# Application of the Fuzzy CODAS Method Based on Fuzzy Envelopes for Hesitant Fuzzy Linguistic Term Sets: A Case Study on a Personnel Selection Problem

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Hesitant Fuzzy Set (HFS)

#### 2.2. Hesitant Fuzzy Linguistic Term Sets (HFLTSs)

#### 2.3. Fuzzy Envelope for HFLTSs

#### 2.4. Trapezoidal Fuzzy Numbers

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

_{E}) and Hamming (d

_{H}) distance between two trapezoidal fuzzy numbers${\tilde{A}}_{1}=\left({a}_{1},{b}_{1},{c}_{1},{d}_{1}\right)$and${\tilde{A}}_{2}=\left({a}_{2},{b}_{2},{c}_{2},{d}_{2}\right)$are defined as follows, respectively [76,89]:

## 3. Proposed Methodology

#### 3.1. Representation of the Proposed Methodology

#### 3.2. The Fuzzy CODAS Method

**Step 1.**Construct the fuzzy decision matrix as $\tilde{X}={\left[{\tilde{x}}_{ij}\right]}_{mxn},\text{\hspace{0.17em}}i=1,2,...,m;\text{\hspace{0.17em}}j=1,2,...,n$, where each ${\tilde{x}}_{ij}$ indicates the fuzzy performance score for the alternative ${A}_{i}$ with respect to the criterion ${C}_{j}$ by decision-makers. The ${\tilde{x}}_{ij}$ is obtained from the fuzzy envelope of the HFLTS for CLEs and stated as ${\tilde{x}}_{ij}=env({H}_{{S}_{ij}})=T({x}_{ij1},{x}_{ij2},{x}_{ij3},{x}_{ij4})$. T denotes the trapezoidal fuzzy number.

**Step 2.**Obtain the fuzzy weight vector of the criteria as $\tilde{W}={\left[{\tilde{w}}_{j}\right]}_{1xn},\text{\hspace{0.17em}}j=1,2,...,n$, where each ${\tilde{w}}_{j}$ identifies the fuzzy criterion’s importance by decision-makers. The ${\tilde{w}}_{j}$ is handled by using the fuzzy envelope of the HFLTS for CLEs and denoted as ${\tilde{w}}_{j}=env({H}_{{U}_{j}})=T({w}_{j1},{w}_{j2},{w}_{j3},{w}_{j4})$. T denotes the trapezoidal fuzzy number.

**Step 3.**Determine the fuzzy normalized decision matrix, $\tilde{N}={\left[{\tilde{n}}_{ij}\right]}_{mxn},\text{\hspace{0.17em}}i=1,2,...,m;\text{\hspace{0.17em}}j=1,2,...,n$, by using

**Step 4.**Construct the fuzzy weighted normalized decision matrix values of $\tilde{R}={\left[{\tilde{r}}_{ij}\right]}_{mxn},\text{\hspace{0.17em}}i=1,2,...,m;\text{\hspace{0.17em}}j=1,2,...,n$ as follows:

**Step 5.**Determine the fuzzy negative ideal solution $\tilde{NS}={\left[{\tilde{ns}}_{j}\right]}_{1\times m}$ as follows:

**Step 6.**Compute the Euclidean distance (ED

_{i}) and Hamming distance (HD

_{i}) of each alternative from the fuzzy negative ideal solution by using

**Step 7.**Define the relative assessment matrix $RA={\left[{p}_{ik}\right]}_{m\times n}$ as follows:

**Step 8.**Calculate the assessment score of each alternative as follows:

**Step 9.**Rank the alternatives according to the decreasing values of $A{S}_{i},\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}i=1,...,m$. The alternative with the highest assessment score is the most desirable alternative.

## 4. A Case Study of a Blue-Collar Personnel Selection Problem

#### 4.1. Application of the Proposed Methodology

_{i}) was computed by using Equation (54), and the elements of the relative assessment matrix are given in Table 6. The ranking of the alternatives was made based on decreasing values of the assessment scores shown in Table 7. The ranking results showed that Alternative 4 is the best among the alternatives.

#### 4.2. Sensitivity Analysis

#### 4.3. Comparative Analysis

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Table 1.**Some of the literature on fuzzy multi-criteria decision-making (MCDM) methods for personnel selection.

Author(s) | Applied Method(s) |
---|---|

Liang and Wang [26] | A two-stage fuzzy MCDM |

Yaakob and Kawata [27] | A fuzzy linguistic evaluation |

Chen [28] | Fuzzy TOPSIS |

Tsao and Chue [29] | Improved fuzzy MCDM algorithm |

Karsak [30] | A distance-based fuzzy TOPSIS |

Capaldo and Zollo [31] | A fuzzy logic evaluation method |

Huang et al. [32] | Fuzzy AHP, Fuzzy Neural Networks, and SAW |

Saghafian and Hejazi [33] | A modified Fuzzy TOPSIS |

Golec and Kahya [34] | A fuzzy rule base approach |

Mahdavi et al. [35] | Fuzzy TOPSIS |

Güngör et al. [36] | Fuzzy AHP |

Ayub et al. [37] | Fuzzy ANP |

Polychroniou and Giannikos [38] | Fuzzy TOPSIS |

Kelemenis and Askounis [39] | Fuzzy TOPSIS |

Kelemenis et al. [40] | A novel fuzzy TOPSIS |

Balezěntis et al. [41] | Fuzzy MULTIMOORA |

Kabak et al. [42] | Fuzzy ANP, Fuzzy TOPSIS and Fuzzy ELECTRE |

Rouyendegh and Erkan [43] | Fuzzy ELECTRE |

Aggarwal [44] | Fuzzy-Delphi and Fuzzy AHP |

Keršulienė and Turskis [45] | A hybrid linguistic fuzzy multiple criteria |

Sang et al. [46] | Karnik–Mendel algorithm-based fuzzy TOPSIS |

Chang [47] | Fuzzy Delphi, ANP, and TOPSIS |

**Table 2.**The linguistic expressions and corresponding triangular fuzzy numbers used for evaluations.

Linguistic Expressions for the Criteria | Linguistic Expressions for the Alternatives | Triangular Fuzzy Numbers |
---|---|---|

Definitely low (DL) | Nothing (N) | (0, 0, 0.17) |

Very low (VL) | Very bad (VB) | (0, 0.17, 0.33) |

Low (L) | Bad (B) | (0.17, 0.33, 0.5) |

Middle (M) | Medium (M) | (0.33, 0.5, 0.67) |

High (H) | Good (G) | (0.5, 0.67, 0.83) |

Very high (VH) | Very Good (VG) | (0.67, 0.83, 1) |

Definitely high (DH) | Perfect (P) | (0.83, 1, 1) |

**Table 3.**The aggregated evaluations of both the criteria and the alternatives using comparative linguistic expressions (CLEs) from the experts.

The Aggregated Evaluations of the Criteria | |||||||||||

Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 |

CLEs | between L and H | DH | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH |

The Aggregated Evaluations of the Alternatives with Respect to the Criteria | |||||||||||

Alternatives\Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 |

A1 | M | at least VG | at least M | at least G | between M and G | at least G | at most M | at least G | between M and VG | M | at least G |

A2 | M | at least G | between M and VG | M | between B and M | at least G | between VB and M | at least G | between M and G | between M and G | at least G |

A3 | between M and VG | at least G | M | M | between B and M | between M and VG | between B and G | between G and VG | between M and G | between M and VG | at least G |

A4 | between M and VG | between G and VG | G | at least G | M | between M and VG | between B and G | at least VG | between G and VG | between M and VG | between G and VG |

A5 | between M and VG | at least VG | M | between M and VG | between M and G | between M and VG | between VB and G | at least G | between M and VG | M | between M and G |

A6 | M | between B and G | between M and VG | between M and VG | between M and G | between M and VG | between VB and G | between M and G | between B and M | between VB and M | between VB and M |

**Table 4.**The HFLTSs and their fuzzy envelopes, defuzzified weights, normalized weights, and rank of the criteria.

Criteria | HFLTS | Fuzzy Envelopes | The Defuzzified Weight | The Normalized Weight | Rank |
---|---|---|---|---|---|

C1 | {L, M, H} | (0.17, 0.47, 0.53, 0.83) | 0.500 | 0.068 | 9 |

C2 | {DH} | (0.83, 1.00, 1.00, 1.00) | 0.943 | 0.128 | 1 |

C3 | {L, M, H, VH, DH} | (0.17, 0.18, 1.00, 1.00) | 0.587 | 0.080 | 7 |

C4 | {M, H, VH} | (0.33, 0.64, 0.70, 1.00) | 0.667 | 0.091 | 6 |

C5 | {DL, VL, L, M, H, VH} | (0.00, 0.00, 0.80, 1.00) | 0.452 | 0.061 | 10 |

C6 | {M, H, VH, DH} | (0.33, 0.65, 1.00, 1.00) | 0.737 | 0.100 | 5 |

C7 | {L, M} | (0.17, 0.33, 0.50, 0.67) | 0.418 | 0.057 | 11 |

C8 | {H, VH} | (0.50, 0.67, 0.83, 1.00) | 0.750 | 0.102 | 4 |

C9 | {H, VH, DH} | (0.50, 0.85, 1.00, 1.00) | 0.822 | 0.112 | 3 |

C10 | {B, VH} | (0.17, 0.43, 0.73, 1.00) | 0.583 | 0.079 | 8 |

C11 | {VH, DH} | (0.67, 0.97, 1.00, 1.00) | 0.889 | 0.121 | 2 |

**Table 5.**The HFLTSs for the alternatives and the fuzzy decision matrix obtained from the fuzzy envelopes of the HFLTSs.

Alternatives\Criteria | The HFLTSs Generated from the CLEs for the Alternatives | ||||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | |

A1 | {M} | {G, VG} | {M, G, VG, P} | {G, VG, P} | {M, G} | {G, VG, P} | {N, VB, B, M} | {G, VG, P} | {M, G, VG} | {M} | {G, VG, P} |

A2 | {M} | {G, VG, P} | {M, G, VG} | {M} | {B, M} | {G, VG, P} | {VB, B, M} | {G, VG, P} | {M, G} | {M, G} | {G, VG, P} |

A3 | {M, G, VG} | {G, VG, P} | {M, G} | {M} | {B, M} | {M, G, VG} | {B, M, G} | {VG, P} | {M, G, VG} | {M, G, VG} | {G, VG, P} |

A4 | {M, G, VG} | {G, VG} | {G} | {G, VG, P} | {M} | {M, G, VG} | {B, M, G} | {G, VG, P} | {G, VG} | {M, G, VG} | {G, VG} |

A5 | {M, G, VG} | {VG, P} | {M, G} | {M, G, VG} | {M, G} | {M, G, VG} | {VB, B, M, G} | {G, VG, P} | {M, G, VG} | {B, M, G} | {M, G} |

A6 | {M} | {B, M, G} | {M, G, VG} | {M, G, VG} | {M, G} | {M, G, VG} | {VB, B, M, G} | {M, G} | {B, M} | {VB, B, M} | {VB, B, M} |

Alternatives\Criteria | The Fuzzy Decision Matrix Formed by the Fuzzy Envelopes of the HFLTSs | ||||||||||

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | |

A1 | (0.33, 0.50, 0.50, 0.67) | (0.67, 0.97, 1.00,100) | (0.33, 0.65, 1.00, 1.00) | (0.50, 0.85, 1.00, 1.00) | (0.33, 0.50, 0.67, 0.83) | (0.50, 0.85, 1.00, 1.00) | (0.00, 0.00, 0.35, 0.67) | (0.50, 0.85, 1.00, 1.00) | (0.33, 0.64, 0.70, 1.00) | (0.33, 0.50, 0.50, 0.67) | (0.50, 0.67, 0.83, 1.00) |

A2 | (0.33, 0.50, 0.50, 0.67) | (0.50, 0.85, 1.00,1.00) | (0.33, 0.64, 0.70, 1.00) | (0.33, 0.50, 0.50, 0.67) | (0.17, 0.33, 0.50, 0.67) | (0.50, 0.85, 1.00,1.00) | (0.00, 0.30, 0.36, 0.67) | (0.50, 0.85, 1.00, 1.00) | (0.33, 0.50, 0.67, 0.83) | (0.33, 0.50, 0.67, 0.83) | (0.50, 0.67, 0.83, 1.00) |

A3 | (0.33, 0.64, 0.70, 1.00) | (0.50, 0.85, 1.00,1.00) | (0.33, 0.50, 0.50, 0.67) | (0.33, 0.50, 0.50, 0.67) | (0.17, 0.33, 0.50, 0.67) | (0.33, 0.64, 0.70, 1.00) | (0.17, 0.47, 0.53, 0.83) | (0.50, 0.67, 0.83, 1.00) | (0.33, 0.50, 0.67, 0.83) | (0.33, 0.64, 0.70, 1.00) | (0.50, 0.67, 0.83, 1.00) |

A4 | (0.33, 0.64, 0.70, 1.00) | (0.50, 0.67, 0.83, 1.00) | (0.50, 0.67, 0.67, 0.83) | (0.50, 0.85, 1.00,1.00) | (0.33, 0.50, 0.50, 0.67) | (0.33, 0.64, 0.70, 1.00) | (0.17, 0.47, 0.53, 0.83) | (0.67, 0.97, 1.00, 1.00) | (0.50, 0.67, 0.83, 1.00) | (0.33, 0.64, 0.70, 1.00) | (0.50, 0.85, 1.00, 1.00) |

A5 | (0.33, 0.64, 0.70, 1.00) | (0.67, 0.97, 1.00, 1.00) | (0.33, 0.50, 0.50, 0.67) | (0.33, 0.64, 0.70, 1.00) | (0.33, 0.50, 0.67, 0.83) | (0.33, 0.64, 0.70, 1.00) | (0.00, 0.17, 0.66, 0.83) | (0.50, 0.85, 1.00, 1.00) | (0.33, 0.64, 0.70, 1.00) | (0.33, 0.50, 0.50, 0.67) | (0.50, 0.67, 0.83, 1.00) |

A6 | (0.33, 0.50, 0.50, 0.67) | (0.17, 0.47, 0.53, 0.83) | (0.33, 0.64, 0.70, 1.00) | (0.33, 0.64, 0.70, 1.00) | (0.33, 0.50, 0.67, 0.83) | (0.33, 0.64, 0.70, 1.00) | (0.00, 0.17, 0.66, 0.83) | (0.33, 0.50, 0.67, 0.83) | (0.17, 0.33, 0.50, 0.67) | (0.00, 0.30, 0.36, 0.67) | (0.00, 0.30, 0.36, 0.67) |

Alternatives\Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | ED_{i} | HD_{i} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A1 | (0.08, 0.35, 0.40, 0.83) | (0.61, 1.07, 1.10, 1.10) | (0.08, 0.16, 1.36, 1.36) | (0.20, 0.66, 0.85, 1.22) | (0.00, 0.00, −0.12, −0.43) | (0.20, 0.67, 1.22, 1.22) | (0.00, 0.00, 0.35, 0.90) | (0.28, 0.64, 0.93, 1.12) | (0.22, 0.73, 0.93, 1.33) | (0.08, 0.32, 0.55, 1.00) | (0.41, 0.79, 1.01, 1.22) | 2.643 | 2.390 |

A2 | (0.08, 0.35, 0.40, 0.83) | (0.46, 0.93, 1.10, 1.10) | (0.08, 0.16, 0.95, 1.36) | (0.13, 0.39, 0.43, 0.82) | (0.00, 0.00, 0.11, −0.15) | (0.20, 0.67, 1.22, 1.22) | (0.00, 0.20, 0.36, 0.90) | (0.28, 0.64, 0.93, 1.12) | (0.22, 0.57, 0.89, 1.11) | (0.08, 0.32, 0.73, 1.24) | (0.41, 0.79, 1.01, 1.22) | 2.331 | 2.062 |

A3 | (0.08, 0.45, 0.56, 1.24) | (0.46, 0.93, 1.10, 1.10) | (0.08, 0.12, 0.68, 0.91) | (0.13, 0.39, 0.43, 0.82) | (0.00, 0.00, 0.11, −0.15) | (0.13, 0.51, 0.85, 1.22) | (0.06, 0.31, 0.53, 1.11) | (0.28, 0.50, 0.77, 1.12) | (0.22, 0.57, 0.89, 1.11) | (0.08, 0.41, 0.77, 1.50) | (0.41, 0.79, 1.01, 1.22) | 2.149 | 1.976 |

A4 | (0.08, 0.45, 0.56, 1.24) | (0.46, 0.74, 0.91, 1.10) | (0.12, 0.16, 0.91, 1.13) | (0.20, 0.66, 0.85, 1.22) | (0.00, 0.00, 0.11, −0.15) | (0.13, 0.51, 0.85, 1.22) | (0.06, 0.31, 0.53, 1.11) | (0.38, 0.73, 0.93, 1.12) | (0.33, 0.76, 1.11, 1.33) | (0.08, 0.41, 0.77, 1.50) | (0.41, 1.00, 1.22, 1.22) | 3.006 | 2.769 |

A5 | (0.08, 0.45, 0.56, 1.24) | (0.61, 1.07, 1.10, 1.10) | (0.08, 0.12, 0.68, 0.91) | (0.13, 0.50, 0.60, 1.22) | (0.00, 0.00, −0.12, −0.43) | (0.13, 0.51, 0.85, 1.22) | (0.00, 0.11, 0.66, 1.11) | (0.28, 0.64, 0.93, 1.12) | (0.22, 0.73, 0.93, 1.33) | (0.08, 0.32, 0.55, 1.00) | (0.41, 0.79, 1.01, 1.22) | 2.249 | 2.066 |

A6 | (0.08, 0.35, 0.40, 0.83) | (0.16, 0.51, 0.59, 0.91) | (0.08, 0.16, 0.95, 1.36) | (0.13, 0.50, 0.60, 1.22) | (0.00, 0.00, −0.12, −0.43) | (0.13, 0.51, 0.85, 1.22) | (0.00, 0.11, 0.66, 1.11) | (0.19, 0.38, 0.63, 0.93) | (0.11, 0.37, 0.67, 0.89) | (0.00, 0.19, 0.40, 1.00) | (0.00, 0.35, 0.44, 0.82) | 0.651 | 0.512 |

${\tilde{ns}}_{j}$ | (0.08, 0.35, 0.40, 0.83) | (0.16, 0.51, 0.59, 0.91) | (0.08, 0.12, 0.68, 0.91) | (0.13, 0.40, 0.43, 0.82) | (0.00, 0.00, −0.12, −0.43) | (0.13, 0.51, 0.85, 1.22) | (0.00, 0.00, 0.35, 0.90) | (0.19, 0.38, 0.63, 0.93) | (0.11, 0.37, 0.67, 0.89) | (0.00, 0.19, 0.40, 1.00) | (0.00, 0.35, 0.44, 0.82) |

Alternatives | RA | AS_{i} | Ranking | |||||
---|---|---|---|---|---|---|---|---|

A1 | A2 | A3 | A4 | A5 | A6 | |||

A1 | 0 | 0.640 | 0.908 | −0.743 | 0.717 | 3.870 | 5.393 | 2 |

A2 | −0.640 | 0 | 0.268 | −1.383 | 0.077 | 3.230 | 1.552 | 3 |

A3 | −0.908 | −0.268 | 0 | −1.650 | −0.191 | 2.962 | −0.054 | 5 |

A4 | 0.743 | 1.383 | 1.650 | 0 | 1.460 | 4.613 | 9.848 | 1 |

A5 | −0.717 | −0.077 | 0.191 | −1.460 | 0 | 3.153 | 1.089 | 4 |

A6 | −3.870 | −3.230 | −2.962 | −4.613 | −3.153 | 0 | −17.828 | 6 |

**Table 8.**The sensitivity analysis for different cases of criteria weights for the proposed methodology.

Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | Ranking of the Alternatives |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Original CLEs | between L and H | DH | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 1 | M | DH | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 2 | between L and H | between L and H | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 3 | between L and H | DH | between M and VH | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 4 | between L and H | DH | at least L | at least VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A5 > A2 > A3 > A6 |

Case 5 | between L and H | DH | at least L | between M and VH | at most M | at least M | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A5 > A2 > A3 > A6 |

Case 6 | between L and H | DH | at least L | between M and VH | at most VH | at least L | between L and M | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 7 | between L and H | DH | at least L | between M and VH | at most VH | at least M | at least H | between H and VH | at least H | between L and VH | at least VH | A4 > A1 > A5 > A3 > A2 > A6 |

Case 8 | between L and H | DH | at least L | between M and VH | at most VH | at least M | between L and M | between VL and M | at least H | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 9 | between L and H | DH | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at most VH | between L and VH | at least VH | A4 > A1 > A2 > A3 > A5 > A6 |

Case 10 | between L and H | DH | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | VL | at least VH | A4 > A1 > A5 > A2 > A3 > A6 |

Case 11 | between L and H | DH | at least L | between M and VH | at most VH | at least M | between L and M | between H and VH | at least H | between L and VH | between L and H | A4 > A1 > A2 > A3 > A5 > A6 |

**Table 9.**The ranking of alternatives with respect to the considered fuzzy MCDM methods and performance scores.

Alternatives | Fuzzy MCDM Methods | Performance Scores | |||||
---|---|---|---|---|---|---|---|

Fuzzy CODAS | Fuzzy EDAS | Fuzzy TOPSIS | Fuzzy WASPAS | Fuzzy ARAS | Fuzzy COPRAS | ||

A1 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |

A2 | 3 | 5 | 3 | 5 | 4 | 5 | 5 |

A3 | 5 | 4 | 5 | 4 | 5 | 4 | 4 |

A4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

A5 | 4 | 2 | 4 | 3 | 3 | 2 | 3 |

A6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |

**Table 10.**The Spearman’s correlation coefficients between the fuzzy MCDM methods and the performance scores.

Fuzzy MCDM Methods | Fuzzy CODAS | Fuzzy EDAS | Fuzzy TOPSIS | Fuzzy WASPAS | Fuzzy ARAS | Fuzzy COPRAS | Performance Scores |
---|---|---|---|---|---|---|---|

Fuzzy CODAS | 1 | 0.714 | 1.000 | 0.829 | 0.943 | 0.714 | 0.829 |

Fuzzy EDAS | – | 1 | 0.714 | 0.943 | 0.886 | 1.000 | 0.943 |

Fuzzy TOPSIS | – | – | 1 | 0.829 | 0.943 | 0.714 | 0.829 |

Fuzzy WASPAS | – | – | – | 1 | 0.943 | 0.943 | 1.000 |

Fuzzy ARAS | – | – | – | – | 1 | 0.886 | 0.943 |

Fuzzy COPRAS | – | – | – | – | – | 1 | 0.943 |

Performance Scores | – | – | – | – | – | – | 1 |

© 2019 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**

Yalçın, N.; Yapıcı Pehlivan, N.
Application of the Fuzzy CODAS Method Based on Fuzzy Envelopes for Hesitant Fuzzy Linguistic Term Sets: A Case Study on a Personnel Selection Problem. *Symmetry* **2019**, *11*, 493.
https://doi.org/10.3390/sym11040493

**AMA Style**

Yalçın N, Yapıcı Pehlivan N.
Application of the Fuzzy CODAS Method Based on Fuzzy Envelopes for Hesitant Fuzzy Linguistic Term Sets: A Case Study on a Personnel Selection Problem. *Symmetry*. 2019; 11(4):493.
https://doi.org/10.3390/sym11040493

**Chicago/Turabian Style**

Yalçın, Neşe, and Nimet Yapıcı Pehlivan.
2019. "Application of the Fuzzy CODAS Method Based on Fuzzy Envelopes for Hesitant Fuzzy Linguistic Term Sets: A Case Study on a Personnel Selection Problem" *Symmetry* 11, no. 4: 493.
https://doi.org/10.3390/sym11040493