# An Integrated Approach of Best-Worst Method (BWM) and Triangular Fuzzy Sets for Evaluating Driver Behavior Factors Related to Road Safety

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Driver Behavior Questionnaire (DBQ) Survey

#### 3.2. Overview on Best Worst Method (BWM)

- The procedure of the BWM can be highlighted as follows:
- Identification of the decision-making problem and its factors
- Determination of the most crucial and least crucial factor
- Determination of the preference of the most crucial factor over all the other factors
- Determination of the preference of the least crucial factor over all the other factors
- Make the consistency check
- Determination of the importance weight of the factors

#### 3.3. The Proposed F-BWM Model

#### 3.3.1. General Information on Fuzzy Sets

#### 3.3.2. Fuzzy Best-Worst Method (F-BWM)

**Step 1. Construct the criteria system.**A set of criteria reflects the performances of different criteria. Suppose there are n decision criteria $\left\{{c}_{1},{c}_{2},\dots ,{c}_{n}\right\}$.

**Step 2. Determine the best criterion and the worst criterion.**In this step, the best criterion and the worst criterion is determined by experts based on the constructed decision criteria system. The best criterion is denoted as ${c}_{B}$, and the worst criterion is also denoted as ${c}_{W}$.

**Step 3. Perform the fuzzy reference comparisons for the best criterion.**According to the pairwise comparison ${\tilde{a}}_{ij}$, ${c}_{B}$ is the best criterion; ${c}_{W}$ is the worst criterion. The fuzzy preferences of the best criterion over all the criteria can be determined. Then, the fuzzy comparisons are converted to triangular fuzzy numbers. The fuzzy Best-to-Others vector is obtained as follows:

**Step 4. Perform the fuzzy reference comparisons for the worst criterion.**In this step, the fuzzy preferences of all the criteria over the worst criterion can be determined. They are transformed into triangular fuzzy numbers. The fuzzy others-to-worst vector can be obtained as:

**Step 5. Determine the optimal fuzzy weights**$\left({\tilde{w}}_{1}^{*},{\tilde{w}}_{2}^{*},\dots ,{\tilde{w}}_{n}^{*}\right)$. In this step, the optimal fuzzy weight for each criterion is determined for each fuzzy pair ${\tilde{w}}_{B}/{\tilde{w}}_{j}$ and ${\tilde{w}}_{j}/{\tilde{w}}_{W}$. It should have ${\tilde{w}}_{B}/{\tilde{w}}_{j}={\tilde{a}}_{Bj}$ and ${\tilde{w}}_{j}/{\tilde{w}}_{W}={\tilde{a}}_{jW}$. A solution is obtained that the maximum absolute gaps $\left|\frac{{\tilde{w}}_{B}}{{\tilde{w}}_{j}}-{\tilde{a}}_{Bj}\right|$ and $\left|\frac{{\tilde{w}}_{j}}{{\tilde{w}}_{W}}-{\tilde{a}}_{jW}\right|$ for all j are minimized to satisfy these conditions for all j. ${\tilde{w}}_{B}$,${\tilde{w}}_{j}$ and ${\tilde{w}}_{W}$ in fuzzy BWM are triangular fuzzy numbers. In some cases, we prefer to use ${\tilde{w}}_{j}=\left({l}_{j}^{w},{m}_{j}^{w},{u}_{j}^{w}\right)$ for optimal criteria selection. The triangular fuzzy weight of the criterion ${\tilde{w}}_{j}=\left({l}_{j}^{w},{m}_{j}^{w},{u}_{j}^{w}\right)$ is transformed to a crisp value using Equation (11). Consequently, the constrained optimization problem is constructed for obtaining the optimal fuzzy weights $\left({\tilde{w}}_{1}^{*},{\tilde{w}}_{2}^{*},\dots ,{\tilde{w}}_{n}^{*}\right)$ as follows:

**Step 6. Determine the consistency ratio**. The consistency ratio is determined in the same way as BWM. In this step, the consistency index for fuzzy BWM is calculated.

## 4. Results

_{1}), lapses (F

_{2}), and errors (F

_{3}). The violations (F

_{1}) and lapses (F

_{2}) are determined as the most significant and the less significant factor, respectively (Step 2). The fuzzy reference comparisons are applied, and the linguistic terms for fuzzy preferences of the most significant factor and the less significant factor are given in Table 4 and Table 5, respectively.

## 5. Comparative Study

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Factor/Sub-Factor/Sub-sub-Factor | Epsilon Value | Consistency Ratio |
---|---|---|

F1, F2, and F3 | 0.3030 | 0.0573 |

F11 and F12: | 0.0000 | 0.0000 |

F21, F22 and F23: | 0.2090 | 0.0312 |

F31, F32 and F33: | 0.0430 | 0.0053 |

F111, F112 and F113: | 0.5000 | 0.0945 |

F121, F122, F123, F124, F125, and F126 | 0.2990 | 0.0372 |

## References

- World Health Organization. The Global Status Report on Road Safety; WHO: Geneva, Switzerland, 2018. [Google Scholar]
- EU Commission. Road Safety Facts & Figures; EU Commission: Brussels, Belgium, 2019. [Google Scholar]
- OECD/ITF. Road Safety Annual Report; OECD: Paris, France; ITF: London, UK, 2016. [Google Scholar]
- Choi, E.H. Crash Factors in Intersection-Related Crashes: An On-Scene Perspective; Technical Report No. DOT HS 811 366; U.S. Department of Transportation, National Highway Traffic Safety Administration (NHTSA): Washington, DC, USA, 2010.
- Evans, L. Traffic Safety; Science Serving Society, Inc.: Bloomfield Hills, MI, USA, 2004. [Google Scholar]
- Papaioannou, P. Driver behavior, dilemma zone and safety effects at urban signalised intersections in Greece. Accid. Anal. Prev.
**2007**, 39, 147–158. [Google Scholar] [CrossRef] [PubMed] - Stanton, N.A.; Salmon, P.M. Human error taxonomies applied to driving: Generic driver error taxonomy and its implications for intelligent transport systems. Saf. Sci.
**2009**, 47, 227–237. [Google Scholar] [CrossRef] - Wang, J.; Li, M.; Liu, Y.; Zhang, H.; Zou, W.; Cheng, L. Safety assessment of shipping routes in the South China Sea based on the fuzzy analytic hierarchy process. Saf. Sci.
**2014**, 62, 46–57. [Google Scholar] [CrossRef] - Wierwille, W.W.; Hanowski, R.J.; Hankey, J.M.; Kieliszewski, C.A.; Lee, S.E.; Medina, A.; Keisler, A.S.; Dingus, T.A. Identification and Evaluation of Driver Errors: Overview and Recommendations; Technical Report No. FHWA-RD-02-003; U.S. Department of Transportation, Federal Highway Administration: Washington, DC, USA, 2002.
- Parker, D.; Reason, J.T.; Manstead, A.S.R.; Stradling, S. Driving errors, driving violations and accident involvement. Ergonomics
**1995**, 38, 1036–1048. [Google Scholar] [CrossRef] - Reason, R.T.; Manstead, A.S.R.; Stradling, S.; Baxter, J.; Campbell, K. Errors and violations on the roads. Ergonomics
**1990**, 33, 1315–1332. [Google Scholar] [CrossRef] - Lajunen, T.; Parker, D.; Summala, H. The Manchester Driver Behaviour Questionnaire: A cross-cultural study. Accid. Anal. Prev.
**2004**, 36, 231–238. [Google Scholar] [CrossRef] - Lawton, R.; Parker, D.; Stradling, S.G.; Manstead, A.S.R. Predicting road traffic accidents: The role of social deviance and violations. Br. J. Psychol.
**1997**, 88, 249–262. [Google Scholar] [CrossRef] - Bener, A.; Özkan, T.; Lajunen, T. The driver behaviour questionnaire in Arab gulf countries: Qatar and United Arab Emirates. Accid. Anal. Prev.
**2008**, 40, 1411–1417. [Google Scholar] [CrossRef] [PubMed] - Mirmohammadi, F.; Khorasani, G.; Tatari, A.; Yadollahi, A.; Taherian, H.; Motamed, H.; Fazelpour, S.; Khorasani, M.; Maleki Verki, M. Investigation of road accidents and casualties’ factors with MCDM methods in Iran. J. Am. Sci.
**2013**, 9, 11–20. [Google Scholar] - Duleba, S.; Moslem, S. Examining Pareto optimality in analytic hierarchy process on real Data: An application in public transport service development. Exp. Syst. Appl.
**2019**, 116, 21–30. [Google Scholar] [CrossRef] - Moslem, S.; Ghorbanzadeh, O.; Blaschke, T.; Duleba, S. Analysing Stakeholder Consensus for a Sustainable Transport Development Decision by the Fuzzy AHP and Interval AHP. Sustainability
**2019**, 11, 3271. [Google Scholar] [CrossRef][Green Version] - Moslem, S.; Duleba, S. Sustainable Urban Transport Development by Applying a Fuzzy-AHP Model: A Case Study from Mersin, Turkey. Urban Sci.
**2019**, 3, 55. [Google Scholar] [CrossRef][Green Version] - Fan, G.; Zhong, D.; Yan, F.; Yue, P. A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers. Exp. Syst. Appl.
**2016**, 44, 289–303. [Google Scholar] [CrossRef] - Pourghasemi, H.R.; Pradhan, B.; Gokceoglu, C. Application of fuzzy logic and analytical hierarchy process (AHP) to landslide susceptibility mapping at Haraz watershed, Iran. Nat. Hazards
**2012**, 63, 965–996. [Google Scholar] [CrossRef] - Gumus, A.T. Evaluation of hazardous waste transportation firms by using a twostep fuzzy-AHP and TOPSIS methodology. Exp. Syst. Appl.
**2009**, 36, 4067–4074. [Google Scholar] [CrossRef] - Kwong, C.K.; Bai, H. A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment. J. Intell. Manuf.
**2002**, 13, 367–377. [Google Scholar] [CrossRef] - Pourghasemi, H.; Moradi, H.; Aghda, S.F.; Gokceoglu, C.; Pradhan, B. GIS-based landslide susceptibility mapping with probabilistic likelihood ratio and spatial multi-criteria evaluation models (North of Tehran, Iran). Arab. J. Geosci.
**2014**, 7, 1857–1878. [Google Scholar] [CrossRef][Green Version] - Ghorbanzadeh, O.; Feizizadeh, B.; Blaschke, T. An interval matrix method used to optimize the decision matrix in AHP technique for land subsidence susceptibility mapping. Environ. Earth Sci.
**2018**, 77, 584. [Google Scholar] [CrossRef] - Rezaei, J. Best-worst multi-criteria decision-making method. Omega
**2015**, 53, 49–57. [Google Scholar] [CrossRef] - Rezaei, J. Best-worst multi-criteria decision-making method: Some properties and a linear model. Omega
**2016**, 64, 126–130. [Google Scholar] [CrossRef] - Hafezalkotob, A.; Hafezalkotob, A. A novel approach for combination of individual and group decisions based on fuzzy best-worst method. Appl. Soft Comput.
**2017**, 59, 316–325. [Google Scholar] [CrossRef] - Saaty, T.L. A scaling method for priorities in hierarchical structures. J. Math. Psychol.
**1977**, 15, 234–281. [Google Scholar] [CrossRef] - Miller, G.A. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychol. Rev.
**1956**, 63, 81. [Google Scholar] [CrossRef] [PubMed][Green Version] - Yucesan, M.; Gul, M. Failure prioritization and control using the neutrosophic best and worst method. Granul. Comput.
**2019**, 1–15. [Google Scholar] [CrossRef] - Badi, I.; Ballem, M. Supplier selection using the rough BWM-MAIRCA model: A case study in pharmaceutical supplying in Libya. Decis. Mak. Appl. Manag. Eng.
**2018**, 1, 16–33. [Google Scholar] [CrossRef] - Tian, Z.P.; Zhang, H.Y.; Wang, J.Q.; Wang, T.L. Green supplier selection using improved TOPSIS and best-worst method under intuitionistic fuzzy environment. Informatica
**2018**, 29, 773–800. [Google Scholar] [CrossRef][Green Version] - Yucesan, M.; Mete, S.; Serin, F.; Celik, E.; Gul, M. An integrated best-worst and interval type-2 fuzzy topsis methodology for green supplier selection. Mathematics
**2019**, 7, 182. [Google Scholar] [CrossRef][Green Version] - Aboutorab, H.; Saberi, M.; Asadabadi, M.R.; Hussain, O.; Chang, E. ZBWM. The Z-number extension of Best Worst Method and its application for supplier development. Exp. Syst. Appl.
**2018**, 107, 115–125. [Google Scholar] [CrossRef] - Ghoushchi, S.J.; Yousefi, S.; Khazaeili, M. An extended FMEA approach based on the Z-MOORA and fuzzy BWM for prioritization of failures. Appl. Soft Comput.
**2019**, 81, 105505. [Google Scholar] [CrossRef] - Chang, T.W.; Lo, H.W.; Chen, K.Y.; Liou, J.J. A novel FMEA model based on rough BWM and rough TOPSIS-AL for risk assessment. Mathematics
**2019**, 7, 874. [Google Scholar] [CrossRef][Green Version] - Lo, H.W.; Liou, J.J.; Huang, C.N.; Chuang, Y.C. A novel failure mode and effect analysis model for machine tool risk analysis. Reliab. Eng. Syst. Saf.
**2019**, 183, 173–183. [Google Scholar] [CrossRef] - Lo, H.W.; Liou, J.J. A novel multiple-criteria decision-making-based FMEA model for risk assessment. Appl. Soft Comput.
**2018**, 73, 684–696. [Google Scholar] [CrossRef] - Tian, Z.P.; Wang, J.Q.; Zhang, H.Y. An integrated approach for failure mode and effects analysis based on fuzzy best-worst, relative entropy, and VIKOR methods. Appl. Soft Comput.
**2018**, 72, 636–646. [Google Scholar] [CrossRef] - Ru-Xin, N.; Tian, Z.P.; Wang, X.K.; Wang, J.Q.; Wang, T.L. Risk evaluation by FMEA of supercritical water gasification system using multi-granular linguistic distribution assessment. Knowl.-Based Syst.
**2018**, 162, 185–201. [Google Scholar] - Mohandes, S.R.; Zhang, X. Towards the development of a comprehensive hybrid fuzzy-based occupational risk assessment model for construction workers. Saf. Sci.
**2019**, 115, 294–309. [Google Scholar] [CrossRef] - Norouzi, A.; Namin, H.G. A Hybrid Fuzzy TOPSIS–Best Worst Method for Risk Prioritization in Megaprojects. Civil Eng. J.
**2019**, 5, 1257–1272. [Google Scholar] [CrossRef] - Rostamabadi, A.; Jahangiri, M.; Zarei, E.; Kamalinia, M.; Alimohammadlou, M. A novel Fuzzy Bayesian Network approach for safety analysis of process systems; An application of HFACS and SHIPP methodology. J. Clean. Prod.
**2020**, 244, 118761. [Google Scholar] [CrossRef] - Rostamabadi, A.; Jahangiri, M.; Zarei, E.; Kamalinia, M.; Banaee, S.; Samaei, M.R. Model for A Novel Fuzzy Bayesian Network-HFACS (FBN-HFACS) model for analyzing Human and Organizational Factors (HOFs) in process accidents. Process Saf. Environ. Prot.
**2019**, 132, 59–72. [Google Scholar] [CrossRef] - Torabi, S.A.; Giahi, R.; Sahebjamnia, N. An enhanced risk assessment framework for business continuity management systems. Saf. Sci.
**2016**, 89, 201–218. [Google Scholar] [CrossRef] - Pamučar, D.; Stević, Ž.; Sremac, S. A new model for determining weight coefficients of criteria in mcdm models: Full consistency method (fucom). Symmetry
**2018**, 10, 393. [Google Scholar] [CrossRef][Green Version] - Stević, Ž.; Brković, N. A Novel Integrated FUCOM-MARCOS Model for Evaluation of Human Resources in a Transport Company. Logistics
**2020**, 4, 4. [Google Scholar] [CrossRef][Green Version] - Pamucar, D.; Deveci, M.; Canıtez, F.; Bozanic, D. A fuzzy Full Consistency Method-Dombi-Bonferroni model for prioritizing transportation demand management measures. Appl. Soft Comput.
**2020**, 87, 105952. [Google Scholar] [CrossRef] - Badi, I.; Abdulshahed, A. Ranking the Libyan airlines by using full consistency method (FUCOM) and analytical hierarchy process (AHP). Oper. Res. Eng. Sci. Theory Appl.
**2019**, 2, 1–14. [Google Scholar] [CrossRef][Green Version] - Farooq, D.; Moslem, S.; Duleba, S. Evaluation of driver behavior criteria for evolution of sustainable traffic safety. Sustainability
**2019**, 11, 3142. [Google Scholar] [CrossRef][Green Version] - Moslem, S.; Farooq, D.; Ghorbanzadeh, O.; Blaschke, T. Application of AHP-BWM Model for Evaluating Driver Behaviour Factors Related to Road Safety: A Case Study for Budapest City. Symmetry
**2020**, 12, 243. [Google Scholar] [CrossRef][Green Version] - Farooq, D.; Moslem, S. A Fuzzy Dynamical Approach for Examining Driver Behavior Criteria Related to Road Safety. In Proceedings of the IEEE 2019 Smart City Symposium Prague (SCSP), Prague, Czech Republic, 23–24 May 2019. [Google Scholar]
- Mahdiraji, A.H.; Arzaghi, S.; Stauskis, G.; Zavadskas, E. A hybrid fuzzy BWM-COPRAS method for analyzing key factors of sustainable architecture. Sustainability
**2018**, 10, 1626. [Google Scholar] [CrossRef][Green Version] - Kolagar, M. Adherence to Urban Agriculture in Order to Reach Sustainable Cities; a BWM–WASPAS Approach. Smart Cities
**2019**, 2, 31–45. [Google Scholar] [CrossRef][Green Version] - Kumar, A.; Aswin, A.; Gupta, H. Evaluating green performance of the airports using hybrid BWM and VIKOR methodology. Tour. Manag.
**2019**, 76, 103941. [Google Scholar] [CrossRef] - Mashunin, K.Y.; Mashunin, Y.K. Vector optimization with equivalent and priority criteria. J. Comput. Syst. Sci. Int.
**2017**, 56, 975–996. [Google Scholar] [CrossRef] - Mashunin, Y.K. Mathematical Apparatus of Optimal Decision-Making Based on Vector Optimization. Appl. Syst. Innov.
**2019**, 2, 32. [Google Scholar] [CrossRef][Green Version] - Zadeh, L.A. Fuzzy sets. Inf. Control
**1965**, 8, 338–353. [Google Scholar] [CrossRef][Green Version] - Celik, E.; Gul, M.; Aydin, N.; Gumus, A.T.; Guneri, A.F. A comprehensive review of multi criteria decision making approaches based on interval type-2 fuzzy sets. Knowl.-Based Syst.
**2015**, 85, 329–341. [Google Scholar] [CrossRef] - Gul, M.; Celik, E.; Aydin, N.; Gumus, A.T.; Guneri, A.F. A state of the art literature review of VIKOR and its fuzzy extensions on applications. Appl. Soft Comput.
**2016**, 46, 60–89. [Google Scholar] [CrossRef] - Qiong, M.; Zeshui, X.; Huchang, L. An intuitionistic fuzzy multiplicative best-worst method for multi-criteria group decision making. Inf. Sci.
**2016**, 374, 224–239. [Google Scholar] - Guo, S.; Zhao, H. Fuzzy best-worst multi-criteria decision-making method and its applications. Knowl.-Based Syst.
**2017**, 121, 23–31. [Google Scholar] [CrossRef] - Li, J.; Wang, J.Q.; Hu, J.H. Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information. Int. J. Mach. Learn. Cybern.
**2019**, 10, 1671–1685. [Google Scholar] [CrossRef] - Wu, Q.; Zhou, L.; Chen, Y.; Chen, H. An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods. Inf. Sci.
**2019**, 502, 394–417. [Google Scholar] [CrossRef] - Qin, J.; Liu, X. Interval Type-2 Fuzzy Group Decision Making by Integrating Improved Best Worst Method with COPRAS for Emergency Material Supplier Selection. In Type-2 Fuzzy Decision-Making Theories, Methodologies and Applications; Springer: Singapore, 2019; pp. 249–271. [Google Scholar]
- Mi, X.; Tang, M.; Liao, H.; Shen, W.; Lev, B. The state-of-the-art survey on integrations and applications of the best worst method in decision making: Why, what, what for and what’s next? Omega
**2019**, 87, 205–225. [Google Scholar] [CrossRef] - Stradling, S.G.; Meadows, M.L.; Beatty, S. Driving as part of your work may damage your health. Behav. Res. Road Saf.
**2000**, IX, 1–9. [Google Scholar] - Ozkan, T.; Lajunen, T.; Chliaoutakis, J.E.I.; Parker, D.; Summala, H. Cross-cultural differences in driving behaviors: A comparison of six countries. Transp. Res. Part F
**2006**, 9, 227–242. [Google Scholar] [CrossRef] - Yanagisawa, M.; Swanson, E.; Najm, W.G. Target Crashes and Safety Benefits Estimation Methodology for Pedestrian Crash Avoidance/Mitigation Systems; Technical Report No. DOT HS 811 998; National Highway Traffic Safety Administration: Washington, DC, USA, 2014.
- Zeng, W.; Chen, P.; Nakamura, H.; Asano, M. Modeling Pedestrian Trajectory for Safety Assessment at Signalized Crosswalks. In Proceedings of the 10th International Conference of the Eastern Asia Society for Transportation Studies, Taipei, Taiwan, 9–12 September 2013. [Google Scholar]
- World Health Organization (WHO). Legal BAC Limits by Country; WHO: Geneva, Switzerland, 2015. [Google Scholar]
- Subramaniam, K.; Phang, W.K.; Hayati, K.S. Traffic light violation among motorists in Malaysia. IATSS Res.
**2007**, 31, 67–73. [Google Scholar] - Gerogiannis, V.C.; Fitsilis, P.; Voulgaridou, D.; Kirytopoulos, K.A.; Sachini, E. A case study for project and portfolio management information system selection: A group AHP-scoring model approach. Int. J. Proj. Organ. Manag.
**2010**, 2, 361–381. [Google Scholar] [CrossRef][Green Version] - Beemsterboer, D.J.C.; Hendrix, E.M.T.; Claassen, G.D.H. On solving the best-worst method in multi-criteria decision-making. IFAC-PapersOnLine
**2018**, 51, 1660–1665. [Google Scholar] [CrossRef] - Sadjadi, S.; Karimi, M. Best-worst multi-criteria decision-making method: A robust approach. Decis. Sci. Lett.
**2018**, 7, 323–340. [Google Scholar] [CrossRef] - Farooq, D.; Moslem, S. Evaluation and Ranking of Driver Behavior Factors Related to Road Safety by Applying Analytic Network Process. Periodica Polytech. Transp. Eng.
**2020**, 48, 189–195. [Google Scholar] [CrossRef][Green Version] - Gul, M.; Guneri, A.F.; Nasirli, S.M. A fuzzy-based model for risk assessment of routes in oil transportation. Int. J. Environ. Sci. Technol.
**2019**, 16, 4671–4686. [Google Scholar] [CrossRef] - Gul, M.; Ak, M.F.; Guneri, A.F. Pythagorean fuzzy VIKOR-based approach for safety risk assessment in mine industry. J. Saf. Res.
**2019**, 69, 135–153. [Google Scholar] [CrossRef] - Ak, M.F.; Gul, M. AHP–TOPSIS integration extended with Pythagorean fuzzy sets for information security risk analysis. Complex Intell. Syst.
**2019**, 5, 113–126. [Google Scholar] [CrossRef][Green Version] - Gündoğdu, F.K.; Kahraman, C. A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets. Eng. Appl. Artif. Intell.
**2019**, 85, 307–323. [Google Scholar] [CrossRef] - Parveen, N.; Kamble, P.N. Decision-Making Problem Using Fuzzy TOPSIS Method with Hexagonal Fuzzy Number. In Computing in Engineering and Technology; Springer: Singapore, 2020; pp. 421–430. [Google Scholar]

**Figure 1.**The hierarchical structure of the problem [50].

Variables | Data Analysis Results |
---|---|

N | 100 |

Age: Mean (SD) | 32.341 (3.421) |

Gender (1 = male, 0 = female): Mean (SD) | 0.845 (0.125) |

Duration of driving license: Mean (SD) | 15.312 (1.589) |

${\mathit{e}}_{\mathit{a}\mathit{b}}$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

$Consistency\text{}Index\left(\mathrm{max}\text{}\xi \right)$ | 0.0 | 0.44 | 1.0 | 1.63 | 2.3 | 3.0 | 3.73 | 4.47 | 5.23 |

Linguistic Term | Triangular Fuzzy Number |
---|---|

Equally Importance (EI) | (1, 1, 1) |

Weakly Important (WI) | (2/3, 1, 1.5) |

Fairly Important (FI) | (1.5, 2, 2.5) |

Very Important (VI) | (2.5, 3, 3.5) |

Absolutely Important (AI) | (3.5, 4, 4.5) |

Factor | F1 | F2 | F3 |
---|---|---|---|

Best factor (F1) | EI | FI | WI |

Factor | Worst Factor (F2) |
---|---|

F1 | FI |

F2 | EI |

F3 | WI |

Linguistic Terms. | Equally Importance (EI) | Weakly Important (WI) | Fairly Important (FI) | Very Important (VI) | Absolutely Important (AI) |
---|---|---|---|---|---|

${\tilde{a}}_{Bw}$ | (1, 1, 1) | (2/3, 1, 3/2) | (3/2, 2, 5/2) | (5/2, 3, 7/2) | (7/2, 4, 9/2) |

CI | 3 | 3.8 | 5.29 | 6.69 | 8.04 |

Factor | Weight | Rank |
---|---|---|

F1 | 0.423 | 1 |

F2 | 0.251 | 3 |

F3 | 0.327 | 2 |

Factor | Weight | Rank |
---|---|---|

F11 | 0.106 | 4 |

F12 | 0.317 | 1 |

F21 | 0.076 | 6 |

F22 | 0.042 | 8 |

F23 | 0.133 | 3 |

F31 | 0.094 | 5 |

F32 | 0.047 | 7 |

F33 | 0.186 | 2 |

Factor | Weight | Rank |
---|---|---|

F111 | 0.068 | 7 |

F112 | 0.112 | 4 |

F113 | 0.071 | 5 |

F121 | 0.114 | 3 |

F122 | 0.177 | 2 |

F123 | 0.114 | 3 |

F124 | 0.057 | 8 |

F125 | 0.070 | 6 |

F126 | 0.216 | 1 |

Factor/Sub-Factor/Sub-sub-Factor | Rank | |
---|---|---|

AHP-BWM Model (Moslem et al. [51]) | F-BWM Model (Existed Study) | |

F1 | 1 | 1 |

F2 | 3 | 3 |

F3 | 2 | 2 |

F11 | 7 | 4 |

F12 | 1 | 1 |

F21 | 4 | 6 |

F22 | 6 | 8 |

F23 | 3 | 3 |

F31 | 5 | 5 |

F32 | 8 | 7 |

F33 | 2 | 2 |

F111 | 9 | 7 |

F112 | 6 | 4 |

F113 | 8 | 5 |

F121 | 7 | 3 |

F122 | 3 | 2 |

F123 | 2 | 3 |

F124 | 5 | 8 |

F125 | 4 | 6 |

F126 | 1 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Moslem, S.; Gul, M.; Farooq, D.; Celik, E.; Ghorbanzadeh, O.; Blaschke, T. An Integrated Approach of Best-Worst Method (BWM) and Triangular Fuzzy Sets for Evaluating Driver Behavior Factors Related to Road Safety. *Mathematics* **2020**, *8*, 414.
https://doi.org/10.3390/math8030414

**AMA Style**

Moslem S, Gul M, Farooq D, Celik E, Ghorbanzadeh O, Blaschke T. An Integrated Approach of Best-Worst Method (BWM) and Triangular Fuzzy Sets for Evaluating Driver Behavior Factors Related to Road Safety. *Mathematics*. 2020; 8(3):414.
https://doi.org/10.3390/math8030414

**Chicago/Turabian Style**

Moslem, Sarbast, Muhammet Gul, Danish Farooq, Erkan Celik, Omid Ghorbanzadeh, and Thomas Blaschke. 2020. "An Integrated Approach of Best-Worst Method (BWM) and Triangular Fuzzy Sets for Evaluating Driver Behavior Factors Related to Road Safety" *Mathematics* 8, no. 3: 414.
https://doi.org/10.3390/math8030414