm{true}$ |

5: foreach $\left({\mathrm{dm}}_{\mathrm{k}}\in \mathrm{DM}\right)$ |

6: if $({\mathrm{AE}}_{\mathrm{DM}}\left[{\mathrm{a}}_{\mathrm{i}}][{\mathrm{dm}}_{\mathrm{k}}\right]<\mathrm{value})$ then $\mathrm{flag}\leftarrow \mathrm{false}$ |

7: end foreach |

8: if $\left(\mathrm{flag}==\mathrm{true}\right)$ then insert ${\mathrm{a}}_{\mathrm{i}}$ into $\mathrm{selectedAltsToPropose}$ |

9: end foreach |

10: $\mathrm{value}\leftarrow \mathrm{value}-1$ |

11: end while |

**Definition**

**18.**

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. |

1: foreach $({\mathrm{a}}_{\mathrm{i}}\in \mathrm{A})$ |

2: foreach $\left({\mathrm{d}\prime}_{{\mathrm{c}}_{{\mathrm{j}}_{{\mathrm{a}}_{\mathrm{i}}}}}\in \mathrm{D}\prime \right)$ |

3: $\mathrm{imp}\leftarrow 1$ |

4: while $\left(\left({\mathrm{d}\prime}_{{\mathrm{c}}_{{\mathrm{j}}_{{\mathrm{a}}_{\mathrm{i}}}}}\le \left(\mathrm{max}\left({\mathrm{d}\prime}_{{\mathrm{c}}_{{\mathrm{a}}_{\mathrm{i}}}}\right)-\mathrm{imp}\times \frac{{\mathrm{F}}_{{\mathrm{Dif}}_{\mathrm{distance}}}\left({\mathrm{d}\prime}_{{\mathrm{c}}_{{\mathrm{a}}_{\mathrm{i}}}}\right)}{\mathrm{l}}\right)\right)\wedge \mathrm{imp}5\right)$ do |

5: $\mathrm{imp}\leftarrow \mathrm{imp}+1$ |

6: end while |

7: ${\mathrm{imp}}_{{\mathrm{d}}_{{\mathrm{c}}_{{\mathrm{j}}_{{\mathrm{a}}_{\mathrm{i}}}}}}\leftarrow 6-\mathrm{imp}$ |

8: end foreach |

9: end foreach |

**Definition**

**19.**

- $CIm{p}_{{a}_{i}}=\left\{im{p}_{{c}_{{1}_{{a}_{i}}}},im{p}_{{c}_{{2}_{{a}_{i}}}},\dots ,im{p}_{{c}_{{p}_{{a}_{i}}}}\right\},p>1$;
- $\langle CIm{p}_{{a}_{i}}\rangle =\langle C\rangle $.

**Definition**

**20.**

**Definition**

**21.**

- ${CM}_{{dm}_{k}}=\left[\begin{array}{cccc}{F}_{CC}({dm}_{k},{c}_{1},{a}_{1})& {F}_{CC}({dm}_{k},{c}_{2},{a}_{1})& \cdots & {F}_{CC}({dm}_{k},{c}_{p},{a}_{1})\\ {F}_{CC}({dm}_{k},{c}_{1},{a}_{2})& {F}_{CC}({dm}_{k},{c}_{2},{a}_{2})& \cdots & {F}_{CC}({dm}_{k},{c}_{p},{a}_{2})\\ \vdots & \vdots & \ddots & \vdots \\ {F}_{CC}({dm}_{k},{c}_{1},{a}_{m})& {F}_{CC}({dm}_{k},{c}_{2},{a}_{m})& \cdots & {F}_{CC}({dm}_{k},{c}_{p},{a}_{m})\end{array}\right]$

**Definition**

**22.**

- ${F}_{AlternativeConsistency}\left(harry,nosh\right)=-15$;
- ${F}_{AlternativeConsistency}\left(george,nosh\right)=-8$;
- ${F}_{AlternativeConsistency}\left(jane,nosh\right)=-15$.

- ${F}_{AlternativeConsistency}\left(harry,zingara\right)=0$;
- ${F}_{AlternativeConsistency}\left(george,zingara\right)=-6$;
- ${F}_{AlternativeConsistency}\left(jane,zingara\right)=0$;
- ${F}_{AlternativeConsistency}\left(harry,thaiPalace\right)=0$;
- ${F}_{AlternativeConsistency}\left(george,thaiPalace\right)=-9$;
- ${F}_{AlternativeConsistency}\left(jane,thaiPalace\right)=0$.

**Definition**

**23.**

#### 3.3.2. Recommending Based on the Prediction of Decision Satisfaction

**Definition**

**24.**

**Definition**

**25.**

**Definition**

**26.**

**Definition**

**27.**

## 4. Scenarios of Application

#### 4.1. Recommending an Alternative(s) to Reject or as a Feasible Solution(s)

#### 4.2. Explaining the Reasons Behind the Different Recommendations/Proposals (to Reject or to Accept)

#### 4.2.1. Step 1

#### 4.2.2. Step 2

#### 4.2.3. Step 3

#### 4.3. Presenting Other Relevant Data to the Decision Process

- Statistical information and aggregation data on preferences, satisfaction predictions, importance predictions according to the decision-makers’ behavior style, their levels of expertise, the preferences of the decision-makers considered most credible, among others;
- To measure the consistency level of the alternative evaluation that each decision-maker made;
- To alert the decision-makers of (too) inconsistent evaluations;
- To suggest the alternative with greater consistency based on the criteria importance given by the decision-maker;
- To present the most consistent alternative to the other decision-makers based on the criteria importance given by them;
- To present statistical information about the criteria importance based on the respective prediction algorithm;
- To explore the motives behind subjective evaluations through the user’s interaction with the System (in our example, it is possible to anticipate that the inconsistency in the evaluation of an alternative is due to the subjective greatness cuisineStyle criterion);
- To justify why a decision-maker prefers a particular alternative (in our example, the framework can demonstrate that George prefers nosh because of the distance, transportExpenses and mealPrice criteria);
- To provide information to the decision-maker to enhance his/her final satisfaction;
- To explore the decision maturity throughout the process and by predicting individual and group satisfaction.

## 5. Implementation and Demonstration

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Consensus-Based Group Decision Support System Architecture (adapted from [40]).

Terminology | Notation |
---|---|

Set of decision-makers | $DM$ |

Decision-maker | $d{m}_{k}$ |

Set of alternatives | $A$ |

Set of criteria | $C$ |

Alternative | ${a}_{i}$ |

Criterion | ${c}_{j}$ |

Decision matrix | $D$ |

Weight or preference given to a certain alternative ${a}_{i}$ by a decision-maker $d{m}_{k}$ | $w{a}_{d{m}_{{k}_{{a}_{i}}}}$ |

Set of alternatives weights of a decision-maker $d{m}_{k}$ | $W{a}_{d{m}_{k}}$ |

Weight or preference given to a certain criterion ${c}_{j}$ by a decision-maker $d{m}_{k}$ | $w{c}_{d{m}_{{k}_{{c}_{j}}}}$ |

Set of criteria weights of a decision-maker $d{m}_{k}$ | $W{c}_{d{m}_{k}}$ |

Set of alternatives weights of a set of decision-makers | $W{a}_{DM}$ |

Set of criteria weights of a set of decision-makers | $W{c}_{DM}$ |

Alternatives preference matrix that relates each alternative with the correspondent evaluation made by each decision-maker | $A{P}_{DM}$ |

Criteria preference matrix that relates each criterion with the correspondent evaluation made by each decision-maker | $C{P}_{DM}$ |

Predicted importance of alternative ${a}_{i}$ to decision-maker $d{m}_{k}$ | $im{p}_{d{m}_{{k}_{{a}_{i}}}}$ |

Set of importance values for all the alternatives to decision-maker $d{m}_{k}$ | $AIm{p}_{d{m}_{k}}$ |

Predicted importance of criterion ${c}_{j}$ to decision-maker $d{m}_{k}$ | $im{p}_{d{m}_{{k}_{{c}_{j}}}}$ |

Set of importance values for all the criteria to decision-maker $d{m}_{k}$ | $CIm{p}_{d{m}_{k}}$ |

Set of importance values for all the alternatives of a set of decision-makers | $AIm{p}_{DM}$ |

Set of importance values for all the criteria of a set of decision-makers | $CIm{p}_{DM}$ |

Alternatives evaluation matrix | $A{E}_{DM}$ |

Normalized decision matrix | $D\prime $ |

Consistency matrix of the decision-maker $d{m}_{k}$ | $C{M}_{d{m}_{k}}$ |

**Table 2.**The operating values of Concern for Self and Concern for Others for the 5 behavior style in [0, 1] interval (adapted from [15]).

Behavior Style | Concern for Self | Concern for Others |
---|---|---|

Dominating | 0.947 | 0.171 |

Obliging | 0.197 | 0.873 |

Avoiding | 0.108 | 0.090 |

Compromising | 0.548 | 0.616 |

Integrating | 0.777 | 0.846 |

Level $\left(\mathit{l}\right)$ | ${\mathit{F}}_{\mathit{D}\mathit{i}\mathit{f}}$ |
---|---|

5 | $dif\ge 0.80$ |

4 | $0.60\le dif<0.80$ |

3 | $0.40\le dif<0.60$ |

2 | $0.20\le dif<0.40$ |

1 | $dif<0.20$ |

Value | $\mathit{i}\mathit{m}\mathit{p}$ | Definition |
---|---|---|

5 | VI | Very Important |

4 | I | Important |

3 | M | Medium |

2 | NI | Not Important |

1 | IN | Insignificant |

Alternatives\Decision-Makers | Harry | George | Jane |
---|---|---|---|

zingara | 5 | 5 | 5 |

thaiPalace | 5 | 5 | 5 |

nosh | 3 | 4 | 3 |

Criteria\Decision-Makers | Harry | George | Jane |
---|---|---|---|

distance | 3 | 5 | 3 |

transportExpenses | 1 | 5 | 1 |

speedOfService | 1 | 1 | 1 |

qualityOfTheFood | 5 | 3 | 5 |

mealPrice | 3 | 5 | 1 |

atmosphere | 5 | 5 | 5 |

wine | 5 | 5 | 5 |

cuisineStyle | 5 | 1 | 5 |

healthy | 5 | 1 | 5 |

Criteria/Alternatives | Zingara | ThaiPalace | Nosh |
---|---|---|---|

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 |

Criteria/Alternatives | Zingara | ThaiPalace | Nosh |
---|---|---|---|

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 |

**Table 9.**Scale of satisfaction (adapted from [38]).

Designation | Interval |
---|---|

Extremely satisfied | $\left[0.75,1\right]$ |

Much satisfaction | $\left[0.5,0.75\right]$ |

Satisfaction | $\left[0.25,0.5\right]$ |

Some satisfaction | $\left[0,0.25\right]$ |

Some dissatisfaction | $\left[-0.25,0\right]$ |

Dissatisfied | $\left[-0.5,-0.25\right]$ |

Very dissatisfied | $\left[-0.75,-0.5\right]$ |

Extremely dissatisfied | $\left[-1,-0.75\right]$ |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Carneiro, J.; Martinho, D.; Alves, P.; Conceição, L.; Marreiros, G.; Novais, P.
A Multiple Criteria Decision Analysis Framework for Dispersed Group Decision-Making Contexts. *Appl. Sci.* **2020**, *10*, 4614.
https://doi.org/10.3390/app10134614

**AMA Style**

Carneiro J, Martinho D, Alves P, Conceição L, Marreiros G, Novais P.
A Multiple Criteria Decision Analysis Framework for Dispersed Group Decision-Making Contexts. *Applied Sciences*. 2020; 10(13):4614.
https://doi.org/10.3390/app10134614

**Chicago/Turabian Style**

Carneiro, João, Diogo Martinho, Patrícia Alves, Luís Conceição, Goreti Marreiros, and Paulo Novais.
2020. "A Multiple Criteria Decision Analysis Framework for Dispersed Group Decision-Making Contexts" *Applied Sciences* 10, no. 13: 4614.
https://doi.org/10.3390/app10134614