# A Large Group Emergency Decision Making Method Considering Scenarios and Unknown Attribute Weights

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- To improve the accuracy of probability by taking into account the scenario probabilities of LGEDM.
- To obtain the best attribute weights by taking into account the difference between alternatives and the difference between alternatives and the ideal solution.
- To assign different weights to experts by using Euclidean distance to measure the contributions of experts to aggregation similarity.

## 2. Preliminaries

#### 2.1. Bayesian Theorem in Emergency Decision-Making

_{k}, but the probability that the decision-making experts judge it as μ

_{l}is p(μ

_{l}|θ

_{k}), and the real emergency scenario is θ

_{k}, but the probability that the decision-making experts judge it as θ

_{k}is p(k = l), then the posterior probability that the emergency scenario is θ

_{k}based on Bayesian theorem is:

#### 2.2. Prospect Theory in Emergency Decision-Making

_{i}) reflects the perceived utility formed by the subject according to the value difference:

_{i}= x

_{i}− x

_{0}represents the difference between the value x

_{i}of the subject and reference point x

_{0}when event i occurs, α is the parameter with respect to gains, and β is the parameter associated with losses; 0 ≤ α, β ≤ 1. The larger the parameter value is, the less sensitive the subject is to the benefit or loss utility, and the greater the possibility that the subject is a risk seeker. λ denotes the parameter of risk aversion; λ > 1. The larger the parameter value is, the more sensitive the subject is to loss and the greater the degree of loss avoidance is. Generally, α = 0.88, β = 0.88, and λ = 1.25.

#### 2.3. Relative Entropy Model in Emergency Decision-Making

_{i}and B

_{i}of two systems A and B can be measured by the Kullback–Leibler distance [27], that is:

#### 2.4. Related Work

## 3. A Large Group Emergency Decision-Making Method Considering Scenarios and Unknown Attribute Weights

- Definition framework. The main features, terminology, and expression domains utilized in the proposed LGEDM problem are defined.
- Calculation of posterior probabilities of scenario. In this part, firstly, cluster analysis is carried out according to the conditional probabilities of the scenario, and the weights of experts are obtained by using the Euclidean distance. The aggregation conditional probabilities are obtained by aggregating the initial conditional probabilities and the expert weights, and the group conditional probabilities are obtained by aggregating the aggregation conditional probabilities and the aggregation weights. Secondly, the posterior probabilities are calculated by using Bayesian theorem and prior probabilities.
- Calculation of the group prospect values. In this part, firstly, the perceived utility of the experts is calculated according to the decision interval and value function, and the initial prospect values of the experts are obtained by combining the posterior probabilities of scenario. Secondly, cluster analysis is carried out on the initial prospect values, and the expert weights are obtained by Euclidean distances. The aggregation prospect values are obtained by aggregating the initial prospect values and the expert weights, and the group prospect values are obtained by aggregating the aggregation prospect values and aggregation weights.
- Calculation of attribute weights. The relative entropy model with completely unknown attribute weights is constructed, and the attribute weights are calculated by using Lagrange algorithm.
- Ranking of alternatives. Combined with the group prospect values and attribute weights, the overall prospect values are obtained. Based on this, the ranking of alternatives is obtained. According to the ranking of alternatives, the experts can select the best or more suitable alternative to cope with the EE.

#### 3.1. Definition Framework

- X = {x
_{1}, x_{2},…, x_{i},…, x_{n}}: refers to the set of different alternatives, in which x_{i}denotes the i-th alternative, i = 1, 2,…, n. - E = {e
_{1}, e_{2},…, e_{j},…, e_{m}}, m ≥ 11: refers to the set of the experts, in which e_{j}denotes the j-th decision expert, j = 1, 2,…, m. - C = {c
_{1}, c_{2},…, c_{l},…, c_{p}}: refers to the set of criteria/attributes, in which cl denotes the l-th criterion/attribute, l = 1, 2,…, p. - W = {w
_{1}, w_{2},…, w_{l},…, w_{p}}: refers to the weighting vector for the criteria, in which w_{l}denotes the criterion weight of the l-th criterion/attribute, l = 1, 2,…, p. - Ω
_{Z}= {Z^{1}, Z^{2},…, Z^{h},…, Z^{k}}: refers to the set of scenario conditional probability aggregations, in which Z^{h}denotes the h-th aggregation, h = 1, 2,..., k. Clustering the conditional probabilities of scenario given by decision experts to form k aggregations, and the number of experts gathered in Z^{h}is n_{h}. - Ω
_{R}= {R^{1}, R^{2},…, R^{f},…, R^{O}}: refers to the set of alternative assessment aggregations, in which Rf denotes the f-th aggregation, f = 1, 2,..., O. Clustering the alternative assessments given by decision experts to form O aggregations, and the number of experts gathered in R^{f}is n_{f}. - ω
^{XE}= {ω_{1}^{XE}, ω_{2}^{XE},…, ω_{m}^{XE}}: refers to weighting vector of decision experts in assessing alternatives. - ω
^{XR}= {ω_{1}^{XR}, ω_{2}^{XR},…, ω_{nf}^{XR}}: refers to weighting vector of aggregations in assessing alternatives. - S = {s
_{1}, s_{2},…, s_{t},…, s_{u}}: refers to the set of different scenarios, in which s_{t}denotes the t-th scenario, t = 1, 2,…,u. p(s_{t}) is the prior probability of scenario s_{t}, p_{j}(s_{d}′|s_{t}) is the probability that the decision expert e_{j}determine the scenario as s_{d}′ under the real scenario s_{t}, p^{Z}(s_{d}′|s_{t}) is the probability that the aggregation Z^{h}determine the scenario as s_{d}′ under the real scenario s_{t}, p^{G}(s_{d}′|s_{t}) is the group conditional probability of scenario, and p(s_{t}|s_{d}′) is the posterior probability of the scenario s_{t}. - ω
^{PE}= {ω_{1}^{PE}, ω_{2}^{PE},…, ω_{m}^{PE}}: refers to weighting vector of decision experts in determining the condition probabilities. - ω
^{PZ}= {ω_{1}^{PZ}, ω_{2}^{PZ},…, ω_{nh}^{PZ}}: refers to weighting vector of aggregations in determining the condition probabilities. - a
_{li}^{jt}= [a_{li}^{jtL}, a_{li}^{jtU}]: refers to the assessment of the i-th alternative by the decision expert e_{j}under the scenario s_{t}and attribute c_{l}, belongs to the interval number, and the assessment matrix A = [a_{li}^{jt}]_{m×n×u×p}given by the decision experts is obtained.

#### 3.2. Posteriori Probabilities of Scenario

#### 3.2.1. Cluster Analysis of Scenario Conditional Probabilities

- (1)
- Cluster the initial condition probabilities

_{j}

_{1}and e

_{j}

_{2}are calculated according to the initial scenario conditional probability matrix P(s

_{d}′|s

_{t}) = [p

_{j}(s

_{d}′|s

_{t})]

_{m×u×u}:

_{p}

^{j}

^{1,j2}]

_{m×m×u×u}is obtained, and the initial condition probability matrix P(s

_{d}′|s

_{t}) is clustered by using the hierarchical clustering algorithm and the clustering algorithm matrix D to form k aggregations Ω

_{Z}= {Z

^{1}, Z

^{2},…, Z

^{h},…, Z

^{k}}. The idea of the hierarchical clustering algorithm is to calculate the distance between samples first, and the nearest points are merged into the same class each time. Then, the distance between classes is calculated, and the nearest classes are merged into a large class. Merging continues until a class is synthesized.

- (2)
- Aggregation conditional probabilities

^{h}is ω

_{h}

^{PZ}= n

_{h}/m. In the existing literature, the aggregation alternative assessments are mostly calculated by using the average value of experts’ alternative assessments, but the aggregation alternative assessments are obtained by experts’ alternative assessments and expert weights. In fact, the weights among experts are different, and it is inaccurate to take the average values of expert assessments as the aggregation assessments. Therefore, this paper proposes to use the Euclidean distance to measure the contribution of experts to the aggregation similarity to calculate the expert weights; ω

_{hq}

^{PE}(0 < q < n

_{h}) is the weight of the q-th expert in the aggregation Z

^{h}to determine the scenarios:

^{Z}(s

_{d}′|s

_{t}) = [p

^{Z}(s

_{d}′|s

_{t})]

_{k×u×u}(h = 1, 2,…, k) is obtained.

- (3)
- Group conditional probabilities

^{G}(s

_{d}′|s

_{t}) = [p

^{G}(s

_{d}′|s

_{t})]

_{u×u}is obtained.

#### 3.2.2. Calculation of Posterior Probabilities

_{t}|s

_{d}$\prime $) = [p(s

_{t}|s

_{d}$\prime $)]

_{u×u}is obtained.

#### 3.3. Group Prospect Values of Alternative Assessments

#### 3.3.1. Perceived Utility Matrix

_{j}under the scenario s

_{t}and attribute c

_{l}, the assessment matrix A = [a

_{li}

^{jt}]

_{m×n×u×p}given by the decision experts is obtained. The alternative assessments are standardized to obtain the standardized matrix B = [b

_{li}

^{jt}]

_{m×n×u×p}according to the attributes’ type. The standardized formulas of benefit type and cost type, respectively, are:

_{li}

^{jt}]

_{m×n×u×p}, the real numbers as the reference points are selected to obtain the difference $\mathsf{\Delta}{b}_{li}^{jtL}={b}_{li}^{jtL}-\overline{{b}_{li}^{jt}},\mathsf{\Delta}{b}_{li}^{jtU}={b}_{li}^{jtU}-\overline{{b}_{li}^{jt}}$ between the alternative assessments and the reference points under different scenarios and attributes, and the difference matrix [Δb

_{li}

^{jt}]

_{m×n×u×p}. Assuming that an alternative assessment is subject to uniform distribution within the decision-making interval [b

_{li}

^{jt}

^{L},b

_{li}

^{jt}

^{U}], the random probability density function of the alternative assessments is:

#### 3.3.2. Prospect Values of Decision Experts

_{d}′, the prospect values of the alternative assessments will be calculated under the posterior probabilities of scenario:

_{li}

^{j}= [v

_{li}

^{j}]

_{m×n×p}is obtained.

#### 3.3.3. Prospect Values Clustering

_{li}

^{j}= [v

_{li}

^{j}]

_{m×n×p}, the Euclidean distance between the prospect values of two decision experts e

_{j}

_{1}and e

_{j}

_{2}is calculated by:

_{V}

^{j}

^{1,j2}]

_{m×m×n×p}is obtained, and the scenario’s prospect values are clustered by using the hierarchical clustering algorithm and the clustering algorithm matrix D to form O aggregations. The idea of the hierarchical clustering algorithm is to calculate the distance between samples first, and the nearest points are merged into the same class each time. Then, the distance between classes is calculated, and the nearest classes are merged into a large class. Merging continues until a class is synthesized.

^{f}is ω

_{f}

^{XE}= n

_{f}/m. The weights of the decision experts in each aggregation are not equal, so the expert weights are calculated according to the contributions of decision experts to the aggregation similarity. ω

_{fq}

^{XE}(0 < q < n

_{f}) is the weight of the q-th decision-making expert in the aggregation R

^{f}:

#### 3.4. Determination of Attribute Weights

_{1}and δ

_{2}refer to the relative importance of the objective function, δ

_{1}+ δ

_{2}= 1.

#### 3.5. Ranking of Alternatives

## 4. Case Study of Group Decision Making Method Considering Scenarios and Unknown Attribute Weights

#### 4.1. Definition Framework

- Concealing and distributing iodine tablets to the public within a 25 km radius, with a total of 117,000 people taking iodine tablets and concealing.
- Evacuate the public within 11km, conceal the public within 11–25 km, and distribute iodine tablets. The evacuated population will reach 10,000, and the number of people hiding and taking iodine will reach 10,000.
- The public within 25 km shall be concealed and iodine tablets shall be distributed to the public in all affected areas. The number of people hiding will reach 120,000, and the number of people evacuating will reach 700,000.
- Take concealment measures first, provide iodine tablets, and implement concealment when the smoke plume passes by; after the smoke plume passes, evacuate the public within 20 km. The number of evacuees will reach 74,000 and the number of iodine users will reach 800,000.

_{1}, s

_{2}, and s

_{3}, respectively. The multi-attribute theory is used to build the attribute tree to get 6 attributes: the maximum avoidable individual dose c

_{1}(unit: mSv), the avoidable collective dose c

_{2}(unit: 10

^{4}mSv), the economic cost c

_{3}(unit: 10

^{6}yuan), the positive social psychosocial impact c

_{4}(range: 0–100), the negative social psychosocial impact c

_{5}(range: 0–100), and the political impact c

_{6}(range: 0–100). Among them, the maximum avoidable individual dose c

_{1}, avoidable collective dose c

_{2}, economic cost c

_{3}, and political influence c

_{6}belong to objective attributes, while positive psychosocial influence c

_{4}and negative psychosocial influence c

_{5}belong to subjective attributes.

#### 4.2. Case Study

_{2}′, the posterior probabilities of the three scenarios are P

^{G}(s

_{t}|s

_{d}′) = {0.2857, 0.6000, 0.1142}.

_{1}, the avoidable collective dose c

_{2}, and the positive social psychosocial impact c

_{4}are benefit type, while the economic cost c

_{3}, the negative social psychological impact c

_{5}, and the political impact c

_{6}are cost type. Therefore, Formulas (7) and (8) were used to standardize the number of assessment intervals provided by decision-making experts, as shown in Table A2.

^{1}= {e

_{3}, e

_{5}}, R

^{2}= {e

_{8}, e

_{9}}, R

^{3}= {e

_{1}, e

_{2}, e

_{4}, e

_{7}, e

_{10}}, and R

^{4}= {e

_{6}, e

_{11}}. The Euclidean distance was used to calculate the contributions of decision experts to the aggregation similarity, and the expert weights were obtained, as shown in Table 3.

_{1}= δ

_{2}= 0.5, and the optimal attribute weights were obtained: w

_{1}= 0.1457, w

_{2}= 0.2109, w

_{3}= 0.3512, w

_{4}= 0.1083, w

_{5}= 0.0772, and w

_{6}= 0.1064.

_{1}

^{G}= 0.6302, V

_{2}

^{G}= 0.6122, V

_{3}

^{G}= 0.7293, and V

_{4}

^{G}= 0.4078, which were used to sort the alternatives, so the optimal alternative is alternative 3.

_{2′}to s

_{3′}, the posterior probabilities of the three scenarios are P

^{G}(s

_{t}|s

_{d}′) = {0.2272, 0.1363, 0.6363}. The perceived utility values and the posterior probabilities of scenario were aggregated to obtain the prospect values. The aggregations were obtained by clustering the prospect values: R

^{1}= {e

_{3}, e

_{4}, e

_{5}}, R

^{2}= {e

_{1}, e

_{2}, e

_{6}, e

_{7}, e

_{8}, e

_{9}}, and R

^{3}= {e

_{10}, e

_{11}}, and aggregated prospect values were obtained by aggregating expert weights and prospect values. The group prospect values were obtained by aggregating aggregated weights and aggregated prospect values. The attribute weights were obtained by using the constructed relative entropy model: w

_{1}= 0.1796, w

_{2}= 0.2668, w

_{3}= 0.4307, w

_{4}= 0.0250, w

_{5}= 0.5180, and w

_{6}= 0.0462. The overall prospect values were obtained by aggregating the attribute weights and group prospect values: V

_{1}

^{G}= 0.5399, V

_{2}

^{G}= 0.6480, V

_{3}

^{G}= 0.7853, and V

_{4}

^{G}= 0.4867. Therefore, when the scenario is s

_{3′}, the final optimal alternative is alternative 3. Assuming that the current scenario determined by the experts is changed from s

_{2′}to s

_{1′}, the posterior probabilities of the three scenarios are P

^{G}(s

_{t}|s

_{d}′) = {0.8140, 0.1395, 0.0465}. The perceived utility values and the posterior probabilities of scenario were aggregated to obtain the prospect values. The aggregations were obtained by clustering the prospect values: R

^{1}= {e

_{3}, e

_{4}, e

_{5}}, R

^{2}= {e

_{1}, e

_{2}, e

_{6}, e

_{8}, e

_{9}, e

_{10}}, and R

^{3}= {e

_{6}}, R

^{4}= {e

_{11}}, and aggregated prospect values were obtained by aggregating expert weights and prospect values. The group prospect values were obtained by aggregating aggregated weights and aggregated prospect values. The attribute weights were obtained by using the constructed relative entropy model: w

_{1}= 0.1185, w

_{2}= 0.1705, w

_{3}= 0.2825, w

_{4}= 0.1406, w

_{5}= 0.1336, and w

_{6}= 0.1542. The overall prospect values were obtained by aggregating the attribute weights and group prospect values: V

_{1}

^{G}= 0.7083, V

_{2}

^{G}= 0.5748, V

_{3}

^{G}= 0.6504, and V

_{4}

^{G}= 0.3477. Therefore, when the scenario is s

_{1′}, the final optimal alternative is alternative 1.

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Scenario | s_{1} | ||||||||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |||||||

a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | ||

e_{1} | x_{1} | 1000 | 1100 | 80 | 90 | 1.6 | 2.6 | 80 | 90 | 0 | 10 | 0 | 5 |

x_{2} | 1000 | 1100 | 120 | 130 | 22.0 | 23.0 | 10 | 20 | 90 | 100 | 0 | 5 | |

x_{3} | 1000 | 1100 | 150 | 160 | 2.2 | 3.2 | 10 | 20 | 80 | 90 | 20 | 30 | |

x_{4} | 1200 | 1300 | 130 | 140 | 160.0 | 170.0 | 0 | 10 | 50 | 60 | 80 | 90 | |

e_{2} | x_{1} | 1000 | 1100 | 80 | 90 | 1.7 | 2.7 | 81 | 91 | 0 | 9 | 0 | 5 |

x_{2} | 1000 | 1100 | 120 | 130 | 23.0 | 24.0 | 10 | 20 | 91 | 100 | 0 | 5 | |

x_{3} | 1000 | 1100 | 150 | 160 | 2.1 | 3.1 | 10 | 20 | 80 | 90 | 21 | 31 | |

x_{4} | 1200 | 1300 | 128 | 138 | 160.0 | 170.1 | 0 | 10 | 49 | 59 | 80 | 90 | |

e_{3} | x_{1} | 990 | 1090 | 80 | 90 | 1.7 | 2.7 | 78 | 88 | 0 | 15 | 0 | 6 |

x_{2} | 990 | 1090 | 122 | 132 | 22.0 | 24.0 | 9 | 19 | 90 | 100 | 0 | 6 | |

x_{3} | 990 | 1090 | 148 | 158 | 2.1 | 3.1 | 9 | 19 | 79 | 89 | 22 | 35 | |

x_{4} | 1188 | 1280 | 128 | 138 | 160.0 | 170.1 | 0 | 10 | 48 | 58 | 81 | 91 | |

e_{4} | x_{1} | 1000 | 1100 | 80 | 90 | 1.7 | 1.8 | 82 | 90 | 0 | 9 | 0 | 5 |

x_{2} | 1000 | 1100 | 122 | 132 | 22.0 | 23.0 | 10 | 19 | 90 | 100 | 0 | 5 | |

x_{3} | 1000 | 1100 | 150 | 160 | 2.3 | 3.3 | 10 | 19 | 80 | 90 | 22 | 32 | |

x_{4} | 1210 | 1290 | 130 | 140 | 162.0 | 172.0 | 0 | 9 | 51 | 61 | 80 | 90 | |

e_{5} | x_{1} | 990 | 1100 | 80 | 89 | 1.7 | 2.7 | 78 | 88 | 0 | 15 | 0 | 5 |

x_{2} | 990 | 1100 | 122 | 132 | 22.0 | 24.0 | 10 | 20 | 90 | 100 | 0 | 5 | |

x_{3} | 990 | 1100 | 148 | 158 | 2.0 | 3.0 | 10 | 20 | 80 | 88 | 22 | 35 | |

x_{4} | 1200 | 1300 | 128 | 138 | 160.0 | 170.0 | 0 | 10 | 49 | 59 | 81 | 91 | |

e_{6} | x_{1} | 1000 | 1100 | 83 | 93 | 1.8 | 2.0 | 80 | 89 | 0 | 10 | 0 | 4 |

x_{2} | 1000 | 1100 | 118 | 128 | 21.0 | 22.0 | 10 | 20 | 88 | 98 | 0 | 4 | |

x_{3} | 1000 | 1100 | 148 | 158 | 2.2 | 3.2 | 9 | 19 | 79 | 89 | 20 | 30 | |

x_{4} | 1189 | 1289 | 127 | 137 | 158.0 | 168.0 | 0 | 9 | 50 | 60 | 80 | 90 | |

e_{7} | x_{1} | 1000 | 1090 | 80 | 90 | 1.5 | 2.0 | 80 | 90 | 0 | 10 | 1 | 4 |

x_{2} | 1000 | 1090 | 120 | 130 | 21.0 | 22.0 | 10 | 20 | 90 | 100 | 1 | 5 | |

x_{3} | 1000 | 1090 | 148 | 158 | 2.1 | 3.1 | 10 | 20 | 80 | 90 | 22 | 32 | |

x_{4} | 1188 | 1290 | 123 | 136 | 158.0 | 168.0 | 1 | 5 | 50 | 60 | 82 | 92 | |

e_{8} | x_{1} | 990 | 1090 | 80 | 90 | 1.7 | 2.0 | 80 | 90 | 0 | 10 | 0 | 4 |

x_{2} | 990 | 1090 | 121 | 131 | 22.0 | 23.0 | 11 | 21 | 90 | 99 | 0 | 4 | |

x_{3} | 990 | 1090 | 148 | 158 | 2.3 | 3.3 | 11 | 21 | 80 | 90 | 16 | 26 | |

x_{4} | 1200 | 1300 | 125 | 135 | 162.0 | 172.0 | 1 | 11 | 50 | 60 | 78 | 88 | |

e_{9} | x_{1} | 990 | 1090 | 80 | 90 | 1.6 | 2.0 | 80 | 90 | 0 | 10 | 0 | 4 |

x_{2} | 990 | 1090 | 121 | 131 | 22.0 | 23.0 | 11 | 21 | 90 | 99 | 0 | 4 | |

x_{3} | 990 | 1090 | 148 | 158 | 2.2 | 3.2 | 11 | 21 | 80 | 90 | 16 | 26 | |

x_{4} | 1198 | 1298 | 125 | 135 | 160.0 | 170.0 | 0 | 10 | 50 | 60 | 78 | 88 | |

e_{10} | x_{1} | 990 | 1100 | 80 | 90 | 1.6 | 2.6 | 80 | 90 | 0 | 10 | 0 | 4 |

x_{2} | 990 | 1100 | 120 | 130 | 22.0 | 23.0 | 10 | 20 | 90 | 99 | 0 | 4 | |

x_{3} | 990 | 1100 | 150 | 160 | 2.0 | 3.0 | 10 | 20 | 80 | 90 | 16 | 26 | |

x_{4} | 1200 | 1300 | 128 | 138 | 160.0 | 170.0 | 0 | 10 | 50 | 60 | 78 | 88 | |

e_{11} | x_{1} | 995 | 1095 | 82 | 92 | 1.6 | 2.6 | 88 | 98 | 0 | 10 | 0 | 4 |

x_{2} | 995 | 1095 | 119 | 129 | 22.0 | 24.9 | 10 | 19 | 90 | 100 | 0 | 4 | |

x_{3} | 995 | 1095 | 146 | 156 | 2.1 | 3.1 | 10 | 19 | 80 | 90 | 15 | 25 | |

x_{4} | 1200 | 1290 | 130 | 140 | 158.0 | 168.0 | 0 | 8 | 50 | 60 | 80 | 89 | |

Scenario | s_{2} | ||||||||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |||||||

a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | ||

e_{1} | x_{1} | 900 | 1000 | 60 | 70 | 3.1 | 4.1 | 70 | 80 | 35 | 45 | 40 | 50 |

x_{2} | 900 | 1000 | 100 | 110 | 38.0 | 48.0 | 50 | 60 | 50 | 60 | 40 | 50 | |

x_{3} | 900 | 1000 | 120 | 130 | 3.8 | 4.8 | 40 | 50 | 45 | 55 | 30 | 40 | |

x_{4} | 1100 | 1200 | 110 | 120 | 170.0 | 180.0 | 35 | 45 | 35 | 45 | 80 | 90 | |

e_{2} | x_{1} | 900 | 1000 | 60 | 70 | 3.1 | 4.1 | 70 | 80 | 35 | 45 | 40 | 50 |

x_{2} | 900 | 1000 | 100 | 110 | 38.4 | 48.4 | 50 | 60 | 50 | 60 | 40 | 50 | |

x_{3} | 900 | 1000 | 120 | 130 | 3.9 | 4.9 | 42 | 52 | 45 | 55 | 30 | 40 | |

x_{4} | 1100 | 1200 | 110 | 120 | 170.0 | 180.1 | 36 | 46 | 35 | 45 | 80 | 90 | |

e_{3} | x_{1} | 890 | 990 | 60 | 70 | 3.2 | 3.5 | 70 | 80 | 35 | 45 | 40 | 46 |

x_{2} | 890 | 990 | 101 | 111 | 38.0 | 49.0 | 49 | 59 | 50 | 60 | 40 | 47 | |

x_{3} | 890 | 990 | 120 | 130 | 3.7 | 4.7 | 39 | 49 | 43 | 53 | 31 | 41 | |

x_{4} | 1088 | 1180 | 118 | 128 | 170.1 | 180.1 | 35 | 45 | 33 | 43 | 80 | 89 | |

e_{4} | x_{1} | 900 | 1000 | 60 | 70 | 3.2 | 4.2 | 71 | 80 | 35 | 45 | 41 | 50 |

x_{2} | 900 | 1000 | 102 | 112 | 38.0 | 47.0 | 50 | 55 | 50 | 60 | 41 | 50 | |

x_{3} | 900 | 1000 | 120 | 129 | 3.9 | 4.9 | 42 | 52 | 45 | 55 | 32 | 42 | |

x_{4} | 1110 | 1210 | 110 | 120 | 172.0 | 173.0 | 36 | 46 | 35 | 45 | 82 | 92 | |

e_{5} | x_{1} | 890 | 990 | 60 | 69 | 3.2 | 3.5 | 70 | 80 | 35 | 45 | 40 | 46 |

x_{2} | 890 | 990 | 100 | 110 | 40.0 | 51.8 | 49 | 59 | 50 | 60 | 40 | 47 | |

x_{3} | 890 | 990 | 120 | 130 | 3.6 | 4.6 | 39 | 49 | 43 | 53 | 31 | 41 | |

x_{4} | 1100 | 1180 | 117 | 127 | 168.0 | 178.0 | 35 | 45 | 33 | 43 | 80 | 89 | |

e_{6} | x_{1} | 900 | 1000 | 63 | 73 | 3.3 | 4.3 | 70 | 79 | 36 | 46 | 41 | 51 |

x_{2} | 900 | 1000 | 100 | 110 | 37.0 | 47.0 | 50 | 60 | 49 | 59 | 41 | 51 | |

x_{3} | 900 | 1000 | 118 | 128 | 4.0 | 5.0 | 39 | 49 | 47 | 57 | 32 | 42 | |

x_{4} | 1100 | 1200 | 109 | 119 | 169.0 | 179.0 | 34 | 44 | 36 | 46 | 80 | 90 | |

e_{7} | x_{1} | 900 | 1000 | 60 | 70 | 3.0 | 3.5 | 70 | 80 | 35 | 45 | 41 | 49 |

x_{2} | 900 | 1000 | 100 | 110 | 36.0 | 46.0 | 50 | 60 | 50 | 60 | 42 | 50 | |

x_{3} | 900 | 1000 | 118 | 128 | 3.9 | 4.9 | 40 | 50 | 45 | 55 | 31 | 41 | |

x_{4} | 1088 | 1190 | 109 | 119 | 168.0 | 178.0 | 35 | 45 | 35 | 45 | 78 | 88 | |

e_{8} | x_{1} | 880 | 1000 | 60 | 70 | 3.2 | 4.2 | 71 | 80 | 35 | 45 | 40 | 49 |

x_{2} | 880 | 1000 | 100 | 112 | 38.0 | 48.8 | 51 | 60 | 48 | 58 | 40 | 49 | |

x_{3} | 880 | 1000 | 120 | 130 | 3.9 | 4.9 | 42 | 52 | 43 | 53 | 29 | 39 | |

x_{4} | 1100 | 1200 | 108 | 118 | 172.0 | 182.0 | 31 | 41 | 35 | 45 | 78 | 88 | |

e_{9} | x_{1} | 880 | 1000 | 60 | 70 | 3.1 | 3.5 | 71 | 80 | 35 | 45 | 40 | 49 |

x_{2} | 880 | 1000 | 100 | 112 | 38.0 | 48.8 | 51 | 60 | 48 | 58 | 40 | 49 | |

x_{3} | 880 | 1000 | 120 | 130 | 3.8 | 4.4 | 42 | 52 | 43 | 53 | 29 | 39 | |

x_{4} | 1100 | 1200 | 108 | 118 | 170.0 | 180.0 | 34 | 44 | 35 | 45 | 78 | 88 | |

e_{10} | x_{1} | 890 | 1000 | 60 | 70 | 3.1 | 4.1 | 70 | 80 | 35 | 45 | 40 | 49 |

x_{2} | 890 | 1000 | 100 | 110 | 38.0 | 48.0 | 52 | 57 | 48 | 58 | 40 | 49 | |

x_{3} | 890 | 1000 | 117 | 127 | 3.6 | 4.6 | 39 | 49 | 43 | 53 | 29 | 39 | |

x_{4} | 1120 | 1220 | 108 | 118 | 169.0 | 179.0 | 35 | 45 | 35 | 45 | 78 | 88 | |

e_{11} | x_{1} | 890 | 990 | 62 | 72 | 3.1 | 4.1 | 68 | 78 | 35 | 45 | 40 | 50 |

x_{2} | 890 | 990 | 100 | 111 | 38.0 | 49.0 | 50 | 60 | 48 | 58 | 40 | 50 | |

x_{3} | 890 | 990 | 115 | 125 | 3.7 | 4.7 | 39 | 49 | 46 | 56 | 28 | 38 | |

x_{4} | 1090 | 1190 | 108 | 118 | 170.0 | 180.0 | 33 | 43 | 34 | 44 | 80 | 90 | |

Scenario | s_{3} | ||||||||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |||||||

a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | ||

e_{1} | x_{1} | 800 | 900 | 40 | 50 | 23.9 | 24.9 | 40 | 50 | 85 | 95 | 80 | 90 |

x_{2} | 800 | 900 | 80 | 90 | 50.0 | 60.0 | 70 | 80 | 10 | 20 | 80 | 90 | |

x_{3} | 800 | 900 | 100 | 110 | 24.1 | 25.1 | 75 | 85 | 10 | 20 | 80 | 90 | |

x_{4} | 1000 | 1100 | 100 | 110 | 190.0 | 200.0 | 75 | 85 | 20 | 30 | 20 | 30 | |

e_{2} | x_{1} | 800 | 900 | 40 | 50 | 23.5 | 24.3 | 42 | 52 | 85 | 95 | 80 | 90 |

x_{2} | 800 | 900 | 80 | 90 | 50.0 | 60.0 | 70 | 80 | 10 | 20 | 80 | 90 | |

x_{3} | 800 | 900 | 100 | 110 | 23.8 | 24.8 | 75 | 85 | 10 | 20 | 80 | 90 | |

x_{4} | 1000 | 1100 | 100 | 110 | 190.0 | 200.1 | 76 | 86 | 20 | 30 | 20 | 30 | |

e_{3} | x_{1} | 790 | 890 | 38 | 48 | 24.0 | 25.0 | 39 | 49 | 83 | 100 | 80 | 90 |

x_{2} | 790 | 890 | 82 | 92 | 50.0 | 61.0 | 69 | 79 | 10 | 20 | 80 | 87 | |

x_{3} | 790 | 890 | 100 | 110 | 24.1 | 25.1 | 76 | 86 | 10 | 20 | 80 | 85 | |

x_{4} | 988 | 1088 | 100 | 110 | 191.0 | 200.1 | 75 | 85 | 19 | 29 | 19 | 29 | |

e_{4} | x_{1} | 800 | 900 | 40 | 50 | 24.0 | 25.0 | 40 | 50 | 86 | 96 | 81 | 91 |

x_{2} | 800 | 900 | 82 | 92 | 50.0 | 59.0 | 70 | 79 | 10 | 20 | 81 | 91 | |

x_{3} | 800 | 900 | 100 | 105 | 24.2 | 25.2 | 76 | 86 | 10 | 20 | 81 | 91 | |

x_{4} | 1010 | 1110 | 100 | 102 | 192.0 | 202.0 | 76 | 86 | 20 | 28 | 20 | 29 | |

e_{5} | x_{1} | 788 | 900 | 38 | 48 | 24.0 | 25.0 | 39 | 49 | 83 | 100 | 80 | 90 |

x_{2} | 788 | 900 | 82 | 92 | 50.0 | 61.0 | 69 | 79 | 10 | 20 | 80 | 87 | |

x_{3} | 788 | 900 | 100 | 110 | 24.1 | 25.1 | 76 | 86 | 10 | 20 | 80 | 85 | |

x_{4} | 1000 | 1100 | 100 | 110 | 191.0 | 200.1 | 75 | 85 | 19 | 29 | 19 | 29 | |

e_{6} | x_{1} | 800 | 900 | 41 | 51 | 24.1 | 25.1 | 40 | 49 | 86 | 96 | 81 | 91 |

x_{2} | 800 | 900 | 80 | 90 | 49.0 | 59.0 | 71 | 81 | 10 | 21 | 81 | 91 | |

x_{3} | 800 | 900 | 100 | 110 | 24.5 | 25.5 | 76 | 86 | 12 | 22 | 81 | 91 | |

x_{4} | 989 | 1089 | 100 | 110 | 189.0 | 199.0 | 75 | 85 | 20 | 30 | 19 | 29 | |

e_{7} | x_{1} | 800 | 900 | 40 | 50 | 23.8 | 24.8 | 40 | 50 | 85 | 95 | 81 | 91 |

x_{2} | 800 | 900 | 80 | 90 | 48.0 | 58.0 | 70 | 80 | 10 | 20 | 81 | 91 | |

x_{3} | 800 | 900 | 100 | 110 | 24.8 | 25.8 | 75 | 85 | 10 | 20 | 81 | 91 | |

x_{4} | 988 | 1090 | 100 | 110 | 188.0 | 198.0 | 75 | 85 | 20 | 30 | 22 | 32 | |

e_{8} | x_{1} | 790 | 890 | 40 | 50 | 24.0 | 25.0 | 41 | 50 | 85 | 95 | 80 | 90 |

x_{2} | 790 | 890 | 81 | 91 | 50.0 | 60.8 | 71 | 80 | 9 | 19 | 80 | 90 | |

x_{3} | 790 | 890 | 100 | 110 | 24.2 | 25.2 | 76 | 86 | 9 | 19 | 80 | 90 | |

x_{4} | 998 | 1098 | 102 | 112 | 192.0 | 202.0 | 75 | 85 | 20 | 30 | 20 | 30 | |

e_{9} | x_{1} | 790 | 890 | 40 | 50 | 23.9 | 24.9 | 41 | 50 | 85 | 95 | 80 | 90 |

x_{2} | 790 | 890 | 81 | 91 | 50.0 | 60.8 | 71 | 80 | 9 | 19 | 80 | 90 | |

x_{3} | 790 | 890 | 100 | 110 | 24.1 | 24.9 | 76 | 86 | 9 | 19 | 80 | 90 | |

x_{4} | 998 | 1098 | 102 | 112 | 190.0 | 199.0 | 75 | 85 | 20 | 30 | 20 | 30 | |

e_{10} | x_{1} | 790 | 890 | 40 | 50 | 23.9 | 24.9 | 39 | 49 | 85 | 95 | 80 | 90 |

x_{2} | 790 | 890 | 80 | 90 | 50.0 | 61.9 | 72 | 82 | 9 | 19 | 80 | 90 | |

x_{3} | 790 | 890 | 100 | 110 | 23.9 | 24.8 | 74 | 84 | 9 | 19 | 80 | 90 | |

x_{4} | 998 | 1098 | 100 | 110 | 189.0 | 199.0 | 74 | 84 | 20 | 30 | 20 | 30 | |

e_{11} | x_{1} | 800 | 900 | 43 | 53 | 23.9 | 24.9 | 41 | 51 | 86 | 96 | 80 | 90 |

x_{2} | 800 | 900 | 79 | 89 | 50.0 | 61.9 | 71 | 81 | 11 | 21 | 80 | 90 | |

x_{3} | 800 | 900 | 100 | 110 | 24.0 | 25.0 | 74 | 84 | 11 | 21 | 78 | 88 | |

x_{4} | 1000 | 1100 | 100 | 110 | 190.0 | 200.0 | 74 | 84 | 19 | 29 | 19 | 29 |

Scenario | s_{1} | ||||||||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |||||||

a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | ||

e_{1} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1250 | 0.9941 | 1.0000 | 0.8889 | 1.0000 | 0.9000 | 1.0000 | 0.9444 | 1.0000 |

x_{2} | 0.0000 | 0.3333 | 0.5000 | 0.6250 | 0.8729 | 0.8789 | 0.1111 | 0.2222 | 0.0000 | 0.1000 | 0.9444 | 1.0000 | |

x_{3} | 0.0000 | 0.3333 | 0.8750 | 1.0000 | 0.9905 | 0.9964 | 0.1111 | 0.2222 | 0.1000 | 0.2000 | 0.6667 | 0.7778 | |

x_{4} | 0.6667 | 1.0000 | 0.6250 | 0.7500 | 0.0000 | 0.0594 | 0.0000 | 0.1111 | 0.4000 | 0.5000 | 0.0000 | 0.1111 | |

e_{2} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1250 | 0.9941 | 1.0000 | 0.8901 | 1.0000 | 0.9100 | 1.0000 | 0.9444 | 1.0000 |

x_{2} | 0.0000 | 0.3333 | 0.5000 | 0.6250 | 0.8676 | 0.8735 | 0.1099 | 0.2198 | 0.0000 | 0.0900 | 0.9444 | 1.0000 | |

x_{3} | 0.0000 | 0.3333 | 0.8750 | 1.0000 | 0.9917 | 0.9976 | 0.1099 | 0.2198 | 0.1000 | 0.2000 | 0.6556 | 0.7667 | |

x_{4} | 0.6667 | 1.0000 | 0.6000 | 0.7250 | 0.0000 | 0.0600 | 0.0000 | 0.1099 | 0.4100 | 0.5100 | 0.0000 | 0.1111 | |

e_{3} | x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1282 | 0.9941 | 1.0000 | 0.8864 | 1.0000 | 0.8500 | 1.0000 | 0.9341 | 1.0000 |

x_{2} | 0.0000 | 0.3448 | 0.5385 | 0.6667 | 0.8676 | 0.8795 | 0.1023 | 0.2159 | 0.0000 | 0.1000 | 0.9341 | 1.0000 | |

x_{3} | 0.0000 | 0.3448 | 0.8718 | 1.0000 | 0.9917 | 0.9976 | 0.1023 | 0.2159 | 0.1100 | 0.2100 | 0.6154 | 0.7582 | |

x_{4} | 0.6828 | 1.0000 | 0.6154 | 0.7436 | 0.0000 | 0.0600 | 0.0000 | 0.1136 | 0.4200 | 0.5200 | 0.0000 | 0.1099 | |

e_{4} | x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1250 | 0.9994 | 1.0000 | 0.9111 | 1.0000 | 0.9100 | 1.0000 | 0.9444 | 1.0000 |

x_{2} | 0.0000 | 0.3448 | 0.5250 | 0.6500 | 0.8749 | 0.8808 | 0.1111 | 0.2111 | 0.0000 | 0.1000 | 0.9444 | 1.0000 | |

x_{3} | 0.0000 | 0.3448 | 0.8750 | 1.0000 | 0.9906 | 0.9965 | 0.1111 | 0.2111 | 0.1000 | 0.2000 | 0.6444 | 0.7556 | |

x_{4} | 0.7241 | 1.0000 | 0.6250 | 0.7500 | 0.0000 | 0.0587 | 0.0000 | 0.1000 | 0.3900 | 0.4900 | 0.0000 | 0.1111 | |

e_{5} | x_{1} | 0.0000 | 0.3548 | 0.0000 | 0.1154 | 0.9941 | 1.0000 | 0.8864 | 1.0000 | 0.8500 | 1.0000 | 0.9451 | 1.0000 |

x_{2} | 0.0000 | 0.3548 | 0.5385 | 0.6667 | 0.8675 | 0.8794 | 0.1136 | 0.2273 | 0.0000 | 0.1000 | 0.9451 | 1.0000 | |

x_{3} | 0.0000 | 0.3548 | 0.8718 | 1.0000 | 0.9923 | 0.9982 | 0.1136 | 0.2273 | 0.1200 | 0.2000 | 0.6154 | 0.7582 | |

x_{4} | 0.6774 | 1.0000 | 0.6154 | 0.7436 | 0.0000 | 0.0594 | 0.0000 | 0.1136 | 0.4100 | 0.5100 | 0.0000 | 0.1099 | |

e_{6} | x_{1} | 0.0000 | 0.3460 | 0.0000 | 0.1333 | 0.9988 | 1.0000 | 0.8989 | 1.0000 | 0.8980 | 1.0000 | 0.9556 | 1.0000 |

x_{2} | 0.0000 | 0.3460 | 0.4667 | 0.6000 | 0.8785 | 0.8845 | 0.1124 | 0.2247 | 0.0000 | 0.1020 | 0.9556 | 1.0000 | |

x_{3} | 0.0000 | 0.3460 | 0.8667 | 1.0000 | 0.9916 | 0.9976 | 0.1011 | 0.2135 | 0.0918 | 0.1939 | 0.6667 | 0.7778 | |

x_{4} | 0.6540 | 1.0000 | 0.5867 | 0.7200 | 0.0000 | 0.0602 | 0.0000 | 0.1011 | 0.3878 | 0.4898 | 0.0000 | 0.1111 | |

e_{7} | x_{1} | 0.0000 | 0.3103 | 0.0000 | 0.1282 | 0.9970 | 1.0000 | 0.8876 | 1.0000 | 0.9000 | 1.0000 | 0.9670 | 1.0000 |

x_{2} | 0.0000 | 0.3103 | 0.5128 | 0.6410 | 0.8769 | 0.8829 | 0.1011 | 0.2135 | 0.0000 | 0.1000 | 0.9560 | 1.0000 | |

x_{3} | 0.0000 | 0.3103 | 0.8718 | 1.0000 | 0.9904 | 0.9964 | 0.1011 | 0.2135 | 0.1000 | 0.2000 | 0.6593 | 0.7692 | |

x_{4} | 0.6483 | 1.0000 | 0.5513 | 0.7179 | 0.0000 | 0.0601 | 0.0000 | 0.0449 | 0.4000 | 0.5000 | 0.0000 | 0.1099 | |

e_{8} | x_{1} | 0.0000 | 0.3226 | 0.0000 | 0.1282 | 0.9982 | 1.0000 | 0.8876 | 1.0000 | 0.8990 | 1.0000 | 0.9545 | 1.0000 |

x_{2} | 0.0000 | 0.3226 | 0.5256 | 0.6538 | 0.8749 | 0.8808 | 0.1124 | 0.2247 | 0.0000 | 0.0909 | 0.9545 | 1.0000 | |

x_{3} | 0.0000 | 0.3226 | 0.8718 | 1.0000 | 0.9906 | 0.9965 | 0.1124 | 0.2247 | 0.0909 | 0.1919 | 0.7045 | 0.8182 | |

x_{4} | 0.6774 | 1.0000 | 0.5769 | 0.7051 | 0.0000 | 0.0587 | 0.0000 | 0.1124 | 0.3939 | 0.4949 | 0.0000 | 0.1136 | |

e_{9} | x_{1} | 0.0000 | 0.3247 | 0.0000 | 0.1282 | 0.9976 | 1.0000 | 0.8889 | 1.0000 | 0.8990 | 1.0000 | 0.9545 | 1.0000 |

x_{2} | 0.0000 | 0.3247 | 0.5256 | 0.6538 | 0.8729 | 0.8789 | 0.1222 | 0.2333 | 0.0000 | 0.0909 | 0.9545 | 1.0000 | |

x_{3} | 0.0000 | 0.3247 | 0.8718 | 1.0000 | 0.9905 | 0.9964 | 0.1222 | 0.2333 | 0.0909 | 0.1919 | 0.7045 | 0.8182 | |

x_{4} | 0.6753 | 1.0000 | 0.5769 | 0.7051 | 0.0000 | 0.0594 | 0.0000 | 0.1111 | 0.3939 | 0.4949 | 0.0000 | 0.1136 | |

e_{10} | x_{1} | 0.0000 | 0.3548 | 0.0000 | 0.1250 | 0.9941 | 1.0000 | 0.8889 | 1.0000 | 0.8990 | 1.0000 | 0.9545 | 1.0000 |

x_{2} | 0.0000 | 0.3548 | 0.5000 | 0.6250 | 0.8729 | 0.8789 | 0.1111 | 0.2222 | 0.0000 | 0.0909 | 0.9545 | 1.0000 | |

x_{3} | 0.0000 | 0.3548 | 0.8750 | 1.0000 | 0.9917 | 0.9976 | 0.1111 | 0.2222 | 0.0909 | 0.1919 | 0.7045 | 0.8182 | |

x_{4} | 0.6774 | 1.0000 | 0.6000 | 0.7250 | 0.0000 | 0.0594 | 0.0000 | 0.1111 | 0.3939 | 0.4949 | 0.0000 | 0.1136 | |

e_{11} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1351 | 0.9940 | 1.0000 | 0.8980 | 1.0000 | 0.9000 | 1.0000 | 0.9551 | 1.0000 |

x_{2} | 0.0000 | 0.3333 | 0.5000 | 0.6351 | 0.8600 | 0.8774 | 0.1020 | 0.1939 | 0.0000 | 0.1000 | 0.9551 | 1.0000 | |

x_{3} | 0.0000 | 0.3333 | 0.8649 | 1.0000 | 0.9910 | 0.9970 | 0.1020 | 0.1939 | 0.1000 | 0.2000 | 0.7191 | 0.8315 | |

x_{4} | 0.6833 | 0.9833 | 0.6486 | 0.7838 | 0.0000 | 0.0601 | 0.0000 | 0.0816 | 0.4000 | 0.5000 | 0.0000 | 0.1011 | |

Scenario | s_{2} | ||||||||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |||||||

a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | a_{li}^{jtL} | a_{li}^{jtU} | ||

e_{1} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1429 | 0.9943 | 1.0000 | 0.7778 | 1.0000 | 0.6000 | 1.0000 | 0.6667 | 0.8333 |

x_{2} | 0.0000 | 0.3333 | 0.5714 | 0.7143 | 0.7462 | 0.8027 | 0.3333 | 0.5556 | 0.0000 | 0.4000 | 0.6667 | 0.8333 | |

x_{3} | 0.0000 | 0.3333 | 0.8571 | 1.0000 | 0.9904 | 0.9960 | 0.1111 | 0.3333 | 0.2000 | 0.6000 | 0.8333 | 1.0000 | |

x_{4} | 0.6667 | 1.0000 | 0.7143 | 0.8571 | 0.0000 | 0.0565 | 0.0000 | 0.2222 | 0.6000 | 1.0000 | 0.0000 | 0.1667 | |

e_{2} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1429 | 0.9944 | 1.0000 | 0.7727 | 1.0000 | 0.6000 | 1.0000 | 0.6667 | 0.8333 |

x_{2} | 0.0000 | 0.3333 | 0.5714 | 0.7143 | 0.7441 | 0.8006 | 0.3182 | 0.5455 | 0.0000 | 0.4000 | 0.6667 | 0.8333 | |

x_{3} | 0.0000 | 0.3333 | 0.8571 | 1.0000 | 0.9898 | 0.9955 | 0.1364 | 0.3636 | 0.2000 | 0.6000 | 0.8333 | 1.0000 | |

x_{4} | 0.6667 | 1.0000 | 0.7143 | 0.8571 | 0.0000 | 0.0571 | 0.0000 | 0.2273 | 0.6000 | 1.0000 | 0.0000 | 0.1667 | |

e_{3} | x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1429 | 0.9983 | 1.0000 | 0.7778 | 1.0000 | 0.5556 | 0.9259 | 0.7414 | 0.8448 |

x_{2} | 0.0000 | 0.3448 | 0.5857 | 0.7286 | 0.7411 | 0.8033 | 0.3111 | 0.5333 | 0.0000 | 0.3704 | 0.7241 | 0.8448 | |

x_{3} | 0.0000 | 0.3448 | 0.8571 | 1.0000 | 0.9915 | 0.9972 | 0.0889 | 0.3111 | 0.2593 | 0.6296 | 0.8276 | 1.0000 | |

x_{4} | 0.6828 | 1.0000 | 0.8286 | 0.9714 | 0.0000 | 0.0565 | 0.0000 | 0.2222 | 0.6296 | 1.0000 | 0.0000 | 0.1552 | |

e_{4} | x_{1} | 0.0000 | 0.3226 | 0.0000 | 0.1449 | 0.9941 | 1.0000 | 0.7955 | 1.0000 | 0.6000 | 1.0000 | 0.7000 | 0.8500 |

x_{2} | 0.0000 | 0.3226 | 0.6087 | 0.7536 | 0.7420 | 0.7951 | 0.3182 | 0.4318 | 0.0000 | 0.4000 | 0.7000 | 0.8500 | |

x_{3} | 0.0000 | 0.3226 | 0.8696 | 1.0000 | 0.9900 | 0.9959 | 0.1364 | 0.3636 | 0.2000 | 0.6000 | 0.8333 | 1.0000 | |

x_{4} | 0.6774 | 1.0000 | 0.7246 | 0.8696 | 0.0000 | 0.0059 | 0.0000 | 0.2273 | 0.6000 | 1.0000 | 0.0000 | 0.1667 | |

e_{5} | x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1286 | 0.9983 | 1.0000 | 0.7778 | 1.0000 | 0.5556 | 0.9259 | 0.7414 | 0.8448 |

x_{2} | 0.0000 | 0.3448 | 0.5714 | 0.7143 | 0.7220 | 0.7895 | 0.3111 | 0.5333 | 0.0000 | 0.3704 | 0.7241 | 0.8448 | |

x_{3} | 0.0000 | 0.3448 | 0.8571 | 1.0000 | 0.9920 | 0.9977 | 0.0889 | 0.3111 | 0.2593 | 0.6296 | 0.8276 | 1.0000 | |

x_{4} | 0.7241 | 1.0000 | 0.8143 | 0.9571 | 0.0000 | 0.0572 | 0.0000 | 0.2222 | 0.6296 | 1.0000 | 0.0000 | 0.1552 | |

e_{6} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1538 | 0.9943 | 1.0000 | 0.8000 | 1.0000 | 0.5652 | 1.0000 | 0.6724 | 0.8448 |

x_{2} | 0.0000 | 0.3333 | 0.5692 | 0.7231 | 0.7513 | 0.8082 | 0.3556 | 0.5778 | 0.0000 | 0.4348 | 0.6724 | 0.8448 | |

x_{3} | 0.0000 | 0.3333 | 0.8462 | 1.0000 | 0.9903 | 0.9960 | 0.1111 | 0.3333 | 0.0870 | 0.5217 | 0.8276 | 1.0000 | |

x_{4} | 0.6667 | 1.0000 | 0.7077 | 0.8615 | 0.0000 | 0.0569 | 0.0000 | 0.2222 | 0.5652 | 1.0000 | 0.0000 | 0.1724 | |

e_{7} | x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1471 | 0.9971 | 1.0000 | 0.7778 | 1.0000 | 0.6000 | 1.0000 | 0.6842 | 0.8246 |

x_{2} | 0.0000 | 0.3448 | 0.5882 | 0.7353 | 0.7543 | 0.8114 | 0.3333 | 0.5556 | 0.0000 | 0.4000 | 0.6667 | 0.8070 | |

x_{3} | 0.0000 | 0.3448 | 0.8529 | 1.0000 | 0.9891 | 0.9949 | 0.1111 | 0.3333 | 0.2000 | 0.6000 | 0.8246 | 1.0000 | |

x_{4} | 0.6483 | 1.0000 | 0.7206 | 0.8676 | 0.0000 | 0.0571 | 0.0000 | 0.2222 | 0.6000 | 1.0000 | 0.0000 | 0.1754 | |

e_{8} | x_{1} | 0.0000 | 0.3750 | 0.0000 | 0.1429 | 0.9944 | 1.0000 | 0.8163 | 1.0000 | 0.5652 | 1.0000 | 0.6610 | 0.8136 |

x_{2} | 0.0000 | 0.3750 | 0.5714 | 0.7429 | 0.7450 | 0.8054 | 0.4082 | 0.5918 | 0.0000 | 0.4348 | 0.6610 | 0.8136 | |

x_{3} | 0.0000 | 0.3750 | 0.8571 | 1.0000 | 0.9905 | 0.9961 | 0.2245 | 0.4286 | 0.2174 | 0.6522 | 0.8305 | 1.0000 | |

x_{4} | 0.6875 | 1.0000 | 0.6857 | 0.8286 | 0.0000 | 0.0559 | 0.0000 | 0.2041 | 0.5652 | 1.0000 | 0.0000 | 0.1695 | |

e_{9} | x_{1} | 0.0000 | 0.3750 | 0.0000 | 0.1429 | 0.9977 | 1.0000 | 0.8043 | 1.0000 | 0.5652 | 1.0000 | 0.6610 | 0.8136 |

x_{2} | 0.0000 | 0.3750 | 0.5714 | 0.7429 | 0.7417 | 0.8027 | 0.3696 | 0.5652 | 0.0000 | 0.4348 | 0.6610 | 0.8136 | |

x_{3} | 0.0000 | 0.3750 | 0.8571 | 1.0000 | 0.9927 | 0.9960 | 0.1739 | 0.3913 | 0.2174 | 0.6522 | 0.8305 | 1.0000 | |

x_{4} | 0.6875 | 1.0000 | 0.6857 | 0.8286 | 0.0000 | 0.0565 | 0.0000 | 0.2174 | 0.5652 | 1.0000 | 0.0000 | 0.1695 | |

e_{10} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1493 | 0.9943 | 1.0000 | 0.7778 | 1.0000 | 0.5652 | 1.0000 | 0.6610 | 0.8136 |

x_{2} | 0.0000 | 0.3333 | 0.5970 | 0.7463 | 0.7447 | 0.8016 | 0.3778 | 0.4889 | 0.0000 | 0.4348 | 0.6610 | 0.8136 | |

x_{3} | 0.0000 | 0.3333 | 0.8507 | 1.0000 | 0.9915 | 0.9972 | 0.0889 | 0.3111 | 0.2174 | 0.6522 | 0.8305 | 1.0000 | |

x_{4} | 0.6970 | 1.0000 | 0.7164 | 0.8657 | 0.0000 | 0.0569 | 0.0000 | 0.2222 | 0.5652 | 1.0000 | 0.0000 | 0.1695 | |

e_{11} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1587 | 0.9943 | 1.0000 | 0.7778 | 1.0000 | 0.5417 | 0.9583 | 0.6452 | 0.8065 |

x_{2} | 0.0000 | 0.3333 | 0.6032 | 0.7778 | 0.7405 | 0.8027 | 0.3778 | 0.6000 | 0.0000 | 0.4167 | 0.6452 | 0.8065 | |

x_{3} | 0.0000 | 0.3333 | 0.8413 | 1.0000 | 0.9910 | 0.9966 | 0.1333 | 0.3556 | 0.0833 | 0.5000 | 0.8387 | 1.0000 | |

x_{4} | 0.6667 | 1.0000 | 0.7302 | 0.8889 | 0.0000 | 0.0565 | 0.0000 | 0.2222 | 0.5833 | 1.0000 | 0.0000 | 0.1613 | |

Alternatives/Attributes | c_{1} | c_{1} | c_{1} | c_{1} | c_{1} | c_{1} | |||||||

a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | a_{li}^{jtL} | ||

e_{1} | x_{2} | 0.0000 | 0.3333 | 0.5714 | 0.7143 | 0.7441 | 0.8006 | 0.3182 | 0.5455 | 0.0000 | 0.4000 | 0.6667 | 0.8333 |

x_{3} | 0.0000 | 0.3333 | 0.8571 | 1.0000 | 0.9898 | 0.9955 | 0.1364 | 0.3636 | 0.2000 | 0.6000 | 0.8333 | 1.0000 | |

x_{4} | 0.6667 | 1.0000 | 0.7143 | 0.8571 | 0.0000 | 0.0571 | 0.0000 | 0.2273 | 0.6000 | 1.0000 | 0.0000 | 0.1667 | |

x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1429 | 0.9983 | 1.0000 | 0.7778 | 1.0000 | 0.5556 | 0.9259 | 0.7414 | 0.8448 | |

e_{2} | x_{2} | 0.0000 | 0.3448 | 0.5857 | 0.7286 | 0.7411 | 0.8033 | 0.3111 | 0.5333 | 0.0000 | 0.3704 | 0.7241 | 0.8448 |

x_{3} | 0.0000 | 0.3448 | 0.8571 | 1.0000 | 0.9915 | 0.9972 | 0.0889 | 0.3111 | 0.2593 | 0.6296 | 0.8276 | 1.0000 | |

x_{4} | 0.6828 | 1.0000 | 0.8286 | 0.9714 | 0.0000 | 0.0565 | 0.0000 | 0.2222 | 0.6296 | 1.0000 | 0.0000 | 0.1552 | |

x_{4} | 0.6667 | 1.0000 | 0.8571 | 1.0000 | 0.0000 | 0.0572 | 0.7727 | 1.0000 | 0.7647 | 0.8824 | 0.8571 | 1.0000 | |

e_{3} | x_{1} | 0.0000 | 0.3356 | 0.0000 | 0.1389 | 0.9943 | 1.0000 | 0.0000 | 0.2128 | 0.0000 | 0.1889 | 0.0000 | 0.1408 |

x_{2} | 0.0000 | 0.3356 | 0.6111 | 0.7500 | 0.7899 | 0.8524 | 0.6383 | 0.8511 | 0.8889 | 1.0000 | 0.0423 | 0.1408 | |

x_{3} | 0.0000 | 0.3356 | 0.8611 | 1.0000 | 0.9938 | 0.9994 | 0.7872 | 1.0000 | 0.8889 | 1.0000 | 0.0704 | 0.1408 | |

x_{4} | 0.6644 | 1.0000 | 0.8611 | 1.0000 | 0.0000 | 0.0517 | 0.7660 | 0.9787 | 0.7889 | 0.9000 | 0.8592 | 1.0000 | |

e_{4} | x_{1} | 0.0000 | 0.3226 | 0.0000 | 0.1538 | 0.9944 | 1.0000 | 0.0000 | 0.2174 | 0.0000 | 0.1163 | 0.0000 | 0.1408 |

x_{2} | 0.0000 | 0.3226 | 0.6462 | 0.8000 | 0.8034 | 0.8539 | 0.6522 | 0.8478 | 0.8837 | 1.0000 | 0.0000 | 0.1408 | |

x_{3} | 0.0000 | 0.3226 | 0.9231 | 1.0000 | 0.9933 | 0.9989 | 0.7826 | 1.0000 | 0.8837 | 1.0000 | 0.0000 | 0.1408 | |

x_{4} | 0.6774 | 1.0000 | 0.9231 | 0.9538 | 0.0000 | 0.0562 | 0.7826 | 1.0000 | 0.7907 | 0.8889 | 0.8732 | 1.0000 | |

e_{5} | x_{1} | 0.0000 | 0.3590 | 0.0000 | 0.1389 | 0.9943 | 1.0000 | 0.0000 | 0.2128 | 0.0000 | 0.1889 | 0.0000 | 0.1408 |

x_{2} | 0.0000 | 0.3590 | 0.6111 | 0.7500 | 0.7899 | 0.8524 | 0.6383 | 0.8511 | 0.8889 | 1.0000 | 0.0423 | 0.1408 | |

x_{3} | 0.0000 | 0.3590 | 0.8611 | 1.0000 | 0.9938 | 0.9994 | 0.7872 | 1.0000 | 0.8889 | 1.0000 | 0.0704 | 0.1408 | |

x_{4} | 0.6795 | 1.0000 | 0.8611 | 1.0000 | 0.0000 | 0.0517 | 0.7660 | 0.9787 | 0.7889 | 0.9000 | 0.8592 | 1.0000 | |

e_{6} | x_{1} | 0.0000 | 0.3460 | 0.0000 | 0.1449 | 0.9943 | 1.0000 | 0.0000 | 0.1957 | 0.0000 | 0.1163 | 0.0000 | 0.1389 |

x_{2} | 0.0000 | 0.3460 | 0.5652 | 0.7101 | 0.8005 | 0.8576 | 0.6739 | 0.8913 | 0.8721 | 1.0000 | 0.0000 | 0.1389 | |

x_{3} | 0.0000 | 0.3460 | 0.8551 | 1.0000 | 0.9920 | 0.9977 | 0.7826 | 1.0000 | 0.8605 | 0.9767 | 0.0000 | 0.1389 | |

x_{4} | 0.6540 | 1.0000 | 0.8551 | 1.0000 | 0.0000 | 0.0572 | 0.7609 | 0.9783 | 0.7674 | 0.8837 | 0.8611 | 1.0000 | |

e_{7} | x_{1} | 0.0000 | 0.3448 | 0.0000 | 0.1429 | 0.9943 | 1.0000 | 0.0000 | 0.2222 | 0.0000 | 0.1176 | 0.0000 | 0.1449 |

x_{2} | 0.0000 | 0.3448 | 0.5714 | 0.7143 | 0.8037 | 0.8611 | 0.6667 | 0.8889 | 0.8824 | 1.0000 | 0.0000 | 0.1449 | |

x_{3} | 0.0000 | 0.3448 | 0.8571 | 1.0000 | 0.9885 | 0.9943 | 0.7778 | 1.0000 | 0.8824 | 1.0000 | 0.0000 | 0.1449 | |

x_{4} | 0.6483 | 1.0000 | 0.8571 | 1.0000 | 0.0000 | 0.0574 | 0.7778 | 1.0000 | 0.7647 | 0.8824 | 0.8551 | 1.0000 | |

e_{8} | x_{1} | 0.0000 | 0.3247 | 0.0000 | 0.1389 | 0.9944 | 1.0000 | 0.0000 | 0.2000 | 0.0000 | 0.1163 | 0.0000 | 0.1429 |

x_{2} | 0.0000 | 0.3247 | 0.5694 | 0.7083 | 0.7933 | 0.8539 | 0.6667 | 0.8667 | 0.8837 | 1.0000 | 0.0000 | 0.1429 | |

x_{3} | 0.0000 | 0.3247 | 0.8333 | 0.9722 | 0.9933 | 0.9989 | 0.7778 | 1.0000 | 0.8837 | 1.0000 | 0.0000 | 0.1429 | |

x_{4} | 0.6753 | 1.0000 | 0.8611 | 1.0000 | 0.0000 | 0.0562 | 0.7556 | 0.9778 | 0.7558 | 0.8721 | 0.8571 | 1.0000 | |

e_{9} | x_{1} | 0.0000 | 0.3247 | 0.0000 | 0.1389 | 0.9943 | 1.0000 | 0.0000 | 0.2000 | 0.0000 | 0.1163 | 0.0000 | 0.1429 |

x_{2} | 0.0000 | 0.3247 | 0.5694 | 0.7083 | 0.7893 | 0.8509 | 0.6667 | 0.8667 | 0.8837 | 1.0000 | 0.0000 | 0.1429 | |

x_{3} | 0.0000 | 0.3247 | 0.8333 | 0.9722 | 0.9943 | 0.9989 | 0.7778 | 1.0000 | 0.8837 | 1.0000 | 0.0000 | 0.1429 | |

x_{4} | 0.6753 | 1.0000 | 0.8611 | 1.0000 | 0.0000 | 0.0514 | 0.7556 | 0.9778 | 0.7558 | 0.8721 | 0.8571 | 1.0000 | |

e_{10} | x_{1} | 0.0000 | 0.3247 | 0.0000 | 0.1429 | 0.9943 | 1.0000 | 0.0000 | 0.2222 | 0.0000 | 0.1163 | 0.0000 | 0.1429 |

x_{2} | 0.0000 | 0.3247 | 0.5714 | 0.7143 | 0.7830 | 0.8509 | 0.7333 | 0.9556 | 0.8837 | 1.0000 | 0.0000 | 0.1429 | |

x_{3} | 0.0000 | 0.3247 | 0.8571 | 1.0000 | 0.9949 | 1.0000 | 0.7778 | 1.0000 | 0.8837 | 1.0000 | 0.0000 | 0.1429 | |

x_{4} | 0.6753 | 1.0000 | 0.8571 | 1.0000 | 0.0000 | 0.0571 | 0.7778 | 1.0000 | 0.7558 | 0.8721 | 0.8571 | 1.0000 | |

e_{11} | x_{1} | 0.0000 | 0.3333 | 0.0000 | 0.1493 | 0.9943 | 1.0000 | 0.0000 | 0.2326 | 0.0000 | 0.1176 | 0.0000 | 0.1408 |

x_{2} | 0.0000 | 0.3333 | 0.5373 | 0.6866 | 0.7842 | 0.8518 | 0.6977 | 0.9302 | 0.8824 | 1.0000 | 0.0000 | 0.1408 | |

x_{3} | 0.0000 | 0.3333 | 0.8507 | 1.0000 | 0.9938 | 0.9994 | 0.7674 | 1.0000 | 0.8824 | 1.0000 | 0.0282 | 0.1690 | |

x_{4} | 0.6667 | 1.0000 | 0.8507 | 1.0000 | 0.0000 | 0.0568 | 0.7674 | 1.0000 | 0.7882 | 0.9059 | 0.8592 | 1.0000 |

Scenario | s_{1} | ||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |

e_{1} | x_{1} | 0.2023 | 0.0853 | 0.9974 | 0.9509 | 0.9558 | 0.9755 |

x_{2} | 0.2023 | 0.6026 | 0.8899 | 0.2062 | 0.0701 | 0.9755 | |

x_{3} | 0.2023 | 0.9447 | 0.9942 | 0.2062 | 0.1880 | 0.7509 | |

x_{4} | 0.8512 | 0.7190 | 0.0443 | 0.0769 | 0.4951 | 0.0769 | |

e_{2} | x_{1} | 0.2023 | 0.0853 | 0.9974 | 0.9514 | 0.9603 | 0.9755 |

x_{2} | 0.2023 | 0.6026 | 0.8851 | 0.2042 | 0.0639 | 0.9755 | |

x_{3} | 0.2023 | 0.9447 | 0.9953 | 0.2042 | 0.1880 | 0.7407 | |

x_{4} | 0.8512 | 0.6959 | 0.0447 | 0.0762 | 0.5048 | 0.0769 | |

e_{3} | x_{1} | 0.2084 | 0.0873 | 0.9974 | 0.9498 | 0.9336 | 0.9709 |

x_{2} | 0.2084 | 0.6402 | 0.8878 | 0.1979 | 0.0701 | 0.9709 | |

x_{3} | 0.2084 | 0.9433 | 0.9953 | 0.1979 | 0.1990 | 0.7183 | |

x_{4} | 0.8585 | 0.7116 | 0.0447 | 0.0785 | 0.5145 | 0.0762 | |

e_{4} | x_{1} | 0.2084 | 0.0853 | 0.9997 | 0.9607 | 0.9603 | 0.9755 |

x_{2} | 0.2084 | 0.6261 | 0.8917 | 0.2002 | 0.0701 | 0.9755 | |

x_{3} | 0.2084 | 0.9447 | 0.9943 | 0.2002 | 0.1880 | 0.7305 | |

x_{4} | 0.8772 | 0.7190 | 0.0439 | 0.0701 | 0.4854 | 0.0769 | |

e_{5} | x_{1} | 0.2137 | 0.0795 | 0.9974 | 0.9498 | 0.9336 | 0.9758 |

x_{2} | 0.2137 | 0.6402 | 0.8877 | 0.2104 | 0.0701 | 0.9758 | |

x_{3} | 0.2137 | 0.9433 | 0.9958 | 0.2104 | 0.1991 | 0.7183 | |

x_{4} | 0.8560 | 0.7116 | 0.0443 | 0.0785 | 0.5048 | 0.0762 | |

e_{6} | x_{1} | 0.2091 | 0.0903 | 0.9995 | 0.9553 | 0.9549 | 0.9804 |

x_{2} | 0.2091 | 0.5750 | 0.8949 | 0.2083 | 0.0714 | 0.9804 | |

x_{3} | 0.2091 | 0.9410 | 0.9952 | 0.1959 | 0.1800 | 0.7509 | |

x_{4} | 0.8454 | 0.6874 | 0.0448 | 0.0708 | 0.4843 | 0.0769 | |

e_{7} | x_{1} | 0.1900 | 0.0873 | 0.9987 | 0.9503 | 0.9558 | 0.9855 |

x_{2} | 0.1900 | 0.6162 | 0.8935 | 0.1959 | 0.0701 | 0.9806 | |

x_{3} | 0.1900 | 0.9433 | 0.9942 | 0.1959 | 0.1880 | 0.7436 | |

x_{4} | 0.8428 | 0.6700 | 0.0448 | 0.0347 | 0.4951 | 0.0762 | |

e_{8} | x_{1} | 0.1965 | 0.0873 | 0.9992 | 0.9503 | 0.9554 | 0.9800 |

x_{2} | 0.1965 | 0.6282 | 0.8917 | 0.2083 | 0.0645 | 0.9800 | |

x_{3} | 0.1965 | 0.9433 | 0.9943 | 0.2083 | 0.1784 | 0.7866 | |

x_{4} | 0.8560 | 0.6760 | 0.0439 | 0.0777 | 0.4898 | 0.0785 | |

e_{9} | x_{1} | 0.1977 | 0.0873 | 0.9990 | 0.9509 | 0.9554 | 0.9800 |

x_{2} | 0.1977 | 0.6282 | 0.8899 | 0.2183 | 0.0645 | 0.9800 | |

x_{3} | 0.1977 | 0.9433 | 0.9942 | 0.2183 | 0.1784 | 0.7866 | |

x_{4} | 0.8551 | 0.6760 | 0.0443 | 0.0769 | 0.4898 | 0.0785 | |

e_{10} | x_{1} | 0.2137 | 0.0853 | 0.9974 | 0.9509 | 0.9554 | 0.9800 |

x_{2} | 0.2137 | 0.6026 | 0.8899 | 0.2062 | 0.0645 | 0.9800 | |

x_{3} | 0.2137 | 0.9447 | 0.9953 | 0.2062 | 0.1784 | 0.7866 | |

x_{4} | 0.8560 | 0.6959 | 0.0443 | 0.0769 | 0.4898 | 0.0785 | |

e_{11} | x_{1} | 0.2023 | 0.0914 | 0.9974 | 0.9549 | 0.9558 | 0.9802 |

x_{2} | 0.2023 | 0.6073 | 0.8835 | 0.1858 | 0.0701 | 0.9802 | |

x_{3} | 0.2023 | 0.9402 | 0.9947 | 0.1858 | 0.1880 | 0.7993 | |

x_{4} | 0.8513 | 0.7454 | 0.0448 | 0.0587 | 0.4951 | 0.0708 | |

Scenario | s_{2} | ||||||

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |

e_{1} | x_{1} | 0.2023 | 0.0960 | 0.9975 | 0.9013 | 0.8208 | 0.7762 |

x_{2} | 0.2023 | 0.6777 | 0.7986 | 0.4893 | 0.2375 | 0.7762 | |

x_{3} | 0.2023 | 0.9368 | 0.9940 | 0.2650 | 0.4445 | 0.9262 | |

x_{4} | 0.8512 | 0.8087 | 0.0424 | 0.1416 | 0.8208 | 0.1099 | |

e_{2} | x_{1} | 0.2023 | 0.0960 | 0.9975 | 0.8990 | 0.8208 | 0.7762 |

x_{2} | 0.2023 | 0.6777 | 0.7966 | 0.4770 | 0.2375 | 0.7762 | |

x_{3} | 0.2023 | 0.9368 | 0.9935 | 0.2941 | 0.4445 | 0.9262 | |

x_{4} | 0.8512 | 0.8087 | 0.0428 | 0.1444 | 0.8208 | 0.1099 | |

e_{3} | x_{1} | 0.2084 | 0.0960 | 0.9993 | 0.9013 | 0.7671 | 0.8154 |

x_{2} | 0.2084 | 0.6910 | 0.7965 | 0.4677 | 0.2219 | 0.8076 | |

x_{3} | 0.2084 | 0.9368 | 0.9950 | 0.2412 | 0.4883 | 0.9236 | |

x_{4} | 0.8585 | 0.9114 | 0.0424 | 0.1416 | 0.8343 | 0.1032 | |

e_{4} | x_{1} | 0.1965 | 0.0972 | 0.9974 | 0.9092 | 0.8208 | 0.7989 |

x_{2} | 0.1965 | 0.7131 | 0.7932 | 0.4217 | 0.2375 | 0.7989 | |

x_{3} | 0.1965 | 0.9423 | 0.9938 | 0.2941 | 0.4445 | 0.9262 | |

x_{4} | 0.8560 | 0.8190 | 0.0058 | 0.1444 | 0.8208 | 0.1099 | |

e_{5} | x_{1} | 0.2084 | 0.0875 | 0.9992 | 0.9013 | 0.7671 | 0.8154 |

x_{2} | 0.2084 | 0.6777 | 0.7815 | 0.4677 | 0.2219 | 0.8076 | |

x_{3} | 0.2084 | 0.9368 | 0.9955 | 0.2412 | 0.4883 | 0.9236 | |

x_{4} | 0.8772 | 0.8986 | 0.0429 | 0.1416 | 0.8343 | 0.1032 | |

e_{6} | x_{1} | 0.2023 | 0.1024 | 0.9975 | 0.9113 | 0.8049 | 0.7840 |

x_{2} | 0.2023 | 0.6807 | 0.8033 | 0.5108 | 0.2556 | 0.7840 | |

x_{3} | 0.2023 | 0.9319 | 0.9940 | 0.2650 | 0.3477 | 0.9236 | |

x_{4} | 0.8512 | 0.8077 | 0.0427 | 0.1416 | 0.8049 | 0.1132 | |

e_{7} | x_{1} | 0.2084 | 0.0985 | 0.9987 | 0.9013 | 0.8208 | 0.7802 |

x_{2} | 0.2084 | 0.6952 | 0.8062 | 0.4893 | 0.2375 | 0.7642 | |

x_{3} | 0.2084 | 0.9349 | 0.9930 | 0.2650 | 0.4445 | 0.9222 | |

x_{4} | 0.8428 | 0.8163 | 0.0429 | 0.1416 | 0.8208 | 0.1150 | |

e_{8} | x_{1} | 0.2244 | 0.0960 | 0.9975 | 0.9186 | 0.8049 | 0.7646 |

x_{2} | 0.2244 | 0.6909 | 0.7992 | 0.5430 | 0.2556 | 0.7646 | |

x_{3} | 0.2244 | 0.9368 | 0.9941 | 0.3728 | 0.4783 | 0.9249 | |

x_{4} | 0.8606 | 0.7827 | 0.0420 | 0.1314 | 0.8049 | 0.1116 | |

e_{9} | x_{1} | 0.2244 | 0.0960 | 0.9990 | 0.9132 | 0.8049 | 0.7646 |

x_{2} | 0.2244 | 0.6909 | 0.7965 | 0.5117 | 0.2556 | 0.7646 | |

x_{3} | 0.2244 | 0.9368 | 0.9950 | 0.3280 | 0.4783 | 0.9249 | |

x_{4} | 0.8606 | 0.7827 | 0.0424 | 0.1389 | 0.8049 | 0.1116 | |

e_{10} | x_{1} | 0.2023 | 0.0997 | 0.9975 | 0.9013 | 0.8049 | 0.7646 |

x_{2} | 0.2023 | 0.7043 | 0.7974 | 0.4789 | 0.2556 | 0.7646 | |

x_{3} | 0.2023 | 0.9339 | 0.9950 | 0.2412 | 0.4783 | 0.9249 | |

x_{4} | 0.8649 | 0.8135 | 0.0427 | 0.1416 | 0.8049 | 0.1116 | |

e_{11} | x_{1} | 0.2023 | 0.1053 | 0.9975 | 0.9013 | 0.7753 | 0.7541 |

x_{2} | 0.2023 | 0.7217 | 0.7960 | 0.5322 | 0.2462 | 0.7541 | |

x_{3} | 0.2023 | 0.9297 | 0.9945 | 0.2884 | 0.3349 | 0.9286 | |

x_{4} | 0.8512 | 0.8302 | 0.0424 | 0.1416 | 0.8132 | 0.1068 | |

Scenario | s_{3} | ||||||

alternatives/attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |

e_{1} | x_{1} | 0.2023 | 0.0960 | 0.9975 | 0.1416 | 0.0809 | 0.0960 |

x_{2} | 0.2023 | 0.6777 | 0.8428 | 0.8013 | 0.9480 | 0.0960 | |

x_{3} | 0.2023 | 0.9368 | 0.9965 | 0.9013 | 0.9480 | 0.0960 | |

x_{4} | 0.8512 | 0.9368 | 0.0426 | 0.9013 | 0.8429 | 0.9368 | |

e_{2} | x_{1} | 0.2023 | 0.0960 | 0.9980 | 0.1444 | 0.0809 | 0.0960 |

x_{2} | 0.2023 | 0.6777 | 0.8412 | 0.7760 | 0.9480 | 0.0960 | |

x_{3} | 0.2023 | 0.9368 | 0.9960 | 0.8787 | 0.9480 | 0.0960 | |

x_{4} | 0.8512 | 0.9368 | 0.0429 | 0.8990 | 0.8429 | 0.9368 | |

e_{3} | x_{1} | 0.2035 | 0.0936 | 0.9975 | 0.1363 | 0.1227 | 0.0948 |

x_{2} | 0.2035 | 0.7126 | 0.8408 | 0.7712 | 0.9509 | 0.1213 | |

x_{3} | 0.2035 | 0.9385 | 0.9970 | 0.9055 | 0.9509 | 0.1381 | |

x_{4} | 0.8501 | 0.9385 | 0.0392 | 0.8865 | 0.8617 | 0.9377 | |

e_{4} | x_{1} | 0.1965 | 0.1024 | 0.9975 | 0.1389 | 0.0801 | 0.0948 |

x_{2} | 0.1965 | 0.7516 | 0.8475 | 0.7761 | 0.9486 | 0.0948 | |

x_{3} | 0.1965 | 0.9660 | 0.9965 | 0.9035 | 0.9486 | 0.0948 | |

x_{4} | 0.8560 | 0.9456 | 0.0422 | 0.9035 | 0.8575 | 0.9439 | |

e_{5} | x_{1} | 0.2159 | 0.0936 | 0.9975 | 0.1363 | 0.1227 | 0.0948 |

x_{2} | 0.2159 | 0.7126 | 0.8408 | 0.7712 | 0.9509 | 0.1213 | |

x_{3} | 0.2159 | 0.9385 | 0.9970 | 0.9055 | 0.9509 | 0.1381 | |

x_{4} | 0.8570 | 0.9385 | 0.0392 | 0.8865 | 0.8617 | 0.9377 | |

e_{6} | x_{1} | 0.2091 | 0.0972 | 0.9975 | 0.1266 | 0.0801 | 0.0936 |

x_{2} | 0.2091 | 0.6729 | 0.8479 | 0.8057 | 0.9434 | 0.0936 | |

x_{3} | 0.2091 | 0.9358 | 0.9955 | 0.9035 | 0.9279 | 0.0936 | |

x_{4} | 0.8454 | 0.9358 | 0.0429 | 0.8840 | 0.8447 | 0.9385 | |

e_{7} | x_{1} | 0.2084 | 0.0960 | 0.9975 | 0.1416 | 0.0809 | 0.0972 |

x_{2} | 0.2084 | 0.6777 | 0.8509 | 0.8013 | 0.9480 | 0.0972 | |

x_{3} | 0.2084 | 0.9368 | 0.9924 | 0.9013 | 0.9480 | 0.0972 | |

x_{4} | 0.8428 | 0.9368 | 0.0430 | 0.9013 | 0.8429 | 0.9358 | |

e_{8} | x_{1} | 0.1977 | 0.0936 | 0.9975 | 0.1290 | 0.0801 | 0.0960 |

x_{2} | 0.1977 | 0.6740 | 0.8430 | 0.7913 | 0.9486 | 0.0960 | |

x_{3} | 0.1977 | 0.9138 | 0.9965 | 0.9013 | 0.9486 | 0.0960 | |

x_{4} | 0.8551 | 0.9385 | 0.0422 | 0.8814 | 0.8342 | 0.9368 | |

e_{9} | x_{1} | 0.1977 | 0.0936 | 0.9975 | 0.1290 | 0.0801 | 0.0960 |

x_{2} | 0.1977 | 0.6740 | 0.8398 | 0.7913 | 0.9486 | 0.0960 | |

x_{3} | 0.1977 | 0.9138 | 0.9970 | 0.9013 | 0.9486 | 0.0960 | |

x_{4} | 0.8551 | 0.9385 | 0.0390 | 0.8814 | 0.8342 | 0.9368 | |

e_{10} | x_{1} | 0.1977 | 0.0960 | 0.9975 | 0.1416 | 0.0801 | 0.0960 |

x_{2} | 0.1977 | 0.6777 | 0.8370 | 0.8615 | 0.9486 | 0.0960 | |

x_{3} | 0.1977 | 0.9368 | 0.9977 | 0.9013 | 0.9486 | 0.0960 | |

x_{4} | 0.8551 | 0.9368 | 0.0428 | 0.9013 | 0.8342 | 0.9368 | |

e_{11} | x_{1} | 0.2023 | 0.0997 | 0.9975 | 0.1474 | 0.0809 | 0.0948 |

x_{2} | 0.2023 | 0.6489 | 0.8379 | 0.8340 | 0.9480 | 0.0948 | |

x_{3} | 0.2023 | 0.9339 | 0.9970 | 0.8967 | 0.9480 | 0.1289 | |

x_{4} | 0.8512 | 0.9339 | 0.0426 | 0.8967 | 0.8640 | 0.9377 |

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | |
---|---|---|---|---|---|---|---|

e_{1} | x_{1} | 0.2023 | 0.0929 | 0.9975 | 0.8286 | 0.7748 | 0.7554 |

x_{2} | 0.2023 | 0.6562 | 0.8297 | 0.4441 | 0.2709 | 0.7554 | |

x_{3} | 0.2023 | 0.9390 | 0.9944 | 0.3209 | 0.4287 | 0.7812 | |

x_{4} | 0.8512 | 0.7977 | 0.0430 | 0.2099 | 0.7303 | 0.1950 | |

e_{2} | x_{1} | 0.2023 | 0.0929 | 0.9975 | 0.8278 | 0.7761 | 0.7554 |

x_{2} | 0.2023 | 0.6562 | 0.8270 | 0.4333 | 0.2691 | 0.7554 | |

x_{3} | 0.2023 | 0.9390 | 0.9943 | 0.3353 | 0.4287 | 0.7783 | |

x_{4} | 0.8512 | 0.7911 | 0.0434 | 0.2112 | 0.7330 | 0.1950 | |

e_{3} | x_{1} | 0.2079 | 0.0932 | 0.9985 | 0.8277 | 0.7410 | 0.7775 |

x_{2} | 0.2079 | 0.6789 | 0.8276 | 0.4253 | 0.2619 | 0.7758 | |

x_{3} | 0.2079 | 0.9388 | 0.9953 | 0.3048 | 0.4585 | 0.7752 | |

x_{4} | 0.8575 | 0.8574 | 0.0427 | 0.2087 | 0.7461 | 0.1909 | |

e_{4} | x_{1} | 0.1999 | 0.0944 | 0.9981 | 0.8359 | 0.7760 | 0.7689 |

x_{2} | 0.1999 | 0.6927 | 0.8276 | 0.3989 | 0.2709 | 0.7689 | |

x_{3} | 0.1999 | 0.9457 | 0.9942 | 0.3369 | 0.4288 | 0.7752 | |

x_{4} | 0.8621 | 0.8049 | 0.0208 | 0.2099 | 0.7292 | 0.1958 | |

e_{5} | x_{1} | 0.2108 | 0.0859 | 0.9985 | 0.8277 | 0.7410 | 0.7789 |

x_{2} | 0.2108 | 0.6710 | 0.8186 | 0.4288 | 0.2619 | 0.7772 | |

x_{3} | 0.2108 | 0.9388 | 0.9957 | 0.3083 | 0.4586 | 0.7752 | |

x_{4} | 0.8688 | 0.8497 | 0.0429 | 0.2087 | 0.7433 | 0.1909 | |

e_{6} | x_{1} | 0.2050 | 0.0984 | 0.9981 | 0.8342 | 0.7649 | 0.7612 |

x_{2} | 0.2050 | 0.6496 | 0.8346 | 0.4581 | 0.2816 | 0.7612 | |

x_{3} | 0.2050 | 0.9349 | 0.9945 | 0.3182 | 0.3661 | 0.7794 | |

x_{4} | 0.8489 | 0.7880 | 0.0433 | 0.2062 | 0.7178 | 0.1972 | |

e_{7} | x_{1} | 0.2031 | 0.0950 | 0.9986 | 0.8285 | 0.7748 | 0.7608 |

x_{2} | 0.2031 | 0.6706 | 0.8362 | 0.4412 | 0.2709 | 0.7498 | |

x_{3} | 0.2031 | 0.9375 | 0.9932 | 0.3180 | 0.4287 | 0.7769 | |

x_{4} | 0.8428 | 0.7883 | 0.0434 | 0.1979 | 0.7303 | 0.1977 | |

e_{8} | x_{1} | 0.2134 | 0.0932 | 0.9980 | 0.8374 | 0.7650 | 0.7497 |

x_{2} | 0.2134 | 0.6711 | 0.8306 | 0.4758 | 0.2802 | 0.7497 | |

x_{3} | 0.2134 | 0.9360 | 0.9944 | 0.3862 | 0.4464 | 0.7906 | |

x_{4} | 0.8587 | 0.7701 | 0.0426 | 0.2017 | 0.7182 | 0.1964 | |

e_{9} | x_{1} | 0.2137 | 0.0932 | 0.9988 | 0.8343 | 0.7650 | 0.7497 |

x_{2} | 0.2137 | 0.6711 | 0.8281 | 0.4598 | 0.2802 | 0.7497 | |

x_{3} | 0.2137 | 0.9360 | 0.9950 | 0.3622 | 0.4464 | 0.7906 | |

x_{4} | 0.8584 | 0.7701 | 0.0426 | 0.2060 | 0.7182 | 0.1964 | |

e_{10} | x_{1} | 0.2050 | 0.0952 | 0.9975 | 0.8286 | 0.7650 | 0.7497 |

x_{2} | 0.2050 | 0.6722 | 0.8284 | 0.4447 | 0.2802 | 0.7497 | |

x_{3} | 0.2050 | 0.9373 | 0.9954 | 0.3067 | 0.4464 | 0.7906 | |

x_{4} | 0.8612 | 0.7940 | 0.0432 | 0.2099 | 0.7182 | 0.1964 | |

e_{11} | x_{1} | 0.2023 | 0.1007 | 0.9975 | 0.8304 | 0.7475 | 0.7433 |

x_{2} | 0.2023 | 0.6807 | 0.8258 | 0.4677 | 0.2761 | 0.7433 | |

x_{3} | 0.2023 | 0.9332 | 0.9949 | 0.3286 | 0.3630 | 0.8002 | |

x_{4} | 0.8512 | 0.8178 | 0.0431 | 0.2042 | 0.7281 | 0.1915 |

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p^{G}(s_{d}′|s_{t}) | s_{1} | s_{2} | s_{3} |
---|---|---|---|

s_{1}′ | 0.7 | 0.2 | 0.1 |

s_{2}′ | 0.2 | 0.7 | 0.2 |

s_{3}′ | 0.1 | 0.1 | 0.7 |

p^{G}(s_{t}|s_{d}′) | s_{1}′ | s_{2}′ | s_{3}′ |
---|---|---|---|

s_{1} | 0.8140 | 0.2857 | 0.2272 |

s_{2} | 0.1395 | 0.6000 | 0.1363 |

s_{3} | 0.0465 | 0.1142 | 0.6363 |

Aggregations | Experts | Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} |
---|---|---|---|---|---|---|---|---|

R^{1} | e_{3} | x_{1} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 |

x_{2} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{3} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{4} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

e_{5} | x_{1} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | |

x_{2} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{3} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{4} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

R^{2} | e_{8} | x_{1} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 |

x_{2} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{3} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{4} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

e_{9} | x_{1} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | |

x_{2} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{3} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{4} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

R^{3} | e_{1} | x_{1} | 0.2001 | 0.2000 | 0.2000 | 0.2002 | 0.2003 | 0.2004 |

x_{2} | 0.2001 | 0.2002 | 0.2002 | 0.2009 | 0.2003 | 0.2004 | ||

x_{3} | 0.2001 | 0.2002 | 0.2000 | 0.2006 | 0.2004 | 0.2002 | ||

x_{4} | 0.2004 | 0.2002 | 0.2005 | 0.2003 | 0.2003 | 0.2000 | ||

e_{2} | x_{1} | 0.2001 | 0.2000 | 0.2000 | 0.2001 | 0.2002 | 0.2004 | |

x_{2} | 0.2001 | 0.2002 | 0.2001 | 0.2007 | 0.2001 | 0.2004 | ||

x_{3} | 0.2001 | 0.2002 | 0.2001 | 0.2000 | 0.2004 | 0.2003 | ||

x_{4} | 0.2004 | 0.2002 | 0.2005 | 0.2002 | 0.2000 | 0.2000 | ||

e_{4} | x_{1} | 0.1998 | 0.2000 | 0.2000 | 0.1993 | 0.2002 | 0.1992 | |

x_{2} | 0.1998 | 0.1982 | 0.2002 | 0.1965 | 0.2003 | 0.1988 | ||

x_{3} | 0.1998 | 0.1994 | 0.2000 | 0.1998 | 0.2004 | 0.2001 | ||

x_{4} | 0.1999 | 0.1993 | 0.1979 | 0.2003 | 0.2003 | 0.2001 | ||

e_{7} | x_{1} | 0.2001 | 0.2000 | 0.1999 | 0.2002 | 0.2003 | 0.2002 | |

x_{2} | 0.2001 | 0.2008 | 0.1994 | 0.2010 | 0.2003 | 0.2002 | ||

x_{3} | 0.2001 | 0.2001 | 0.1999 | 0.2005 | 0.2004 | 0.2003 | ||

x_{4} | 0.1994 | 0.1999 | 0.2005 | 0.1989 | 0.2003 | 0.1999 | ||

e_{10} | x_{1} | 0.1999 | 0.2000 | 0.2000 | 0.2002 | 0.1991 | 0.1997 | |

x_{2} | 0.1999 | 0.2007 | 0.2002 | 0.2008 | 0.1992 | 0.2002 | ||

x_{3} | 0.1999 | 0.2001 | 0.1999 | 0.1991 | 0.1983 | 0.1991 | ||

x_{4} | 0.2000 | 0.2003 | 0.2005 | 0.2003 | 0.1990 | 0.2000 | ||

R^{4} | e_{6} | x_{1} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 |

x_{2} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{3} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{4} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

e_{11} | x_{1} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | |

x_{2} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{3} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | ||

x_{4} | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 | 0.5000 |

Aggregations | Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} |
---|---|---|---|---|---|---|---|

R^{1} | x_{1} | 0.2093 | 0.0896 | 0.9985 | 0.8277 | 0.7410 | 0.7782 |

x_{2} | 0.2093 | 0.6750 | 0.8231 | 0.4271 | 0.2619 | 0.7765 | |

x_{3} | 0.2093 | 0.9388 | 0.9955 | 0.3066 | 0.4586 | 0.7752 | |

x_{4} | 0.8632 | 0.8536 | 0.0428 | 0.2087 | 0.7447 | 0.1909 | |

R^{2} | x_{1} | 0.2135 | 0.0932 | 0.9984 | 0.8359 | 0.7650 | 0.7497 |

x_{2} | 0.2135 | 0.6711 | 0.8294 | 0.4678 | 0.2802 | 0.7497 | |

x_{3} | 0.2135 | 0.9360 | 0.9947 | 0.3742 | 0.4464 | 0.7906 | |

x_{4} | 0.8585 | 0.7701 | 0.0426 | 0.2039 | 0.7182 | 0.1964 | |

R^{3} | x_{1} | 0.2025 | 0.0941 | 0.9978 | 0.8299 | 0.7734 | 0.7580 |

x_{2} | 0.2025 | 0.6696 | 0.8298 | 0.4326 | 0.2724 | 0.7558 | |

x_{3} | 0.2025 | 0.9397 | 0.9943 | 0.3236 | 0.4322 | 0.7805 | |

x_{4} | 0.8537 | 0.7952 | 0.0388 | 0.2078 | 0.7282 | 0.1960 | |

R^{4} | x_{1} | 0.2036 | 0.0995 | 0.9978 | 0.8323 | 0.7562 | 0.7523 |

x_{2} | 0.2036 | 0.6652 | 0.8302 | 0.4629 | 0.2788 | 0.7523 | |

x_{3} | 0.2036 | 0.9341 | 0.9947 | 0.3234 | 0.3645 | 0.7898 | |

x_{4} | 0.8500 | 0.8029 | 0.0432 | 0.2052 | 0.7230 | 0.1943 |

Alternatives/Attributes | c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} |
---|---|---|---|---|---|---|

x_{1} | 0.2060 | 0.0941 | 0.9980 | 0.8310 | 0.7628 | 0.7591 |

x_{2} | 0.2060 | 0.6700 | 0.8286 | 0.4435 | 0.2731 | 0.7578 |

x_{3} | 0.2060 | 0.9379 | 0.9947 | 0.3296 | 0.4273 | 0.7830 |

x_{4} | 0.8556 | 0.8026 | 0.0410 | 0.2068 | 0.7284 | 0.1948 |

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**MDPI and ACS Style**

Wang, P.; Chen, J.
A Large Group Emergency Decision Making Method Considering Scenarios and Unknown Attribute Weights. *Symmetry* **2023**, *15*, 223.
https://doi.org/10.3390/sym15010223

**AMA Style**

Wang P, Chen J.
A Large Group Emergency Decision Making Method Considering Scenarios and Unknown Attribute Weights. *Symmetry*. 2023; 15(1):223.
https://doi.org/10.3390/sym15010223

**Chicago/Turabian Style**

Wang, Pingping, and Jiahua Chen.
2023. "A Large Group Emergency Decision Making Method Considering Scenarios and Unknown Attribute Weights" *Symmetry* 15, no. 1: 223.
https://doi.org/10.3390/sym15010223