# The Location Selection for Roundabout Construction Using Rough BWM-Rough WASPAS Approach Based on a New Rough Hamy Aggregator

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Review of MCDM Methods in Traffic Engineering

#### 2.2. Review of Methods for Location Selection Problems

#### 2.3. Summarized Overview of Used MCDM Approaches and a Brief Overview of the Advantages of the Proposed Model

## 3. Materials and Methods

#### 3.1. Proposed Methodology

#### 3.2. Novel Rough Hamy Mean Operators and Their Operations

**Definition**

**1.**

**Definition**

**2.**

**Theorem**

**1.**

**Example**

**1.**

- (i).
- $\frac{1}{\left(\begin{array}{l}n\\ k\end{array}\right)}=\frac{k!(n-k)!}{n!}=\frac{2!(4-2)!}{2!}=\frac{1}{6}$
- (ii).
- $\underset{\_}{Lim}({\phi}_{\alpha})=\frac{{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le 4}{\left({\displaystyle \prod _{j=1}^{2}\underset{\_}{Lim}({\phi}_{{i}_{j}})}\right)}^{1/2}}}{\left(\begin{array}{c}4\\ 2\end{array}\right)}=\frac{{\left(2\times 3\right)}^{1/2}+{\left(2\times 1\right)}^{1/2}+{\left(2\times 5\right)}^{1/2}+{\left(3\times 1\right)}^{1/2}+{\left(3\times 5\right)}^{1/2}+{\left(1\times 5\right)}^{1/2}}{6}=2.478$
- (iii).
- $\underset{\_}{Lim}({\phi}_{\alpha})=\frac{{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le 4}{\left({\displaystyle \prod _{j=1}^{2}\overline{Lim}({\phi}_{{i}_{j}})}\right)}^{1/2}}}{\left(\begin{array}{c}4\\ 2\end{array}\right)}=\frac{{\left(3\times 5\right)}^{1/2}+{\left(3\times 3\right)}^{1/2}+{\left(3\times 8\right)}^{1/2}+{\left(5\times 3\right)}^{1/2}+{\left(5\times 8\right)}^{1/2}+{\left(3\times 8\right)}^{1/2}}{6}=4.478$

**Theorem**

**2.**

**Theorem**

**3.**

**Theorem**

**4.**

**Theorem**

**5.**

**Case**

**1.**

**Case**

**2.**

## 4. The Location Selection for Roundabout Construction in Doboj

#### 4.1. Forming a Multi-Criteria Model

#### 4.2. Data Collection

#### 4.3. Criteria Weight Calculation Using Rough BWM

#### 4.4. Aggregation of an Initial Matrix on the Basis of the Developed Rough Hamy Aggregator

_{1}–C

_{1}, we obtain the following values in expert correspondent matrices: $RN({x}_{11}^{E1})=\left[2.67,3.33\right]$, $RN({x}_{11}^{E2})=\left[2.67,3.33\right]$, $RN({x}_{11}^{E3})=[3.00,5.00]$, $RN({x}_{11}^{E4})=[2.67,3.33]$, $RN({x}_{11}^{E5})=[2.67,3.33]$, $RN({x}_{11}^{E6})=[2.67,3.33]$ and $RN({x}_{11}^{E7})=[1.00,3.00]$. Based on the proposed values, the expression (3) and taking that $k=2$, in position A

_{1}-C

_{1}, the aggregation of values is performed:

- (a)
- $\frac{1}{\left(\begin{array}{l}n\\ k\end{array}\right)}=\frac{k!(n-k)!}{n!}=\frac{2!(7-2)!}{7!}=\frac{1}{21}$
- (b)
- $\begin{array}{l}\underset{\_}{Lim}({x}_{11})=\frac{{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le 7}{\left({\displaystyle \prod _{j=1}^{2}\underset{\_}{Lim}({x}_{{i}_{j}})}\right)}^{1/2}}}{\left(\begin{array}{c}7\\ 2\end{array}\right)}=\\ =\frac{{\left(2.67\times 2.67\right)}^{1/2}+{\left(2.67\times 3\right)}^{1/2}+{\left(2.67\times 3\right)}^{1/2}+{\left(2.67\times 2.67\right)}^{1/2}+\dots +{\left(2.67\times 1\right)}^{1/2}+{\left(2.67\times 1\right)}^{1/2}}{21}=2.417\end{array}$
- (c)
- $\begin{array}{l}\underset{\_}{Lim}({x}_{11})=\frac{{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le 7}{\left({\displaystyle \prod _{j=1}^{2}\overline{Lim}({\phi}_{{i}_{j}})}\right)}^{1/2}}}{\left(\begin{array}{c}7\\ 2\end{array}\right)}=\\ =\frac{{\left(3.33\times 3.33\right)}^{1/2}+{\left(3.33\times 5\right)}^{1/2}+{\left(2\times 5\right)}^{1/2}+{\left(3.33\times 3.33\right)}^{1/2}+\dots +{\left(3.33\times 3\right)}^{1/2}+{\left(3.33\times 3\right)}^{1/2}}{21}=3.494\end{array}$

#### 4.5. Evaluation of Locations Using Rough WASPAS Methods

_{i}. is obtained. Applying the Equation (13) from step 8 from [58], the following matrix is obtained:

## 5. Sensitivity Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Proof of**

**the Theorem 1.**

- (1)
- $\prod _{j=1}^{k}RN({\phi}_{{i}_{j}})}=\left[{\displaystyle \prod _{j=1}^{k}\underset{\_}{Lim}({\phi}_{{i}_{j}})},{\displaystyle \prod _{j=1}^{k}\overline{Lim}({\phi}_{{i}_{j}})}\right]$,
- (2)
- ${\left({\displaystyle \prod _{j=1}^{k}RN({\phi}_{{i}_{j}})}\right)}^{1/k}=\left[{\left({\displaystyle \prod _{j=1}^{k}\underset{\_}{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k},{\left({\displaystyle \prod _{j=1}^{k}\overline{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}\right]$,
- (3)
- $\sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}RN({\phi}_{{i}_{j}})}\right)}^{1/k}}=\left[{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\underset{\_}{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}},{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\overline{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}}\right]$,
- (4)
- $\frac{1}{\left(\begin{array}{l}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}RN({\phi}_{{i}_{j}})}\right)}^{1/k}}=\left[\frac{1}{\left(\begin{array}{l}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\underset{\_}{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}},\frac{1}{\left(\begin{array}{l}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\overline{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}}\right]$.

**Proof of**

**the Theorem 2.**

**Proof of**

**the Theorem 3.**

**Proof of**

**the Theorem 4.**

**Proof of**

**the Theorem 5.**

- (1)
- If $\underset{\_}{Lim}(\phi )\le \underset{\_}{Lim}(\varphi )$ and $\overline{Lim}(\phi )\le \overline{Lim}(\varphi )$, then it is obtained that $RNHM\left\{RN({\phi}_{1}),RN({\phi}_{2}),\dots ,RN({\phi}_{n})\right\}\le RNHM\left\{RN({\varphi}_{1}),RN({\varphi}_{2}),\dots ,RN({\varphi}_{n})\right\}$;
- (2)
- If $\underset{\_}{Lim}(\phi )=\underset{\_}{Lim}(\varphi )$ and $\overline{Lim}(\phi )=\overline{Lim}(\varphi )$, then it can be concluded that there are the following equalities:$$\frac{1}{\left(\begin{array}{c}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\underset{\_}{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}}=\frac{1}{\left(\begin{array}{c}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\underset{\_}{Lim}({\varphi}_{{i}_{j}})}\right)}^{1/k}}$$$$\frac{1}{\left(\begin{array}{c}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\overline{Lim}({\phi}_{{i}_{j}})}\right)}^{1/k}}=\frac{1}{\left(\begin{array}{c}n\\ k\end{array}\right)}{\displaystyle \sum _{1\le {i}_{1}<\dots <{i}_{k}\le n}{\left({\displaystyle \prod _{j=1}^{k}\overline{Lim}({\varphi}_{{i}_{j}})}\right)}^{1/k}}$$

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**Table 1.**Overview of the used Multi-criteria Decision Making (MCDM) methods in road engineering and location selection.

Ref. | Approach | Purpose of Application |
---|---|---|

[11] | AHP | elimination of unnecessary overpasses that had lost their positive function in the traffic flow |

[12] | AHP | determination of the influence of traffic factor interaction on the rate of traffic accidents |

[13] | MOO and AHP | evaluation and ranking traffic and geometric elements |

[14] | AHP | evaluation of road section design in an urban environment |

[15] | TOPSIS | evaluation of locations with roundabouts and noise analysis in them |

[16] | Delphi and TOPSIS | identification of priority black spots in order to increase the safety in traffic |

[17] | AHP | evaluation of four types of intersections |

[18] | AHP | evaluation of variants for roundabout reconstruction |

[19] | Fuzzy AHP, WSM ELECTRE and TOPSIS | evaluation of the alternatives for noise reduction in traffic |

[20] | Fuzzy AHP | prioritizing road stretches included in a noise action plans |

[21] | AHP | evaluation of the effectiveness of traffic calming measures |

[22] | Fuzzy AHP and TOPSIS | evaluation of traffic congestion rates |

[23] | ANP, DEMATEL, fuzzy set theory and TOPSIS | mitigation of congestion at the Ninoy Aquino airport |

[24] | SWARA and VIKOR | selection of the optimal alternative of mechanical longitudinal ventilation of tunnel pollutants during automobile accidents |

[25] | PROMETHEE | determination of urban road safety |

[27] | AHP | ranking various on-road emission mitigation strategies |

[39] | WASPAS with interval neutrosophic sets | the solar-wind power station location selection |

[40] | Fuzzy AHP and Fuzzy PROMETHEE II | selection the best location for a solar power plant |

[41] | AHP and TOPSIS | construction of a metro-integrated logistics system |

[42] | TOPSIS | selection of suitable site for photovoltaic installation |

[43] | WASPAS with single-valued neutrosophic sets | determination of the location problem of a garage for a residential house |

Ord. No. | Criterion | Criterion Description |
---|---|---|

1 | Flow of vehicles | The number of vehicles passing through the observed road intersection in a unit of time in both directions. |

2 | Flow of pedestrians | The number of pedestrians crossing the observed intersection at the point for pedestrian movement (pedestrian crossing, zebra, etc.) at a given time interval. |

3 | Traffic safety indicator | The number of traffic accidents on the observed section of the road |

4 | Costs of construction and exploitation | Cost estimation (construction, exploitation and maintenance) |

5 | Type of intersection | Three-way or four-way intersections |

6 | Average vehicle intensity per access arm | The limit intensity is the intensity at the entry arm into the intersection of 360 PA/h |

7 | Functional criterion of spatial fitting | What is the primary role of the intersection observed? This section analyzes what type of intersection is the most acceptable due to its role in traffic. |

8 | Public opinion | It implies a survey of local population that have chosen one of the offered locations as a priority for the construction of a roundabout. |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | |
---|---|---|---|---|---|---|---|---|

A_{1} | 1256 | 8 | 2 | 3 | 3 | 419 | 7 | 85 |

A_{2} | 2194 | 4 | 2 | 9 | 3 | 731 | 5 | 89 |

A_{3} | 1037 | 5 | 4 | 7 | 3 | 346 | 3 | 45 |

A_{4} | 2878 | 32 | 3 | 7 | 4 | 720 | 5 | 8 |

A_{5} | 1052 | 2 | 4 | 5 | 4 | 263 | 5 | 27 |

A_{6} | 4197 | 124 | 1 | 3 | 4 | 1050 | 7 | 74 |

Location 1—Exit from the Old Town onto the M17 Main Road | |||||||||||||

Direction | Bare-Maglaj | Bare-Old Town | Maglaj-Bare | Maglaj-Old Town | Old Town-Bare | Old Town-Maglaj | Ʃ | ||||||

Trucks | 64 | 12 | 64 | 12 | 12 | 24 | 176 | ||||||

Passenger vehicles | 268 | 84 | 388 | 108 | 160 | 72 | 1080 | ||||||

Location 2—The Bridge, So-Called “Japanac”, Which Represents the Entrance into the Town from Tuzla | |||||||||||||

Direction | “Japanac”-Maglaj | “Japanac“-Bare | Maglaj-“Japanac” | Maglaj-Bare | Bare-Maglaj | Bare-“Japanac” | Ʃ | ||||||

Trucks | 60 | 52 | 72 | 84 | 112 | 80 | 462 | ||||||

Passenger vehicles | 200 | 240 | 360 | 380 | 272 | 280 | 1732 | ||||||

Location 3—The Intersection on the M17 Main Road at Flea Market | |||||||||||||

Direction | Bare-Maglaj | Bare-Town Entrance | Maglaj-Bare | Maglaj-Town Entrance | Town Exit-Bare | Town Exit-Maglaj | Ʃ | ||||||

Trucks | 76 | 0 | 80 | 0 | 0 | 0 | 156 | ||||||

Passenger vehicles | 244 | 108 | 384 | 24 | 100 | 24 | 884 | ||||||

Location 4—Traffic-Light Intersection on the M17 Main Road | |||||||||||||

Direction | Town-Railwaysstation | Town-Maglaj | Town-Bare | Bare-Maglaj | Bare-Town | Bare-r. Stat. | Maglaj-Bare | Mag.-Town | Mag.-r. Station | R. stat.-Bare | R. Stat.-Maglaj | R. Stat.-Town | Ʃ |

Trucks | 9 | 15 | 24 | 90 | 15 | 27 | 96 | 27 | 24 | 30 | 25 | 15 | 397 |

Passenger vehicles | 153 | 225 | 240 | 270 | 105 | 135 | 300 | 270 | 120 | 132 | 246 | 285 | 2481 |

Location 5—Intersection at the Entrance into/Exit from the Town via Usora | |||||||||||||

Direction | Bare-Maglaj | Bare-Usora | Maglaj-Bare | Maglaj-Usora | Usora-Bare | Usora-Maglaj | Ʃ | ||||||

Trucks | 68 | 0 | 100 | 4 | 0 | 4 | 176 | ||||||

Passenger vehicles | 232 | 140 | 288 | 152 | 24 | 40 | 876 | ||||||

Location 6—Intersection in the Town at the Junction of Jug Bogdana and Cara Dušana Street | |||||||||||||

Direction | Church-Vladimirka | Church-Center | Church-Bingo | Vlad.-Church | Vlad.-Center | Vlad.-Bingo | Center-Church | Center-Vlad. | Center-Bingo | Bingo.-Center | Bingo-Church | Bingo-Vlad. | Ʃ |

Trucks | 9 | 15 | 24 | 90 | 15 | 27 | 96 | 27 | 24 | 30 | 25 | 15 | 397 |

Passenger vehicles | 569 | 292 | 478 | 507 | 139 | 234 | 222 | 129 | 374 | 403 | 365 | 88 | 3800 |

BO | OW | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Criteria | E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} | E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} |

C_{1} | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 6 | 6 | 4 | 6 | 8 | 7 | 7 |

C_{2} | 2 | 3 | 3 | 4 | 4 | 1 | 2 | 5 | 4 | 3 | 3 | 3 | 6 | 5 |

C_{3} | 1 | 2 | 1 | 2 | 2 | 1 | 1 | 6 | 5 | 5 | 5 | 5 | 6 | 6 |

C_{4} | 3 | 4 | 4 | 3 | 3 | 4 | 5 | 3 | 3 | 2 | 4 | 4 | 3 | 2 |

C_{5} | 2 | 3 | 3 | 3 | 5 | 2 | 2 | 4 | 4 | 3 | 4 | 2 | 5 | 5 |

C_{6} | 4 | 5 | 4 | 4 | 6 | 1 | 5 | 2 | 2 | 2 | 3 | 1 | 6 | 2 |

C_{7} | 3 | 4 | 4 | 5 | 7 | 5 | 2 | 3 | 3 | 2 | 2 | 1 | 2 | 5 |

C_{8} | 6 | 6 | 5 | 6 | 8 | 7 | 7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

BO | |||||||

Criteria | E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} |

C_{1} | [1, 1.14] | [1, 1.16] | [1.16, 2] | [1, 1.02] | [1, 1.04] | [1, 1.04] | [1, 1.04] |

C_{2} | [1.67, 2.96] | [2.34, 3.5] | [2.08, 3.67] | [2.53, 4] | [2.26, 4] | [1, 2.05] | [1.84, 2.32] |

C_{3} | [1, 1.43] | [1.49, 2] | [1, 1.35] | [1.42, 2] | [1.27, 2] | [1, 1.19] | [1, 1.23] |

C_{4} | [3, 3.71] | [3.62, 4.25] | [3.45, 4.33] | [3, 3.62] | [3, 3.68] | [3.46, 4.5] | [3.54, 5] |

C_{5} | [2, 2.86] | [2.64, 3.5] | [2.48, 3.67] | [2.42, 4] | [2.71, 5] | [2, 2.34] | [2, 2.44] |

C_{6} | [3.25, 4.59] | [3.86, 5.33] | [3.06, 4.63] | [3.03, 4.79] | [3.76, 6] | [1, 3.33] | [3.73, 5] |

C_{7} | [2.5, 4.61] | [3.33, 4.88] | [2.83, 5.06] | [3.69, 5.67] | [3.85, 7] | [3.38, 5] | [2, 3.21] |

C_{8} | [5.75, 6.63] | [5.67, 6.74] | [5, 6.45] | [5.81, 6.89] | [6.41, 8] | [6.09, 7] | [6.01, 7] |

OW | |||||||

Criteria | E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} | E_{7} |

C_{1} | [5.5, 6.61] | [5.33, 6.71] | [4, 6.26] | [5.61, 6.86] | [6.16, 8] | [5.82, 7] | [5.7, 7] |

C_{2} | [3.88, 5.33] | [3.25, 4.79] | [3, 4] | [3, 4.04] | [3, 4.04] | [4.04, 6] | [3.61, 5] |

C_{3} | [5.43, 6] | [5, 5.35] | [5, 5.41] | [5, 5.41] | [5, 5.41] | [5.41, 6] | [5.27, 6] |

C_{4} | [2.67, 3.33] | [2.6, 3.4] | [2, 2.95] | [3.04, 4] | [2.75, 4] | [2.55, 3.01] | [2, 2.58] |

C_{5} | [3.48, 4.4] | [3.37, 4,5] | [2.5, 4.06] | [3.34, 4.67] | [2, 3.6] | [3.79, 5] | [3.36, 5] |

C_{6} | [1.8, 2.8] | [1.75, 2.93] | [1.7, 3.11] | [2.02, 4.5] | [1, 2.4] | [2.55, 6] | [1.65, 2.2] |

C_{7} | [2.22, 3.67] | [2.1, 4] | [1.75, 2.63] | [1.67, 2.65] | [1, 2.38] | [1.81, 2.78] | [2.33, 5] |

C_{8} | [1, 1] | [1, 1] | [1, 1] | [1, 1] | [1, 1] | [1, 1] | [1, 1] |

Best: C_{1} | RN | Worst: C_{8} | RN |
---|---|---|---|

C_{1} | [1.02, 1.18] | C_{1} | [5.42, 6.91] |

C_{2} | [2.10, 3.16] | C_{2} | [3.38, 4.71] |

C_{3} | [1.41, 1.58] | C_{3} | [5.16, 5.65] |

C_{4} | [3.33, 4.14] | C_{4} | [2.50, 3.30] |

C_{5} | [2.78, 3.34] | C_{5} | [3.08, 4.45] |

C_{6} | [3.10, 4.77] | C_{6} | [1.75, 3.30] |

C_{7} | [3.58, 5.00] | C_{7} | [1.81, 3.24] |

C_{8} | [6.13, 6.95] | C_{8} | [1.00, 1.00] |

A_{1} | A_{2} | A_{3} | |||||||||||||||||||

C_{1} | 3 | 3 | 5 | 3 | 3 | 3 | 1 | 5 | 5 | 7 | 5 | 5 | 5 | 3 | 1 | 1 | 3 | 3 | 3 | 3 | 1 |

C_{2} | 5 | 3 | 3 | 3 | 3 | 3 | 1 | 3 | 1 | 3 | 1 | 3 | 1 | 1 | 3 | 1 | 3 | 3 | 3 | 1 | 1 |

C_{3} | 5 | 3 | 1 | 5 | 3 | 3 | 3 | 5 | 3 | 1 | 5 | 3 | 3 | 3 | 9 | 7 | 5 | 9 | 7 | 5 | 7 |

C_{4} | 5 | 3 | 5 | 3 | 1 | 3 | 3 | 7 | 1 | 7 | 5 | 5 | 7 | 9 | 5 | 1 | 5 | 3 | 3 | 7 | 7 |

C_{5} | 7 | 5 | 7 | 7 | 5 | 7 | 5 | 7 | 5 | 7 | 7 | 5 | 7 | 5 | 7 | 5 | 7 | 7 | 5 | 7 | 5 |

C_{6} | 5 | 5 | 3 | 5 | 3 | 5 | 3 | 7 | 7 | 5 | 7 | 5 | 7 | 5 | 3 | 5 | 1 | 5 | 3 | 3 | 1 |

C_{7} | 7 | 7 | 9 | 7 | 9 | 7 | 7 | 9 | 9 | 7 | 7 | 7 | 7 | 5 | 5 | 7 | 5 | 5 | 7 | 7 | 3 |

C_{8} | 9 | 7 | 9 | 7 | 9 | 7 | 9 | 9 | 7 | 9 | 7 | 9 | 7 | 9 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |

A_{4} | A_{5} | A_{6} | |||||||||||||||||||

C_{1} | 7 | 5 | 7 | 5 | 5 | 5 | 5 | 1 | 1 | 3 | 3 | 3 | 3 | 1 | 9 | 7 | 9 | 7 | 9 | 7 | 7 |

C_{2} | 7 | 7 | 5 | 5 | 7 | 5 | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9 | 9 | 7 | 9 | 9 | 9 | 9 |

C_{3} | 7 | 5 | 3 | 7 | 5 | 3 | 5 | 9 | 7 | 5 | 9 | 7 | 5 | 7 | 1 | 1 | 1 | 3 | 1 | 1 | 1 |

C_{4} | 5 | 3 | 7 | 5 | 3 | 3 | 7 | 3 | 1 | 3 | 5 | 3 | 3 | 5 | 5 | 1 | 3 | 3 | 3 | 1 | 3 |

C_{5} | 9 | 7 | 9 | 9 | 7 | 9 | 7 | 9 | 7 | 9 | 9 | 7 | 9 | 7 | 9 | 7 | 9 | 9 | 7 | 9 | 7 |

C_{6} | 7 | 7 | 5 | 7 | 5 | 7 | 5 | 1 | 3 | 1 | 3 | 3 | 1 | 1 | 9 | 9 | 7 | 9 | 9 | 9 | 7 |

C_{7} | 5 | 7 | 5 | 3 | 3 | 7 | 5 | 7 | 7 | 7 | 5 | 5 | 9 | 5 | 5 | 9 | 5 | 7 | 7 | 7 | 7 |

C_{8} | 1 | 3 | 1 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 5 | 3 | 5 | 3 | 7 | 7 | 7 | 5 | 7 | 5 | 7 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | |
---|---|---|---|---|---|---|---|---|

A_{1} | [2.42, 3.49] | [2.42, 3.49] | [2.49, 3.97] | [2.49, 3.97] | [5.63, 6.62] | [3.63, 4.62] | [7.16, 7.96] | [7.64, 8.63] |

A_{2} | [4.45, 5.5] | [1.33, 2.31] | [2.49, 3.97] | [4.07, 7.21] | [5.63, 6.62] | [5.63, 6.62] | [6.54, 7.98] | [7.64, 8.63] |

A_{3} | [1.59, 2.61] | [1.59, 2.61] | [6.06, 7.89] | [2.89, 5.73] | [5.63, 6.62] | [1.99, 3.87] | [4.69, 6.35] | [5, 5] |

A_{4} | [5.16, 5.96] | [5.36, 6.33] | [4.04, 5.89] | [3.68, 5.69] | [7.64, 8.63] | [5.63, 6.62] | [4.04, 5.89] | [1.04, 1.48] |

A_{5} | [1.59, 2.61] | [1, 1] | [6.06, 7.89] | [2.49, 3.97] | [7.64, 8.63] | [1.33, 2.31] | [5.62, 7.23] | [3.16, 3.95] |

A_{6} | [7.36, 8.34] | [8.45, 8.96] | [1.04, 1.48] | [1.93, 3.39] | [7.64, 8.63] | [8.01, 8.83] | [5.98, 7.41] | [6, 6.83] |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | |
---|---|---|---|---|---|---|---|---|

A_{1} | [0.29, 0.47] | [0.29, 0.41] | [0.32, 0.65] | [0.49, 1.36] | [0.65, 0.87] | [0.41, 0.58] | [0.9, 1.11] | [0.89, 1.13] |

A_{2} | [0.53, 0.75] | [0.43, 0.75] | [0.32, 0.65] | [0.27, 0.83] | [0.65, 0.87] | [0.64, 0.83] | [0.82, 1.11] | [0.89, 1.13] |

A_{3} | [0.19, 0.35] | [0.38, 0.63] | [0.77, 1.3] | [0.34, 1.17] | [0.65, 0.87] | [0.23, 0.48] | [0.59, 0.89] | [0.58, 0.65] |

A_{4} | [0.62, 0.81] | [0.16, 0.19] | [0.51, 0.97] | [0.34, 0.92] | [0.89, 1.13] | [0.64, 0.83] | [0.51, 0.82] | [0.12, 0.19] |

A_{5} | [0.19, 0.35] | [1, 1] | [0.77, 1.3] | [0.49, 1.36] | [0.89, 1.13] | [0.15, 0.29] | [0.7, 1.01] | [0.37, 0.52] |

A_{6} | [0.88, 1.13] | [0.11, 0.12] | [0.13, 0.24] | [0.57, 1.76] | [0.89, 1.13] | [0.91, 1.1] | [0.75, 1.04] | [0.7, 0.89] |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | |
---|---|---|---|---|---|---|---|---|

A_{1} | [0.07, 0.14] | [0.04, 0.05] | [0.05, 0.11] | [0.03, 0.13] | [0.08, 0.10] | [0.02, 0.05] | [0.05, 0.08] | [0.03, 0.04] |

A_{2} | [0.13, 0.22] | [0.06, 0.10] | [0.05, 0.11] | [0.01, 0.08] | [0.08, 0.10] | [0.04, 0.07] | [0.04, 0.09] | [0.03, 0.04] |

A_{3} | [0.05, 0.10] | [0.05, 0.08] | [0.13, 0.21] | [0.02, 0.02] | [0.08, 0.10] | [0.01, 0.04] | [0.03, 0.07] | [0.02, 0.02] |

A_{4} | [0.15, 0.24] | [0.02, 0.02] | [0.08, 0.16] | [0.02, 0.09] | [0.11, 0.14] | [0.04, 0.07] | [0.03, 0.06] | [0, 0.01] |

A_{5} | [0.05, 0.10] | [0.13, 0.13] | [0.13, 0.21] | [0.03, 0.13] | [0.11, 0.14] | [0.01, 0.02] | [0.04, 0.08] | [0.01, 0.02] |

A_{6} | [0.21, 0.33] | [0.01, 0.02] | [0.02, 0.04] | [0.03, 0.17] | [0.11, 0.14] | [0.05, 0.09] | [0.04, 0.08] | [0.03, 0.03] |

$\mathit{\lambda}\times {\mathit{Q}}_{\mathit{i}}$ | $(1-\mathit{\lambda})\times {\mathit{P}}_{\mathit{i}}$ | A_{i} | Rank | |
---|---|---|---|---|

A_{1} | [0.303, 0.891] | [−0.113, 0.113] | [0.189, 1.004] | 6 |

A_{2} | [0.364, 1.007] | [−0.137, 0.137] | [0.227, 1.144] | 3 |

A_{3} | [0.317, 0.940] | [−0.113, 0.115] | [0.205, 1.055] | 5 |

A_{4} | [0.369, 0.983] | [−0.128, 0.119] | [0.240, 1.102] | 4 |

A_{5} | [0.409, 1.050] | [−0.131, 0.123] | [0.278, 1.172] | 2 |

A_{6} | [0.415, 1.124] | [−0.122, 0.116] | [0.293, 1.240] | 1 |

Alte. | k = 1 | k = 2 | k = 3 | k = 4 | k = 5 | k = 6 | k = 7 |
---|---|---|---|---|---|---|---|

A1 | 0.595 | 0.597 | 0.599 | 0.669 | 0.679 | 0.681 | 0.682 |

A2 | 0.702 | 0.686 | 0.685 | 0.739 | 0.746 | 0.747 | 0.748 |

A3 | 0.638 | 0.630 | 0.631 | 0.694 | 0.703 | 0.704 | 0.705 |

A4 | 0.684 | 0.671 | 0.669 | 0.718 | 0.726 | 0.727 | 0.728 |

A5 | 0.734 | 0.725 | 0.726 | 0.749 | 0.754 | 0.755 | 0.756 |

A6 | 0.767 | 0.766 | 0.768 | 0.774 | 0.778 | 0.778 | 0.779 |

Ranking | A6 > A5 > A2 > A4 > A3 > A1 | A6 > A5 > A2 > A4 > A3 > A1 | A6 > A5 > A2 > A4 > A3 > A1 | A6 > A5 > A2 > A4 > A3 > A1 | A6 > A5 > A2 > A4 > A3 > A1 | A6 > A5 > A2 > A4 > A3 > A1 | A6 > A5 > A2 > A4 > A3 > A1 |

Methods | RBWM-RWASPAS | RBWM-RSAW | RBWM-RMABAC | RBWM-RVIKOR | RBWM-RMAIRCA | RBWM-RTOPSIS | RBWM-REDAS | Average |
---|---|---|---|---|---|---|---|---|

RBWM-RWASPAS | 1.000 | 1.000 | 0.771 | 0.771 | 0.771 | 0.771 | 0.886 | 0.853 |

RBWM-RSAW | - | 1.000 | 0.771 | 0.771 | 0.771 | 0.771 | 0.886 | 0.828 |

RBWM-RMABAC | - | - | 1.000 | 0.886 | 1.000 | 0.886 | 0.943 | 0.943 |

RBWM-RVIKOR | - | - | - | 1.000 | 0.886 | 1.000 | 0.771 | 0.914 |

RBWM-RMAIRCA | - | - | - | - | 1.000 | 0.886 | 0.943 | 0.943 |

RBWM-RTOPSIS | - | - | - | - | - | 1.000 | 0.771 | 0.886 |

RBWM-REDAS | - | - | - | - | - | - | 1.000 | 1.000 |

Overall average | 0.910 |

© 2018 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**

Stević, Ž.; Pamučar, D.; Subotić, M.; Antuchevičiene, J.; Zavadskas, E.K.
The Location Selection for Roundabout Construction Using Rough BWM-Rough WASPAS Approach Based on a New Rough Hamy Aggregator. *Sustainability* **2018**, *10*, 2817.
https://doi.org/10.3390/su10082817

**AMA Style**

Stević Ž, Pamučar D, Subotić M, Antuchevičiene J, Zavadskas EK.
The Location Selection for Roundabout Construction Using Rough BWM-Rough WASPAS Approach Based on a New Rough Hamy Aggregator. *Sustainability*. 2018; 10(8):2817.
https://doi.org/10.3390/su10082817

**Chicago/Turabian Style**

Stević, Željko, Dragan Pamučar, Marko Subotić, Jurgita Antuchevičiene, and Edmundas Kazimieras Zavadskas.
2018. "The Location Selection for Roundabout Construction Using Rough BWM-Rough WASPAS Approach Based on a New Rough Hamy Aggregator" *Sustainability* 10, no. 8: 2817.
https://doi.org/10.3390/su10082817