# Enhancing Contractor Selection Process by a New Interval-Valued Fuzzy Decision-Making Model Based on SWARA and CoCoSo Methods

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Interval-Valued Fuzzy Numbers

- i
- If ${\tilde{A}}^{l}={\tilde{A}}^{u}$, then the triangular IVFN $\tilde{A}$ can be considered as a generalized triangular fuzzy number.
- ii
- If ${{a}^{\prime}}^{l}={{a}^{\prime}}^{u},{a}^{l}={a}^{u},{{a}^{\u2033}}^{l}={{a}^{\u2033}}^{u}$ and ${\widehat{y}}_{\tilde{A}}^{l}={\widehat{y}}_{\tilde{A}}^{u}$, then the triangular IVFN $\tilde{A}$ is a crisp value.
- iii
- If ${\widehat{y}}_{\tilde{A}}^{l}={\widehat{y}}_{\tilde{A}}^{u}=1$ and ${a}^{l}={a}^{u}$, then the triangular IVFN $\tilde{A}$ can be represented as $\tilde{A}=\left[{\tilde{A}}_{x}^{l},{\tilde{A}}_{x}^{u}\right]=\left[\left({{a}^{\prime}}^{u},{{a}^{\prime}}^{l}\right),\left({a}^{l}={a}^{u}\right),\left({{a}^{\u2033}}^{l},{{a}^{\u2033}}^{u}\right)\right]$.

- Addition of IVFNs $\oplus $:$$\tilde{A}\oplus \tilde{B}=\left[\left({{a}^{\prime}}^{u},{{a}^{\prime}}^{l}\right),a,\left({{a}^{\u2033}}^{l},{{a}^{\u2033}}^{u}\right)\right]\oplus \left[\left({{b}^{\prime}}^{u},{{b}^{\prime}}^{l}\right),b,\left({{b}^{\u2033}}^{l},{{b}^{\u2033}}^{u}\right)\right]\phantom{\rule{0ex}{0ex}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\left[\left({{a}^{\prime}}^{u}+{{b}^{\prime}}^{u},{{a}^{\prime}}^{l}+{{b}^{\prime}}^{l}\right),a+b,\left({{a}^{\u2033}}^{l}+{{b}^{\u2033}}^{l},{{a}^{\u2033}}^{u}+{{b}^{\u2033}}^{u}\right)\right]$$
- Subtraction of IVFNs $\ominus $:$$\tilde{A}\ominus \tilde{B}=\left[\left({{a}^{\prime}}^{u},{{a}^{\prime}}^{l}\right),a,\left({{a}^{\u2033}}^{l},{{a}^{\u2033}}^{u}\right)\right]\ominus \left[\left({{b}^{\prime}}^{u},{{b}^{\prime}}^{l}\right),b,\left({{b}^{\u2033}}^{l},{{b}^{\u2033}}^{u}\right)\right]\phantom{\rule{0ex}{0ex}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\left[\left({{a}^{\prime}}^{u}-{{b}^{\prime}}^{u},{{a}^{\prime}}^{\mathrm{l}}-{{b}^{\prime}}^{l}\right),a-b,\left({{a}^{\u2033}}^{l}-{{b}^{\u2033}}^{l},{{a}^{\u2033}}^{u}-{{b}^{\u2033}}^{u}\right)\right]$$
- Multiplication of IVFNs $\otimes $:$$\tilde{A}\otimes \tilde{B}=\left[\left({{a}^{\prime}}^{u},{{a}^{\prime}}^{l}\right),a,\left({{a}^{\u2033}}^{l},{{a}^{\u2033}}^{u}\right)\right]\otimes \left[\left({{b}^{\prime}}^{u},{{b}^{\prime}}^{l}\right),b,\left({{b}^{\u2033}}^{l},{{b}^{\u2033}}^{u}\right)\right]\phantom{\rule{0ex}{0ex}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\left[\left({{a}^{\prime}}^{u}\times {{b}^{\prime}}^{u},{{a}^{\prime}}^{l}\times {{b}^{\prime}}^{l}\right),a\times b,\left({{a}^{\u2033}}^{l}\times {{b}^{\u2033}}^{l},{{a}^{\u2033}}^{u}\times {{b}^{\u2033}}^{u}\right)\right]$$
- Generalized division of IVFNs $\oslash $:$$\tilde{A}\oslash \tilde{B}=\left[\left({{a}^{\prime}}^{u},{{a}^{\prime}}^{l}\right),a,\left({{a}^{\u2033}}^{l},{{a}^{\u2033}}^{u}\right)\right]\oslash \left[\left({{b}^{\prime}}^{u},{{b}^{\prime}}^{l}\right),b,\left({{b}^{\u2033}}^{l},{{b}^{\u2033}}^{u}\right)\right]\phantom{\rule{0ex}{0ex}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\left[\left({{a}^{\prime}}^{u}\xf7{{b}^{\u2033}}^{u},{{a}^{\prime}}^{l}\xf7{{b}^{\u2033}}^{l}\right),a\xf7b,\left({{a}^{\u2033}}^{l}\xf7{{b}^{\prime}}^{l},{{a}^{\u2033}}^{u}\xf7{{b}^{\prime}}^{u}\right)\right]$$

## 4. Proposed Methodology

#### 4.1. Primitive SWARA and CoCoSo Methods

#### 4.1.1. SWARA Method

#### 4.1.2. CoCoSo Method

#### 4.2. Proposed IVF-SWARA and IVF-CoCoSo Methods

#### 4.2.1. Proposed IVF-SWARA Method

#### 4.2.2. Proposed IVF-CoCoSo Method

## 5. Numerical Example

## 6. Result Discussion and Sensitivity Analysis

#### 6.1. Result Discussion

#### 6.2. Sensitivity Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Linguistic Variable | Abbreviation | IVFN |
---|---|---|

Absolutely Low | AL | [(0, 0.025), 0.075, (0.15, 0.2)] |

Very Low | VL | [(0.1, 0.125), 0.175, (0.25, 0.3)] |

Low | L | [(0.2, 0.225), 0.275, (0.35, 0.4)] |

Medium Low | ML | [(0.3, 0.325), 0.375, (0.45, 0.5)] |

Medium | M | [(0.4, 0.425), 0.475, (0.55, 0.6)] |

Medium High | MH | [(0.5, 0.525), 0.575, (0.65, 0.7)] |

High | H | [(0.6, 0.625), 0.675, (0.75, 0.8)] |

Very High | VH | [(0.7, 0.725), 0.775, (0.85, 0.9)] |

Absolutely High | AH | [(0.8, 0.825), 0.875, (0.95, 1)] |

**Table 2.**IVFNs corresponding to linguistic variables for performance of each alternative and importance of each criterion.

Linguistic Variable | Abbreviation | IVFN |
---|---|---|

Extremely Unimportant/Extremely Bad | EU/EB | [(0, 0.25), 0.75, (1.5, 2)] |

Very Unimportant/Very Bad | VU/VB | [(1, 1.25), 1.75, (2.5, 3)] |

Unimportant/Bad | U/B | [(2, 2.25), 2.75, (3.5, 4)] |

Moderately Unimportant/Moderately Bad | MU/MB | [(3, 3.25), 3.75, (4.5, 5)] |

Fair | F | [(4, 4.25), 4.75, (5.5, 6)] |

Moderately Important/Moderately Good | MI/MG | [(5, 5.25), 5.75, (6.5, 7)] |

Important/Good | I/G | [(6, 6.25), 6.75, (7.5, 8)] |

Very Important/Very Good | VI/VG | [(7, 7.25), 7.75, (8.5, 9)] |

Extremely Important/Excellent | EI/E | [(8, 8.25), 8.75, (9.5, 10)] |

Decision Maker | R | FS | TA | HS | MC |
---|---|---|---|---|---|

DM1 | MU | U | VI | F | EI |

DM2 | MI | MU | VI | F | I |

DM3 | MU | VU | I | I | EI |

DM4 | F | U | VI | MI | EI |

DM5 | I | MU | I | MI | VI |

DM6 | MU | F | I | F | EI |

**Table 4.**Assigned IVFN to each linguistic variable of Table 3.

Decision Maker | R | FS | TA | HS | MC |
---|---|---|---|---|---|

DM1 | [(3, 3.25), 3.75, (4.5, 5)] | [(2, 2.25), 2.75, (3.5, 4)] | [(7, 7.25), 7.75, (8.5, 9)] | [(4, 4.25), 4.75, (5.5, 6)] | [(8, 8.25), 8.75, (9.5, 10)] |

DM2 | [(5, 5.25), 5.75, (6.5, 7)] | [(3, 3.25), 3.75, (4.5, 5)] | [(7, 7.25), 7.75, (8.5, 9)] | [(4, 4.25), 4.75, (5.5, 6)] | [(6, 6.25), 6.75, (7.5, 8)] |

DM3 | [(3, 3.25), 3.75, (4.5, 5)] | [(1, 1.25), 1.75, (2.5, 3)] | [(6, 6.25), 6.75, (7.5, 8)] | [(6, 6.25), 6.75, (7.5, 8)] | [(8, 8.25), 8.75, (9.5, 10)] |

DM4 | [(4, 4.25), 4.75, (5.5, 6)] | [(2, 2.25), 2.75, (3.5, 4)] | [(7, 7.25), 7.75, (8.5, 9)] | [(5, 5.25), 5.75, (6.5, 7)] | [(8, 8.25), 8.75, (9.5, 10)] |

DM5 | [(6, 6.25), 6.75, (7.5, 8)] | [(3, 3.25), 3.75, (4.5, 5)] | [(6, 6.25), 6.75, (7.5, 8)] | [(5, 5.25), 5.75, (6.5, 7)] | [(7, 7.25), 7.75, (8.5, 9)] |

DM6 | [(3, 3.25), 3.75, (4.5, 5)] | [(4, 4.25), 4.75, (5.5, 6)] | [(6, 6.25), 6.75, (7.5, 8)] | [(4, 4.25), 4.75, (5.5, 6)] | [(8, 8.25), 8.75, (9.5, 10] |

Average | [(4, 4.25), 4.75, (5.5, 6)] | [(2.5, 2.75), 3.25, (4, 4.5)] | [(6.5, 6.75), 7.25, (8, 8.5)] | [(4.67, 4.92), 5.42, (6.2, 6.67)] | [(7.5, 7.75), 8.25, (9, 9.5)] |

Criteria | DM1 | DM2 | DM3 | DM4 | DM5 | DM6 |
---|---|---|---|---|---|---|

MC | - | - | - | - | - | - |

TA | VL | AL | L | VL | VL | L |

HS | ML | ML | AL | L | VL | L |

R | VL | VL | ML | VL | VL | VL |

FS | VL | L | L | L | ML | VL |

Criteria | DM1 | DM2 | DM3 |
---|---|---|---|

MC | [(0, 0), 0, (0, 0)] | [(0, 0), 0, (0, 0)] | [(0, 0), 0, (0, 0)] |

TA | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0, 0.025), 0.075, (0.15, 0.2)] | [(0.2, 0.225), 0.275, (0.35, 0.4)] |

HS | [(0.3, 0.325), 0.375, (0.45, 0.5)] | [(0.3, 0.325), 0.375, (0.45, 0.5)] | [(0, 0.025), 0.075, (0.15, 0.2)] |

R | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.3, 0.325), 0.375, (0.45, 0.5)] |

FS | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.2, 0.225), 0.275, (0.35, 0.4)] | [(0.2, 0.225), 0.275, (0.35, 0.4)] |

DM4 | DM5 | DM6 | |

MC | [(0, 0), 0, (0, 0)] | [(0, 0), 0, (0, 0)] | [(0, 0), 0, (0, 0)] |

TA | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.2, 0.225), 0.275, (0.35, 0.4)] |

HS | [(0.2, 0.225), 0.275, (0.35, 0.4)] | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.2, 0.225), 0.275, (0.35, 0.4)] |

R | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.1, 0.125), 0.175, (0.25, 0.3)] | [(0.1, 0.125), 0.175, (0.25, 0.3)] |

FS | [(0.2, 0.225), 0.275, (0.35, 0.4)] | [(0.3, 0.325), 0.375, (0.45, 0.5)] | [(0.1, 0.125), 0.175, (0.25, 0.3)] |

Average | |||

MC | [(0, 0), 0, (0, 0)] | ||

TA | [(0.117, 0.142), 0.191, (0.267, 0.317)] | ||

HS | [(0.183, 0.208), 0.258, (0.333, 0.383)] | ||

R | [(0.133, 0.158), 0.208, (0.283, 0.333)] | ||

FS | [(0.183, 0.208), 0.258, (0.333, 0.383)] |

Criteria | ${\mathit{D}}_{\mathit{j}}$ | ${\mathit{T}}_{\mathit{j}}$ | ${\mathit{Q}}_{\mathit{j}}$ | ${\mathit{W}}_{\mathit{j}}$ |
---|---|---|---|---|

MC | [(0, 0), 0, (0, 0)] | [(1, 1), 1, (1, 1)] | [(1, 1), 1, (1, 1)] | [(0.257, 0.267), 0.286, (0.314, 0.331)] |

TA | [(0.117, 0.142), 0.192, (0.267, 0.317)] | [(1.117, 1.142), 1.192, (1.267, 1.317)] | [(0.759, 0.789), 0.839, (0.876, 0.896)] | [(0.196, 0.211), 0.240, (0.275, 0.297)] |

HS | [(0.183, 0.208), 0.258, (0.333, 0.383)] | [(1.183, 1.208), 1.258, (1.333, 1.383)] | [(0.549, 0.592), 0.667, (0.725, 0.757)] | [(0.141, 0.158), 0.191, (0.227, 0.251)] |

R | [(0.133, 0.158), 0.208, (0.283, 0.333)] | [(1.133, 1.158), 1.208, (1.283, 1.333)] | [(0.412, 0.461), 0.552, (0.626, 0.668)] | [(0.106, 0.123), 0.158, (0.196, 0.221)] |

FS | [(0.183, 0.208), 0.258, (0.333, 0.383)] | [(1.183, 1.208), 1.258, (1.333, 1.383)] | [(0.298, 0.346), 0.439, (0.518, 0.564)] | [(0.077, 0.092), 0.125, (0.162, 0.187)] |

Decision Maker | Reputation | |||||
---|---|---|---|---|---|---|

Contractor 1 | Contractor 2 | Contractor 3 | Contractor 4 | Contractor 5 | Contractor 6 | |

DM1 | MG | MB | MG | B | VG | EB |

DM2 | MG | B | VG | MB | G | VB |

DM3 | MG | B | VG | MB | VG | EB |

DM4 | F | MB | G | MB | G | B |

DM5 | MB | F | G | VB | VG | VB |

DM6 | MB | F | MG | MB | VG | EB |

Financial soundness | ||||||

Contractor 1 | Contractor 2 | Contractor 3 | Contractor 4 | Contractor 5 | Contractor 6 | |

DM1 | F | MG | MB | G | MG | MG |

DM2 | MG | MG | MB | VG | MB | G |

DM3 | MG | VG | F | MG | MG | VG |

DM4 | MG | G | MB | VG | B | E |

DM5 | F | VG | MG | G | F | G |

DM6 | G | G | F | G | MB | E |

Technical ability | ||||||

Contractor 1 | Contractor 2 | Contractor 3 | Contractor 4 | Contractor 5 | Contractor 6 | |

DM1 | MG | MG | MB | EB | F | MB |

DM2 | MG | MG | MB | MB | G | MB |

DM3 | F | G | MB | EB | F | B |

DM4 | MG | G | MB | B | MG | F |

DM5 | G | MG | MB | EB | MG | MB |

DM6 | G | G | MG | MB | F | MB |

Health and safety | ||||||

Contractor 1 | Contractor 2 | Contractor 3 | Contractor 4 | Contractor 5 | Contractor 6 | |

DM1 | B | B | G | G | MB | G |

DM2 | B | B | MG | G | F | F |

DM3 | MB | VB | VG | G | MB | G |

DM4 | MB | EB | VG | VG | MG | G |

DM5 | F | EB | MG | E | F | F |

DM6 | B | B | G | G | MG | MG |

Management capability | ||||||

Contractor 1 | Contractor 2 | Contractor 3 | Contractor 4 | Contractor 5 | Contractor 6 | |

DM1 | F | MG | G | MB | VG | VG |

DM2 | F | MG | MG | F | VG | VG |

DM3 | F | MG | MG | F | VG | VG |

DM4 | MG | F | MG | MB | G | VG |

DM5 | MG | F | MG | B | G | MG |

DM6 | MB | MB | G | MB | G | VG |

Contractor | R | FS | TA | HS | MC |
---|---|---|---|---|---|

Cont 1 | [(4.17, 4.42), 4.92, (5.67, 6.17)] | [(4.83, 5.08), 5.58, (6.33, 6.83)] | [(5.17, 5.42), 5.92, (6.67, 7.17)] | [(2.67, 2.92), 3.42, (4.17, 4.67)] | [(4.17, 4.42), 4.92, (5.67, 6.17)] |

Cont 2 | [(2.75, 3.25), 3.75, (4.25, 4.75)] | [(6.00, 6.25), 6.75, (7.50, 8.00)] | [(5.50, 5.75), 6.25, (7.00, 7.50)] | [(1.17, 1.42), 1.92, (2.67, 3.17)] | [(4.33, 4.58), 5.08, (5.83, 6.33)] |

Cont 3 | [(5.75, 6.25), 6.75, (7.25, 7.75)] | [(3.67, 3.92), 4.42, (5.17, 5.67)] | [(3.33, 3.58), 4.08, (4.83, 5.33)] | [(6.00, 6.25), 6.75, (7.50, 8.00)] | [(5.33, 5.58), 6.08, (6.83, 7.33)] |

Cont 4 | [(2.25, 2.75), 3.25, (3.75, 4.25)] | [(6.17, 6.42), 6.92, (7.67, 8.17)] | [(1.33, 1.58), 2.08, (2.83, 3.33)] | [(6.50, 6.75), 7.25, (8.00, 8.50)] | [(3.17, 3.42), 3.92, (4.67, 5.17)] |

Cont 5 | [(6.42, 6.92), 7.42, (7.92, 8.42)] | [(3.67, 3.92), 4.42, (5.17, 5.67)] | [(4.67, 4.92), 5.42, (6.17, 6.67)] | [(4.00, 4.25), 4.75, (5.50, 6.00)] | [(6.50, 6.75), 7.25, (8.00, 8.50)] |

Cont 6 | [(0.42, 0.92), 1.42, (1.92, 2.42)] | [(6.67, 6.92), 7.42, (8.17, 8.67)] | [(3.00, 3.25), 3.75, (4.50, 5.00)] | [(5.17, 5.42), 5.92, (6.67, 7.17)] | [(6.67, 6.92), 7.42, (8.17, 8.67)] |

Contractor | R | FS | TA | HS | MC |
---|---|---|---|---|---|

Cont 1 | [(0.47, 0.50), 0.56, (0.66, 0.72)] | [(0.23, 0.28), 0.38, (0.53, 0.63)] | [(0.62, 0.66), 0.74, (0.86, 0.95)] | [(0.20, 0.24), 0.31, (0.41, 0.48)] | [(0.18, 0.23), 0.32, (0.45, 0.55)] |

Cont 2 | [(0.29, 0.35), 0.42, (0.48, 0.54)] | [(0.47, 0.52), 0.62, (0.77, 0.87)] | [(0.68, 0.72), 0.80, (0.92, 1.00)] | [(0.00, 0.03), 0.10, (0.20, 0.27)] | [(0.21, 0.26), 0.35, (0.48, 0.58)] |

Cont 3 | [(0.67, 0.73), 0.79, (0.85, 0.92)] | [(0.00, 0.05), 0.15, (0.30, 0.40)] | [(0.32, 0.36), 0.45, (0.57, 0.65)] | [(0.66, 0.69), 0.76, (0.86, 0.93)] | [(0.39, 0.44), 0.53, (0.67, 0.76)] |

Cont 4 | [(0.23, 0.29), 0.35, (0.42, 0.48)] | [(0.50, 0.55), 0.65, (0.80, 0.90)] | [(0.00, 0.04), 0.12, (0.24, 0.32)] | [(0.73, 0.76), 0.83, (0.93, 1.00)] | [(0.00, 0.05), 0.14, (0.27, 0.36)] |

Cont 5 | [(0.75, 0.81), 0.88, (0.94, 1.00)] | [(0.00, 0.05), 0.15, (0.30, 0.40)] | [(0.54, 0.58), 0.66, (0.78, 0.86)] | [(0.39, 0.42), 0.49, (0.59, 0.66)] | [(0.61, 0.65), 0.74, (0.88, 0.97)] |

Cont 6 | [(0.00, 0.06), 0.13, (0.19, 0.25)] | [(0.60, 0.65), 0.75, (0.90, 1.00)] | [(0.27, 0.31), 0.39, (0.51, 0.59)] | [(0.55, 0.58), 0.65, (0.75, 0.82)] | [(0.64, 0.68), 0.77, (0.91, 1.00)] |

Contractor | ${\mathit{S}}_{\mathit{i}}^{\mathit{l}}$ | ${\mathit{S}}_{\mathit{i}}^{\mathit{u}}$ | ${\mathit{P}}_{\mathit{i}}^{\mathit{l}}$ | ${\mathit{P}}_{\mathit{i}}^{\mathit{u}}$ |
---|---|---|---|---|

Contractor 1 | 0.493 | 0.529 | 4.276 | 4.301 |

Contractor 2 | 0.480 | 0.515 | 4.159 | 3.989 |

Contractor 3 | 0.575 | 0.610 | 4.377 | 4.149 |

Contractor 4 | 0.389 | 0.424 | 3.925 | 3.650 |

Contractor 5 | 0.649 | 0.685 | 4.482 | 4.255 |

Contractor 6 | 0.580 | 0.616 | 4.350 | 4.140 |

Contractor | ${\mathit{K}}_{\mathit{i}\mathit{a}}^{\mathit{l}}$ | ${\mathit{K}}_{\mathit{i}\mathit{a}}^{\mathit{u}}$ | ${\mathit{K}}_{\mathit{i}\mathit{b}}^{\mathit{l}}$ | ${\mathit{K}}_{\mathit{i}\mathit{b}}^{\mathit{u}}$ | ${\mathit{K}}_{\mathit{i}\mathit{c}}^{\mathit{l}}$ | ${\mathit{K}}_{\mathit{i}\mathit{c}}^{\mathit{u}}$ |
---|---|---|---|---|---|---|

Contractor 1 | 0.166 | 0.173 | 2.356 | 2.428 | 0.929 | 0.969 |

Contractor 2 | 0.161 | 0.162 | 2.293 | 2.308 | 0.904 | 0.903 |

Contractor 3 | 0.172 | 0.171 | 2.591 | 2.577 | 0.965 | 0.954 |

Contractor 4 | 0.150 | 0.146 | 2.000 | 2.000 | 0.841 | 0.817 |

Contractor 5 | 0.179 | 0.177 | 2.810 | 2.784 | 1.000 | 0.991 |

Contractor 6 | 0.172 | 0.171 | 2.598 | 2.588 | 0.961 | 0.954 |

Contractors | ${\mathit{K}}_{\mathit{i}}^{\mathit{l}}$ | ${\mathit{K}}_{\mathit{i}}^{\mathit{u}}$ | ${\mathit{K}}_{\mathit{i}}$ | Rank |
---|---|---|---|---|

Contractor 1 | 1.864 | 1.931 | 1.898 | 4 |

Contractor 2 | 1.814 | 1.820 | 1.817 | 5 |

Contractor 3 | 1.998 | 1.983 | 1.991 | 3 |

Contractor 4 | 1.629 | 1.608 | 1.619 | 6 |

Contractor 5 | 2.124 | 2.105 | 2.115 | 1 |

Contractor 6 | 1.997 | 1.987 | 1.992 | 2 |

Test | Rank | |||||
---|---|---|---|---|---|---|

Contractor 1 | Contractor 2 | Contractor 3 | Contractor 4 | Contractor 5 | Contractor 6 | |

Test 1 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 2 | 4 | 5 | 2 | 6 | 1 | 3 |

Test 3 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 4 | 3 | 6 | 2 | 4 | 1 | 5 |

Test 5 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 6 | 4 | 5 | 2 | 6 | 1 | 3 |

Test 7 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 8 | 5 | 6 | 2 | 3 | 4 | 1 |

Test 9 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 10 | 2 | 3 | 5 | 6 | 1 | 4 |

Test 11 | 4 | 5 | 3 | 6 | 1 | 2 |

Test 12 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 13 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 14 | 5 | 6 | 3 | 2 | 4 | 1 |

Test 15 | 3 | 6 | 2 | 5 | 1 | 4 |

Test 16 | 2 | 1 | 5 | 6 | 3 | 4 |

Test 17 | 5 | 6 | 3 | 2 | 4 | 1 |

Test 18 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 19 | 2 | 3 | 4 | 6 | 1 | 5 |

Test 20 | 5 | 6 | 3 | 4 | 2 | 1 |

Test 21 | 4 | 5 | 2 | 6 | 1 | 3 |

Test 22 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 23 | 1 | 3 | 4 | 6 | 2 | 5 |

Test 24 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 25 | 4 | 6 | 2 | 5 | 1 | 3 |

Test 26 | 3 | 6 | 1 | 4 | 2 | 5 |

Test 27 | 4 | 6 | 3 | 5 | 2 | 1 |

Test 28 | 4 | 5 | 2 | 6 | 1 | 3 |

Test 29 | 2 | 3 | 4 | 6 | 1 | 5 |

Test 30 | 4 | 5 | 2 | 6 | 1 | 3 |

Test 31 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 32 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 33 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 34 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 35 | 4 | 5 | 2 | 6 | 1 | 3 |

Test 36 | 3 | 4 | 2 | 6 | 1 | 5 |

Test 37 | 3 | 6 | 2 | 5 | 1 | 4 |

Test 38 | 3 | 5 | 2 | 6 | 1 | 4 |

Test 39 | 5 | 4 | 3 | 6 | 2 | 1 |

Test 40 | 3 | 5 | 4 | 6 | 1 | 2 |

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## Share and Cite

**MDPI and ACS Style**

Karami, S.; Mousavi, S.M.; Antucheviciene, J.
Enhancing Contractor Selection Process by a New Interval-Valued Fuzzy Decision-Making Model Based on SWARA and CoCoSo Methods. *Axioms* **2023**, *12*, 729.
https://doi.org/10.3390/axioms12080729

**AMA Style**

Karami S, Mousavi SM, Antucheviciene J.
Enhancing Contractor Selection Process by a New Interval-Valued Fuzzy Decision-Making Model Based on SWARA and CoCoSo Methods. *Axioms*. 2023; 12(8):729.
https://doi.org/10.3390/axioms12080729

**Chicago/Turabian Style**

Karami, Sajjad, Seyed Meysam Mousavi, and Jurgita Antucheviciene.
2023. "Enhancing Contractor Selection Process by a New Interval-Valued Fuzzy Decision-Making Model Based on SWARA and CoCoSo Methods" *Axioms* 12, no. 8: 729.
https://doi.org/10.3390/axioms12080729