# An Integrated Decision-Making Method Based on Neutrosophic Numbers for Investigating Factors of Coastal Erosion

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1**

**.**Let $X$ be a space of points, with generic elements in $X$ denoted by $x$. A neutrosophic set $Q$ in $X$ is denoted by $Q=\left\{\langle x,{T}_{Q}\left(x\right),{I}_{Q}\left(x\right),{F}_{Q}\left(x\right)\rangle |x\in X\right\}$ where ${T}_{Q}\left(x\right)$ is the truth-membership function, ${I}_{Q}\left(x\right)$ is the indeterminacy-membership function, and ${F}_{Q}\left(x\right)$ is the falsity-membership function. The functions ${T}_{Q}\left(x\right),{I}_{Q}\left(x\right)$ and ${F}_{Q}\left(x\right)$ are real standard subsets of $\left]{0}^{-},{1}^{+}\right[$. That is, ${T}_{Q}\left(x\right),{I}_{Q}\left(x\right),\text{}{F}_{Q}\left(x\right)\to \left]{0}^{-},{1}^{+}\right[$. Thus, the sum of ${T}_{Q}\left(x\right),{I}_{Q}\left(x\right)$ and ${F}_{Q}\left(x\right)$ is ${0}^{-}\le \mathrm{sup}{T}_{Q}\left(x\right)+\mathrm{sup}{I}_{Q}\left(x\right)+\mathrm{sup}{F}_{Q}\left(x\right)\le {3}^{+}$.

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

## 3. Proposed Method

**Step 1.**Establish the neutrosophic aggregated direct-influence matrix ${A}^{G}$.

**Step 2.**Construct the neutrosophic normalized direct-influence matrix, B.

**Step 3.**Acquire the total direct-influence matrix, S.

**Step 4.**Draw the network relationship map (NRM).

**Step 5.**Form the unweighted supermatrix.

**Step 6.**Construct the weighted supermatrix.

**Step 7.**Construct the limited supermatrix.

## 4. Case Study

#### 4.1. Background of the Problem

#### 4.2. Data Collection and Decision Makers

#### 4.3. Dimensions and Factors

#### 4.4. The Analysis of Data Using the Proposed NS-DANP Method

_{9}) is the most important factor, with a weight of 0.164, followed by sand mining activities (C

_{8}) at 0.153 and coastal protection (C

_{10}) and budgetary revenue (C

_{11}), which are both at 0.116. Relative to other factors, the DM suggests that the storm surge (C

_{3}), tidal range (C

_{4}), and global warming (C

_{5}) are the least important factors with the global weights of 0.045. With respect to each dimension, the DMs indicate that sediment transport (C

_{2}) is the most important factor in the dimension of natural factors (D

_{1}), while coastal development (C

_{9}) is the most important of the man-made factors (D

_{2}). It also concludes that coastal protection (C

_{10}) and budgetary revenue (C

_{11}) are the most important factors under socio-economic factors (D

_{3}).

#### 4.5. Discussion and Implications

_{c}of DEMATEL is incorporated into the ANP method, which is able to consider the influential weight of each cluster. The findings show that the coastal development with the weightage of 0.164 is the most important factor for coastal erosion. Consequently, this study clearly shows the influence of the man-made factors on coastal erosion. Man-made factors such as coastal development are one of the factors that influenced the coastal environment and triggered the destruction of the natural dynamic ecosystem and coastline changes. Human influence on coastal environment and erosion can be connected to the demands and effects of coastal development. The development along coastal areas includes the engineering works such as land reclamation for urban expansion and airport extension, the dredging of navigational channels, and the construction of ports, harbors, groynes, breakwaters, and jetties. These developments can cause the interruption of long-shore sediment supply, which can cause either coastal erosion or accretion. Therefore, the government or stakeholders should pay more attention to the development projects near the coastal zone areas.

_{i}+ b

_{i}) indicates the degree of influences given and received, and it shows the importance index that each dimension and factor contributed to the problem. On the other hand, (a

_{i}− b

_{i}) categorizes the factors into net causer and net receiver groups. If the (a

_{i}− b

_{i}) value is positive, it indicates that the particular factor is influenced by the other factors, and if (a

_{i}− b

_{i}) is negative, then it means that the factor is being influenced by other factors. Considering the (a

_{i}+ b

_{i}) and (a

_{i}− b

_{i}) values in Figure 2, it seems that the man-made factor should first be improved, because it influences the other dimensions the most. That is, if stakeholders plan the man-made factor well, it will improve the other two dimensions. They also can begin on the coastal development factor and sand-mining activities to improve the man-made factors dimension. As seen in Figure 2, it also determines that the natural factors dimension is being influenced the most, followed by the socio-economic factors dimension.

## 5. Comparative Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Hsu, C.; Kuo, T.; Chen, S. Using DEMATEL to develop a carbon management model of supplier selection in green supply chain management. J. Clean. Prod.
**2013**, 56, 164–172. [Google Scholar] [CrossRef] - Lee, W.; Yihou, A.; Chang, Y. Analysis of decision making factors for equity investment by DEMATEL and Analytic Network Process. Expert Syst. Appl.
**2011**, 38, 8375–8383. [Google Scholar] [CrossRef] - Al-Faifi, A.; Song, B.; Hassan, M.M.; Alamri, A.; Gumaei, A. A hybrid multi criteria decision method for cloud service selection from Smart data. Future Gener. Comput. Syst.
**2019**, 93, 43–57. [Google Scholar] [CrossRef] - Mavi, R.K.; Standing, C. Cause and effect analysis of business intelligence (BI) benefits with fuzzy DEMATEL. Knowl. Manag. Res. Pract.
**2018**, 16, 245–257. [Google Scholar] [CrossRef] - Bahadori, M.; Ravangard, R.; Nezhad, M.T. Designing an interactive model of factors affecting the health technology assessment (HTA) in Iran. Int. J. Health Gov.
**2018**, 23, 301–311. [Google Scholar] - Yadegaridehkordi, E.; Hourmand, M.; Nilashi, M. Influence of big data adoption on manufacturing companies’ performance: An integrated DEMATEL-ANFIS approach. Technol. Forecast. Soc. Chang.
**2018**, 137, 199–210. [Google Scholar] [CrossRef] - Chirra, S.; Kumar, D. Evaluation of Supply Chain Flexibility in Automobile Industry with Fuzzy DEMATEL Approach. Glob. J. Flex. Syst. Manag.
**2018**, 19, 305–319. [Google Scholar] [CrossRef] - Ramezankhani, M.J.; Torabi, S.A.; Vahidi, F. Supply chain performance measurement and evaluation: A mixed sustainability and resilience approach. Comput. Ind. Eng.
**2018**, 126, 531–548. [Google Scholar] [CrossRef] - Awang, A.; Ghani, A.T.A.; Abdullah, L. The Shapley weighting vector-based neutrosophic aggregation operator in DEMATEL method. J. Phys. Conf. Ser.
**2018**, 1132, 012059. [Google Scholar] [CrossRef] - Li, Y.; Mathiyazhagan, K. Application of DEMATEL approach to identify the influential indicators towards sustainable supply chain adoption in the auto components manufacturing sector. J. Clean. Prod.
**2016**, 172, 2931–2941. [Google Scholar] [CrossRef] - Rad, T.G.; Sadeghi-Niaraki, A.; Abbasi, A. A methodological framework for assessment of ubiquitous cities using ANP and DEMATEL methods. Sustain. Cities Soc.
**2018**, 37, 608–618. [Google Scholar] - Saaty, T.L. The Analytic Hierarchy Process; McGraw-Hill: New York, NY, USA, 1980. [Google Scholar]
- Shyur, H.J. COTS evaluation using modified TOPSIS and ANP. Appl. Math. Comput.
**2006**, 177, 251–259. [Google Scholar] [CrossRef] - Saaty, T.L. Decision Making with Dependence and Feedback: The Analytic Network Process; RWS Publications: Pittsburgh, PA, USA, 1996; p. 370. ISBN 0-9620317-9-8. [Google Scholar]
- Daǧdeviren, M.; Yüksel, I. A fuzzy analytic network process (ANP) model for measurement of the sectoral competititon level (SCL). Expert Syst. Appl.
**2010**, 37, 1005–1014. [Google Scholar] [CrossRef] - Abdullah, L.; Zulkifli, N. Integration of fuzzy AHP and interval type-2 fuzzy DEMATEL: An application to human resource management. Expert Syst. Appl.
**2015**, 42, 4397–4409. [Google Scholar] [CrossRef] - Bhowmik, S.; Jagadish, G.K. Modeling and Optimization of Abrasive Water Jet Machining Process. In Modeling and Optimization of Advanced Manufacturing Processes; Springer: Cham, Switzerland, 2019; pp. 29–44. [Google Scholar]
- Moktadir, M.A.; Ali, S.M.; Rajesh, R. Modeling the interrelationships among barriers to sustainable supply chain management in leather industry. J. Clean. Prod.
**2018**, 181, 631–651. [Google Scholar] - Ashtarinezhad, E.; Sarfaraz, A.H.; Navabakhsh, M. Supplier evaluation and categorize with combine Fuzzy Dematel and Fuzzy Inference System. Data Brief
**2018**, 18, 1149–1156. [Google Scholar] [CrossRef] [PubMed] - Chakraborty, S.; Chatterjee, P.; Prasad, K. An Integrated DEMATEL–VIKOR Method-Based Approach for Cotton Fibre Selection and Evaluation. J. Inst. Eng. Ser. E
**2018**, 99, 63–73. [Google Scholar] [CrossRef] - Cedolin, M.; Sener, Z. A fuzzy group decision making approach for supplier evaluation and selection in textile industry. In Uncertainty Modelling in Knowledge Engineering and Decision Making, Proceedings of the 12th International FLINS Conference, Roubaix, France, 24–26 August 2016; ENSAIT: Roubaix, France, 2016; pp. 794–799. [Google Scholar]
- Tavana, M.; Khalili-Damghani, K.; Rahmatian, R. A hybrid fuzzy MCDM method for measuring the performance of publicly held pharmaceutical companies. Ann. Oper. Res.
**2014**, 226, 589–621. [Google Scholar] [CrossRef] - Adalı, E.A.; Işık, A.T. Integration of DEMATEL, ANP and DEA methods for third party logistics providers’ selection. Manag. Sci. Lett.
**2016**, 6, 325–340. [Google Scholar] [CrossRef] - Bongo, M.F.; Alimpangog, K.M.S.; Loar, J.F. An application of DEMATEL-ANP and PROMETHEE II approach for air traffic controllers’ workload stress problem: A case of Mactan Civil Aviation Authority of the Philippines. J. Air Transp. Manag.
**2018**, 68, 198–213. [Google Scholar] [CrossRef] - Mihajlovi, M.; Pamučar, D.; Mihajlović, M. Novel approach to group multi-criteria decision making based on interval rough numbers: Hybrid DEMATEL-ANP-MAIRCA model. Expert Syst. Appl.
**2017**, 88, 58–80. [Google Scholar] - Fetanat, A.; Khorasaninejad, E. A novel hybrid MCDM approach for offshore wind farm site selection: A case study of Iran. Ocean Coast. Manag.
**2015**, 109, 17–28. [Google Scholar] [CrossRef] - Lu, M.T.; Lin, S.W.; Tzeng, G.H. Improving RFID adoption in Taiwan’s healthcare industry based on a DEMATEL technique with a hybrid MCDM model. Decis. Support Syst.
**2013**, 56, 259–269. [Google Scholar] [CrossRef] - Tzeng, G.; Huang, C. Combined DEMATEL technique with hybrid MCDM methods for creating the aspired intelligent global manufacturing & logistics systems. Ann. Oper. Res.
**2012**, 197, 159–190. [Google Scholar] - Ju, Y.; Wang, A.; You, T. Emergency alternative evaluation and selection based on ANP, DEMATEL, and TL-TOPSIS. Nat. Hazards
**2015**, 75, 347–379. [Google Scholar] [CrossRef] - Baykasoklu, A.; Golcuk, I. An analysis of DEMATEL approaches for criteria interaction handling within ANP. Expert Syst. Appl.
**2016**, 46, 346–366. [Google Scholar] - Zadeh, L.A. Fuzzy Sets. Inf. Control.
**1965**, 8, 338–353. [Google Scholar] [CrossRef] - Lin, K.P.; Tseng, M.L.; Pai, P.F. Sustainable supply chain management using approximate fuzzy DEMATEL method. Resour. Conserv. Recycl.
**2018**, 128, 134–142. [Google Scholar] [CrossRef] - Abdullah, L.; Zulkifli, N. A new DEMATEL method based on interval type-2 fuzzy sets for developing causal relationship of knowledge management criteria. Neural Comput. Appl.
**2018**, 1–17. [Google Scholar] [CrossRef] - Senturk, S.; Erginel, N.; Binici, Y. Interval type-2 fuzzy analytic network process for modelling a third-party logistics (3PL) company. J. Mult.-Valued Log. Soft Comput.
**2017**, 28, 311–333. [Google Scholar] - Ozdemir, A.; Tuysuz, F. An Integrated Fuzzy DEMATEL and Fuzzy ANP Based Balanced Scorecard Approach: Application in Turkish Higher Education Institutions. J. Mult.-Valued Log. Soft Comput.
**2017**, 28, 251–287. [Google Scholar] - Chen, J.K.; Chen, I.S. Using a novel conjunctive MCDM approach based on DEMATEL, fuzzy ANP, and TOPSIS as an innovation support system for Taiwanese higher education. Expert Syst. Appl.
**2010**, 37, 1981–1990. [Google Scholar] [CrossRef] - Mavi, K.R.; Standing, C. Critical success factors of sustainable project management in construction: A fuzzy DEMATEL-ANP approach. J. Clean. Prod.
**2018**, 194, 751–765. [Google Scholar] [CrossRef] - George-Ufot, G.; Qu, Y.; Orji, I.J. Sustainable lifestyle factors influencing industries’ electric consumption patterns using Fuzzy logic and DEMATEL: The Nigerian perspective. J. Clean. Prod.
**2017**, 162, 624–634. [Google Scholar] [CrossRef] - Gan, J.; Luo, L. Using DEMATEL and Intuitionistic Fuzzy Sets to Identify Critical Factors Influencing the Recycling Rate of End-Of-Life Vehicles in China. Sustainability
**2017**, 9, 1873. [Google Scholar] [CrossRef] - Pandey, A.; Kumar, A. Commentary on “Evaluating the criteria for human resource for science and technology (HRST) based on an integrated fuzzy AHP and fuzzy DEMATEL approach”. Appl. Soft Comput. J.
**2017**, 51, 351–352. [Google Scholar] [CrossRef] - Seker, S.; Zavadskas, E.K. Application of fuzzy DEMATEL method for analyzing occupational risks on construction sites. Sustainability
**2017**, 9, 2083. [Google Scholar] [CrossRef] - Alam-tabriz, A.; Rajabani, N.; Farrokh, M. An Integrated Fuzzy DEMATEL-ANP-TOPSIS Methodology for Supplier Selection Problem. Glob. J. Manag. Stud. Res.
**2014**, 1, 85–99. [Google Scholar] - Hiete, M.; Merz, M.; Comes, T. Trapezoidal fuzzy DEMATEL method to analyze and correct for relations between variables in a composite indicator for disaster resilience. OR Spectr.
**2012**, 34, 971–995. [Google Scholar] [CrossRef] - Hosseini, M.B.; Tarokh, M.J. Type-2 fuzzy set extension of DEMATEL method combined with perceptual computing for decision making. J. Ind. Eng. Int.
**2013**, 9, 1–10. [Google Scholar] [CrossRef] - Baykasoğlu, A.; Gölcük, İ.; Han, W. Development of an interval type-2 fuzzy sets based hierarchical MADM model by combining DEMATEL and TOPSIS. Expert Syst. Appl.
**2017**, 70, 37–51. [Google Scholar] [CrossRef] - Büyüközkan, G.; Güleryüz, S.; Karpak, B. A new combined IF-DEMATEL and IF-ANP approach for CRM partner evaluation. Int. J. Prod. Econ.
**2017**, 191, 194–206. [Google Scholar] [CrossRef] - Govindan, K.; Khodaverdi, R.; Vafadarnikjoo, A. Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Syst. Appl.
**2015**, 42, 7207–7220. [Google Scholar] [CrossRef] - Keshavarzfard, R.; Makui, A. An IF-DEMATEL-AHP based on Triangular Intuitionistic Fuzzy Numbers (TIFNs). Decis. Sci. Lett.
**2015**, 4, 237–246. [Google Scholar] [CrossRef] - Han, W.; Sun, Y.; Xie, H. Hesitant Fuzzy Linguistic Group DEMATEL Method with Multi-granular Evaluation Scales. Int. J. Fuzzy Syst.
**2018**, 20, 2187–2201. [Google Scholar] [CrossRef] - Asan, U.; Kadaifci, C.; Bozdag, E. A new approach to DEMATEL based on interval-valued hesitant fuzzy sets. Appl. Soft Comput. J.
**2018**, 66, 34–49. [Google Scholar] [CrossRef] - Wang, H.; Smarandache, F.; Zhang, Y. Single Valued Neutrosophic Sets. Multisp. Multistruc.
**2010**, 4, 410–413. [Google Scholar] - Atanassov, T. Intuitionistic Fuzzy Sets. Fuzzy Sets Syst.
**1986**, 20, 87–96. [Google Scholar] [CrossRef] - Atanassov, K.; Gargov, G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst.
**1989**, 31, 343–349. [Google Scholar] [CrossRef] - Smarandache, F.A. Unifying Field in Logics: Neutrosophic Logic. Neutrosophy: Neutrosophic Probability, Set and Logic; American Research Press: Rehoboth, DE, USA, 1999. [Google Scholar]
- Ye, J. Clustering methods using distance-based similarity measures of single-valued neutrosophic sets. J. Intell. Syst.
**2014**, 23, 379–389. [Google Scholar] [CrossRef] - Peng, J.; Wang, J.; Wang, J. Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int. J. Syst. Sci.
**2016**, 47, 2342–2358. [Google Scholar] [CrossRef] - Liu, P.; Wang, Y. Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput. Appl.
**2014**, 25, 2001–2010. [Google Scholar] [CrossRef] - Şahin, R.; Kucuk, A. Subsethood measure for single valued neutrosophic sets. J. Intell. Fuzzy Syst.
**2015**, 29, 525–530. [Google Scholar] [CrossRef] - Pramanik, S.; Dalapati, S.; Roy, T.K. Logistics Center Location Selection Approach Based on Neutrosophic Multi-Criteria Decision Making. In New Trends in Neutrosophic Theory and Applications; Pons-Editions: Brussels, Belgium, 2016; pp. 161–174. [Google Scholar]
- Mondal, K.; Pramanik, S. Multi-criteria Group Decision Making Approach for Teacher Recruitment in Higher Education under Simplified Neutrosophic Environment. Glob. J. Eng. Sci. Res. Manag.
**2014**, 6, 28–34. [Google Scholar] - Ye, J.; Fu, J. Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function. Comput. Methods Programs Biomed.
**2016**, 123, 142–149. [Google Scholar] [CrossRef] [PubMed] - Mao, X.B.; Wu, M.; Dong, J.Y. A new method for probabilistic linguistic multi-attribute group decision making: Application to the selection of financial technologies. Appl. Soft Comput. J.
**2019**, 77, 155–175. [Google Scholar] [CrossRef] - Zhao, N.; Xu, Z.; Ren, Z. Hesitant fuzzy linguistic prioritized superiority and inferiority ranking method and its application in sustainable energy technology evaluation. Inf. Sci.
**2019**, 478, 239–257. [Google Scholar] [CrossRef] - Hu, J.; Pan, L.; Yang, Y. A group medical diagnosis model based on intuitionistic fuzzy soft sets. Appl. Soft Comput.
**2019**, 77, 453–466. [Google Scholar] [CrossRef] - Biswas, P.; Pramanik, S.; Giri, B.C. TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput. Appl.
**2016**, 27, 727–737. [Google Scholar] [CrossRef] - Ye, J. A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J. Intell. Fuzzy Syst.
**2014**, 26, 2459–2466. [Google Scholar] - Luo, S.; Wang, H.; Cai, F. An integrated risk assessment of coastal erosion based on fuzzy set theory along Fujian coast, southeast China. Ocean Coast. Manag.
**2013**, 84, 68–76. [Google Scholar] [CrossRef]

**Figure 1.**The framework of the proposed neutrosophic Decision Making Trial and Evaluation Laboratory (DEMATEL)-based Analytic Hierarchy Process (ANP) (NS-DANP) method.

**Figure 5.**The NRM within factors of socio-economic factors $\left({D}_{3}\right)$ of coastal erosion.

**Table 1.**Linguistic variable and its corresponding single-valued neutrosophic numbers (SVNNs) [65].

Integer | Linguistic Variable | SVNNs |
---|---|---|

0 | Very unimportant (VU) | $\langle 0.1,0.8,0.9\rangle $ |

1 | Unimportant (U) | $\langle 0.35,0.6,0.7\rangle $ |

2 | Medium important (M) | $\langle 0.5,0.4,0.45\rangle $ |

3 | Important (I) | $\langle 0.8,0.2,0.15\rangle $ |

4 | Absolutely important (AI) | $\langle 0.9,0.1,0.1\rangle $ |

DM | Position | Sector | Experience |
---|---|---|---|

1 | Coastal engineer | Private | 20 years |

2 | Lecturer | Government | 5 years |

3 | Coastal engineer | Private | 26 years |

Dimensions | Factors |
---|---|

Natural factors $\left({D}_{1}\right)$ | Wave and current $\left({c}_{1}\right)$ |

Sediment transport $\left({c}_{2}\right)$ | |

Storm surge $\left({c}_{3}\right)$ | |

Tidal range $\left({c}_{4}\right)$ | |

Global warming $\left({c}_{5}\right)$ | |

Beach profile and stability $\left({c}_{6}\right)$ | |

Sea level rise $\left({c}_{7}\right)$ | |

Man-made factors $\left({D}_{2}\right)$ | Sand mining activities $\left({c}_{8}\right)$ |

Coastal development $\left({c}_{9}\right)$ | |

Socio-economic factors $\left({D}_{3}\right)$ | Coastal protection $\left({c}_{10}\right)$ |

Budgetary revenue $\left({c}_{11}\right)$ | |

Coastal zone management $\left({c}_{12}\right)$ |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.85,0015,0.13\rangle $ | $\langle 0.65,0.31,0.30\rangle $ | $\langle 0.65,0.34,0.29\rangle $ | $\langle 0.39,0.54,0.63\rangle $ | $\langle 0.87,0.13,0.12\rangle $ | $\langle 0.62,0.34,0.33\rangle $ | $\langle 0.42,0.48,0.54\rangle $ | $\langle 0.58,0.40,0.39\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.79,0.20,0.19\rangle $ |

${c}_{2}$ | $\langle 0.61,0.36,0.35\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.87,0.13,0.12\rangle $ | $\langle 0.49,0.48,0.46\rangle $ | $\langle 0.59,0.37,0.36\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.71,0.28,0.24\rangle $ | $\langle 0.55,0.43,0.42\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.81,0.18,0.17\rangle $ |

${c}_{3}$ | $\langle 0.80,0.20,0.15\rangle $ | $\langle 0.80,0.20,0.15\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.65,0.34,0.29\rangle $ | $\langle 0.59,0.37,0.36\rangle $ | $\langle 0.83,0.17,0.14\rangle $ | $\langle 0.73,0.26,0.22\rangle $ | $\langle 0.59,0.37,0.36\rangle $ | $\langle 0.78,0.20,0.19\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.72,0.26,0.23\rangle $ | $\langle 0.85,0.15,0.13\rangle $ |

${c}_{4}$ | $\langle 0.69,0.30,0.27\rangle $ | $\langle 0.75,0.24,0.20\rangle $ | $\langle 0.43,0.30,0.27\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.41,0.52,0.59\rangle $ | $\langle 0.87,0.13,0.12\rangle $ | $\langle 0.80,0.20,0.15\rangle $ | $\langle 0.73,0.26,0.22\rangle $ | $\langle 0.76,0.23,0.23\rangle $ | $\langle 0.80,0.20,0.15\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.80,0.20,0.15\rangle $ |

${c}_{5}$ | $\langle 0.83,0.17,0.14\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.88,0.12,0.11\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.80,0.20,0.15\rangle $ | $\langle 0.90,0.10,0.10\rangle $ | $\langle 0.62,0.34,0.33\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.81,0.18,0.17\rangle $ |

${c}_{6}$ | $\langle 0.72,0.26,0.23\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.47,0.44,0.50\rangle $ | $\langle 0.65,0.31,0.30\rangle $ | $\langle 0.55,0.43,0.42\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.61,0.36,0.35\rangle $ | $\langle 0.77,0.22,0.20\rangle $ | $\langle 0.72,0.26,0.23\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.80,0.20,0.15\rangle $ | $\langle 0.75,0.24,0.20\rangle $ |

${c}_{7}$ | $\langle 0.81,0.28,0.30\rangle $ | $\langle 0.73,0.26,0.22\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.72,0.26,0.23\rangle $ | $\langle 0.77,0.22,0.20\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.73,0.26,0.22\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.85,0.15,0.13\rangle $ |

${c}_{8}$ | $\langle 0.61,0.36,0.35\rangle $ | $\langle 0.85,0.14,0.15\rangle $ | $\langle 0.73,0.26,0.22\rangle $ | $\langle 0.61,0.36,0.35\rangle $ | $\langle 0.75,0.24,0.20\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.72,0.26,0.23\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.75,0.24,0.20\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.78,0.20,0.19\rangle $ |

${c}_{9}$ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.88,0.12,0.11\rangle $ | $\langle 0.77,0.22,0.20\rangle $ | $\langle 0.58,0.40,0.39\rangle $ | $\langle 0.62,0.34,0.33\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.75,0.24,0.20\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.73,0.24,0.26\rangle $ |

${c}_{10}$ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.42,0.48,0.54\rangle $ | $\langle 0.62,0.34,0.33\rangle $ | $\langle 0.62,0.34,0.33\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.42,0.48,0.54\rangle $ | $\langle 0.71,0.28,0.24\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.45,0.47,0.53\rangle $ |

${c}_{11}$ | $\langle 0.61,0.36,0.35\rangle $ | $\langle 0.70,0.28,0.30\rangle $ | $\langle 0.41,0.52,0.59\rangle $ | $\langle 0.31,0.60,0.69\rangle $ | $\langle 0.41,0.52,0.59\rangle $ | $\langle 0.56,0.39,0.40\rangle $ | $\langle 0.68,0.31,0.34\rangle $ | $\langle 0.73,0.26,0.22\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.10,0.80,0.90\rangle $ | $\langle 0.85,0.15,0.13\rangle $ |

${c}_{12}$ | $\langle 0.41,0.52,0.59\rangle $ | $\langle 0.76,0.23,0.23\rangle $ | $\langle 0.20,0.72,0.82\rangle $ | $\langle 0.20,0.72,0.82\rangle $ | $\langle 0.35,0.60,0.70\rangle $ | $\langle 0.58,0.40,0.39\rangle $ | $\langle 0.55,0.43,0.42\rangle $ | $\langle 0.79,0.20,0.19\rangle $ | $\langle 0.81,0.18,0.17\rangle $ | $\langle 0.87,0.13,0.12\rangle $ | $\langle 0.85,0.15,0.13\rangle $ | $\langle 0.10,0.80,0.90\rangle $ |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.07,0.03,0.03\rangle $ | $\langle 0.07,0.04,0.03\rangle $ | $\langle 0.04,0.06,0.07\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.05,0.05,0.05\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ |

${c}_{2}$ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.04,0.06,0.07\rangle $ | $\langle 0.05,0.05,0.05\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.08,0.03,0.03\rangle $ | $\langle 0.06,0.05,0.05\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ |

${c}_{3}$ | $\langle 0.09,0.04,0.03\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.07,0.04,0.03\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ |

${c}_{4}$ | $\langle 0.08,0.03,0.03\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.05,0.06,0.07\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.08,0.03,0.03\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ |

${c}_{5}$ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.01,0.09,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ |

${c}_{6}$ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.05,0.05,0.06\rangle $ | $\langle 0.07,0.03,0.03\rangle $ | $\langle 0.06,0.05,0.05\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.05,0.04\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.02\rangle $ |

${c}_{7}$ | $\langle 0.09,0.03,0.03\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ |

${c}_{8}$ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ |

${c}_{9}$ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.08,0.03,0.03\rangle $ |

${c}_{10}$ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.05,0.05,0.06\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.05,0.05,0.06\rangle $ | $\langle 0.08,0.03,0.03\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.05,0.05,0.06\rangle $ |

${c}_{11}$ | $\langle 0.07,0.04,0.04\rangle $ | $\langle 0.08,0.03,0.03\rangle $ | $\langle 0.05,0.06,0.07\rangle $ | $\langle 0.03,0.07,0.08\rangle $ | $\langle 0.05,0.06,0.07\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.07,0.03,0.04\rangle $ | $\langle 0.08,0.03,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.01,0.09,0.1\rangle $ | $\langle 0.01,0.09,0.1\rangle $ |

${c}_{12}$ | $\langle 0.05,0.06,0.07\rangle $ | $\langle 0.08,0.03,0.03\rangle $ | $\langle 0.02,0.08,0.09\rangle $ | $\langle 0.02,0.08,0.09\rangle $ | $\langle 0.04,0.07,0.08\rangle $ | $\langle 0.06,0.04,0.04\rangle $ | $\langle 0.06,0.05,0.05\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.09,0.02,0.02\rangle $ | $\langle 0.10,0.01,0.01\rangle $ | $\langle 0.09,0.02,0.01\rangle $ | $\langle 0.01,0.09,0.1\rangle $ |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | $\langle 0.46,0.12,0.13\rangle $ | $\langle 0.59,0.04,0.03\rangle $ | $\langle 0.44,0.06,0.06\rangle $ | $\langle 0.43,0.07,0.07\rangle $ | $\langle 0.40,0.1,0.11\rangle $ | $\langle 0.58,0.03,0.03\rangle $ | $\langle 0.52,0.06,0.06\rangle $ | $\langle 0.46,0.08,0.09\rangle $ | $\langle 0.55,0.07,0.07\rangle $ | $\langle 0.6,0.04,0.04\rangle $ | $\langle 0.6,0.04,0.04\rangle $ | $\langle 0.57,0.04,0.04\rangle $ |

${c}_{2}$ | $\langle 0.51,0.07,0.07\rangle $ | $\langle 0.51,0.11,0.12\rangle $ | $\langle 0.41,0.09,0.11\rangle $ | $\langle 0.42,0.09,0.09\rangle $ | $\langle 0.42,0.08,0.08\rangle $ | $\langle 0.58,0.04,0.03\rangle $ | $\langle 0.53,0.06,0.05\rangle $ | $\langle 0.48,0.08,0.08\rangle $ | $\langle 0.57,0.04,0.04\rangle $ | $\langle 0.6,0.04,0.04\rangle $ | $\langle 0.6,0.04,0.03\rangle $ | $\langle 0.57,0.04,0.04\rangle $ |

${c}_{3}$ | $\langle 0.58,0.04,0.04\rangle $ | $\langle 0.64,0.04,0.03\rangle $ | $\langle 0.42,0.12,0.13\rangle $ | $\langle 0.47,0.07,0.06\rangle $ | $\langle 0.46,0.07,0.07\rangle $ | $\langle 0.63,0.03,0.03\rangle $ | $\langle 0.58,0.05,0.04\rangle $ | $\langle 0.52,0.07,0.06\rangle $ | $\langle 0.62,0.04,0.04\rangle $ | $\langle 0.66,0.03,0.03\rangle $ | $\langle 0.64,0.05,0.04\rangle $ | $\langle 0.62,0.03,0.03\rangle $ |

${c}_{4}$ | $\langle 0.57,0.06,0.05\rangle $ | $\langle 0.64,0.04,0.04\rangle $ | $\langle 0.51,0.04,0.03\rangle $ | $\langle 0.42,0.12,0.13\rangle $ | $\langle 0.45,0.09,0.1\rangle $ | $\langle 0.64,0.03,0.03\rangle $ | $\langle 0.59,0.04,0.03\rangle $ | $\langle 0.54,0.05,0.05\rangle $ | $\langle 0.62,0.04,0.04\rangle $ | $\langle 0.66,0.04,0.03\rangle $ | $\langle 0.66,0.04,0.03\rangle $ | $\langle 0.63,0.04,0.03\rangle $ |

${c}_{5}$ | $\langle 0.62,0.04,0.03\rangle $ | $\langle 0.69,0.04,0.03\rangle $ | $\langle 0.54,0.03,0.03\rangle $ | $\langle 0.53,0.04,0.03\rangle $ | $\langle 0.44,0.12,0.13\rangle $ | $\langle 0.68,0.04,.03\rangle $ | $\langle 0.64,0.03,0.02\rangle $ | $\langle 0.57,0.06,0.06\rangle $ | $\langle 0.67,0.03,0.03\rangle $ | $\langle 0.7,0.04,0.03\rangle $ | $\langle 0.7,0.03,0.03\rangle $ | $\langle 0.67,0.03,0.03\rangle $ |

${c}_{6}$ | $\langle 0.54,0.05,0.05\rangle $ | $\langle 0.61,0.04,0.04\rangle $ | $\langle 0.44,0.08,0.09\rangle $ | $\langle 0.45,0.07,0.06\rangle $ | $\langle 0.43,0.08,0.08\rangle $ | $\langle 0.52,0.11,0.12\rangle $ | $\langle 0.54,0.06,0.06\rangle $ | $\langle 0.51,0.05,0.05\rangle $ | $\langle 0.58,0.05,0.04\rangle $ | $\langle 0.62,0.03,0.03\rangle $ | $\langle 0.62,0.04,0.03\rangle $ | $\langle 0.58,0.05,0.04\rangle $ |

${c}_{7}$ | $\langle 0.61,0.05,0.05\rangle $ | $\langle 0.67,0.05,0.04\rangle $ | $\langle 0.53,0.04,0.04\rangle $ | $\langle 0.51,0.05,0.05\rangle $ | $\langle 0.5,0.05,0.05\rangle $ | $\langle 0.66,0.03,0.03\rangle $ | $\langle 0.55,0.11,0.12\rangle $ | $\langle 0.57,0.05,0.05\rangle $ | $\langle 0.66,0.03,0.03\rangle $ | $\langle 0.69,0.03,0.03\rangle $ | $\langle 0.69,0.03,0.03\rangle $ | $\langle 0.66,0.03,0.03\rangle $ |

${c}_{8}$ | $\langle 0.57,0.06,0.06\rangle $ | $\langle 0.65,0.03,0.03\rangle $ | $\langle 0.5,0.05,0.05\rangle $ | $\langle 0.47,0.07,0.07\rangle $ | $\langle 0.48,0.06,0.05\rangle $ | $\langle 0.64,0.03,0.03\rangle $ | $\langle 0.59,0.05,0.04\rangle $ | $\langle 0.48,0.12,0.13\rangle $ | $\langle 0.63,0.04,0.04\rangle $ | $\langle 0.66,0.04,0.04\rangle $ | $\langle 0.66,0.03,0.03\rangle $ | $\langle 0.63,0.04,0.04\rangle $ |

${c}_{9}$ | $\langle 0.59,0.04,0.03\rangle $ | $\langle 0.66,0.03,0.03\rangle $ | $\langle 0.5,0.05,0.05\rangle $ | $\langle 0.48,0.07,0.07\rangle $ | $\langle 0.47,0.07,0.07\rangle $ | $\langle 0.64,0.04,0.04\rangle $ | $\langle 0.6,0.04,0.04\rangle $ | $\langle 0.55,0.05,0.04\rangle $ | $\langle 0.56,0.11,0.12\rangle $ | $\langle 0.67,0.03,0.03\rangle $ | $\langle 0.66,0.04,0.03\rangle $ | $\langle 0.62,0.04,0.05\rangle $ |

${c}_{10}$ | $\langle 0.53,0.05,0.05\rangle $ | $\langle 0.59,0.04,0.03\rangle $ | $\langle 0.42,0.09,0.1\rangle $ | $\langle 0.43,0.07,0.07\rangle $ | $\langle 0.42,0.08,0.08\rangle $ | $\langle 0.58,0.04,0.04\rangle $ | $\langle 0.54,0.05,0.05\rangle $ | $\langle 0.46,0.09,0.09\rangle $ | $\langle 0.56,0.05,0.05\rangle $ | $\langle 0.53,0.11,0.12\rangle $ | $\langle 0.59,0.04,0.04\rangle $ | $\langle 0.53,0.08,0.09\rangle $ |

${c}_{11}$ | $\langle 0.48,0.07,0.07\rangle $ | $\langle 0.55,0.05,0.06\rangle $ | $\langle 0.39,0.09,0.11\rangle $ | $\langle 0.38,0.11,0.12\rangle $ | $\langle 0.38,0.1,0.12\rangle $ | $\langle 0.52,0.07,0.07\rangle $ | $\langle 0.5,0.06,0.07\rangle $ | $\langle 0.47,0.06,0.06\rangle $ | $\langle 0.54,0.04,0.04\rangle $ | $\langle 0.57,0.04,0.04\rangle $ | $\langle 0.49,0.11,0.13\rangle $ | $\langle 0.54,0.04,0.03\rangle $ |

${c}_{12}$ | $\langle 0.43,0.09,0.1\rangle $ | $\langle 0.52,0.05,0.05\rangle $ | $\langle 0.35,0.12,0.14\rangle $ | $\langle 0.34,0.13,0.14\rangle $ | $\langle 0.35,0.12,0.14\rangle $ | $\langle 0.49,0.07,0.07\rangle $ | $\langle 0.45,0.08,0.08\rangle $ | $\langle 0.44,0.06,0.06\rangle $ | $\langle 0.51,0.05,0.05\rangle $ | $\langle 0.54,0.04,0.03\rangle $ | $\langle 0.53,0.04,0.04\rangle $ | $\langle 0.43,0.12,0.13\rangle $ |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | 0.671 | 0.763 | 0.673 | 0.668 | 0.643 | 0.758 | 0.719 | 0.681 | 0.734 | 0.766 | 0.765 | 0.748 |

${c}_{2}$ | 0.713 | 0.705 | 0.652 | 0.657 | 0.660 | 0.757 | 0.726 | 0.691 | 0.750 | 0.768 | 0.768 | 0.750 |

${c}_{3}$ | 0.753 | 0.791 | 0.653 | 0.691 | 0.681 | 0.786 | 0.754 | 0.719 | 0.778 | 0.801 | 0.790 | 0.781 |

${c}_{4}$ | 0.749 | 0.791 | 0.715 | 0.650 | 0.670 | 0.792 | 0.763 | 0.732 | 0.780 | 0.802 | 0.800 | 0.782 |

${c}_{5}$ | 0.782 | 0.819 | 0.735 | 0.727 | 0.662 | 0.812 | 0.792 | 0.745 | 0.810 | 0.827 | 0.825 | 0.807 |

${c}_{6}$ | 0.731 | 0.772 | 0.669 | 0.677 | 0.664 | 0.709 | 0.728 | 0.716 | 0.755 | 0.781 | 0.776 | 0.756 |

${c}_{7}$ | 0.770 | 0.807 | 0.724 | 0.712 | 0.709 | 0.804 | 0.722 | 0.746 | 0.802 | 0.822 | 0.817 | 0.801 |

${c}_{8}$ | 0.744 | 0.799 | 0.706 | 0.692 | 0.696 | 0.791 | 0.758 | 0.682 | 0.783 | 0.799 | 0.803 | 0.781 |

${c}_{9}$ | 0.763 | 0.803 | 0.711 | 0.692 | 0.689 | 0.790 | 0.765 | 0.736 | 0.730 | 0.806 | 0.802 | 0.780 |

${c}_{10}$ | 0.725 | 0.762 | 0.657 | 0.666 | 0.660 | 0.753 | 0.730 | 0.680 | 0.742 | 0.710 | 0.763 | 0.722 |

${c}_{11}$ | 0.695 | 0.734 | 0.641 | 0.628 | 0.631 | 0.718 | 0.705 | 0.687 | 0.732 | 0.748 | 0.690 | 0.733 |

${c}_{12}$ | 0.663 | 0.719 | 0.609 | 0.604 | 0.611 | 0.700 | 0.678 | 0.676 | 0.713 | 0.732 | 0.729 | 0.657 |

${\mathit{D}}_{1}$ | ${\mathit{D}}_{2}$ | ${\mathit{D}}_{3}$ | |
---|---|---|---|

${D}_{1}$ | 0.30 | 0.36 | 0.35 |

${D}_{2}$ | 0.33 | 0.26 | 0.36 |

${D}_{3}$ | 0.37 | 0.38 | 0.29 |

Dimensions/Factors | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{b}}_{\mathit{i}}$ | ${\mathit{a}}_{\mathit{i}}+{\mathit{b}}_{\mathit{i}}$ | ${\mathit{a}}_{\mathit{i}}-{\mathit{b}}_{\mathit{i}}$ |
---|---|---|---|---|

Natural factors $\left({D}_{1}\right)$ | 2.37 | 2.47 | 4.84 | −0.10 |

Wave and current $\left({c}_{1}\right)$ | 8.59 | 8.76 | 17.35 | −0.17 |

Sediment transport $\left({c}_{2}\right)$ | 8.60 | 9.27 | 17.86 | −0.67 |

Storm surge $\left({c}_{3}\right)$ | 8.98 | 8.15 | 17.12 | 0.83 |

Tidal range $\left({c}_{4}\right)$ | 9.03 | 8.06 | 17.09 | 0.96 |

Global warming $\left({c}_{5}\right)$ | 9.34 | 7.98 | 17.32 | 1.37 |

Beach profile and stability $\left({c}_{6}\right)$ | 8.74 | 9.17 | 17.91 | −0.44 |

Sea level rise $\left({c}_{7}\right)$ | 9.24 | 8.84 | 18.07 | 0.40 |

Man-made factors $\left({D}_{2}\right)$ | 2.52 | 2.38 | 4.89 | 0.14 |

Sand mining activities $\left({c}_{8}\right)$ | 9.03 | 8.49 | 17.53 | 0.54 |

Coastal development $\left({c}_{9}\right)$ | 9.07 | 9.11 | 18.18 | −0.04 |

Socio-economic factors $\left({D}_{3}\right)$ | 2.51 | 2.55 | 5.06 | −0.04 |

Coastal protection $\left({c}_{10}\right)$ | 8.57 | 9.36 | 17.93 | −0.79 |

Budgetary revenue $\left({c}_{11}\right)$ | 8.34 | 9.33 | 17.67 | −0.98 |

Coastal zone management $\left({c}_{12}\right)$ | 8.09 | 9.10 | 17.19 | −1.01 |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | 0.137 | 0.156 | 0.138 | 0.137 | 0.131 | 0.155 | 0.147 | 0.481 | 0.519 | 0.336 | 0.336 | 0.328 |

${c}_{2}$ | 0.146 | 0.145 | 0.134 | 0.135 | 0.135 | 0.155 | 0.149 | 0.479 | 0.521 | 0.336 | 0.336 | 0.328 |

${c}_{3}$ | 0.147 | 0.155 | 0.128 | 0.135 | 0.133 | 0.154 | 0.148 | 0.480 | 0.520 | 0.338 | 0.333 | 0.329 |

${c}_{4}$ | 0.146 | 0.154 | 0.139 | 0.127 | 0.131 | 0.154 | 0.149 | 0.484 | 0.516 | 0.336 | 0.335 | 0.328 |

${c}_{5}$ | 0.147 | 0.154 | 0.138 | 0.136 | 0.124 | 0.152 | 0.149 | 0.479 | 0.521 | 0.336 | 0.336 | 0.328 |

${c}_{6}$ | 0.148 | 0.156 | 0.135 | 0.137 | 0.134 | 0.143 | 0.147 | 0.487 | 0.513 | 0.338 | 0.335 | 0.327 |

${c}_{7}$ | 0.147 | 0.154 | 0.138 | 0.136 | 0.135 | 0.153 | 0.137 | 0.482 | 0.518 | 0.337 | 0.335 | 0.328 |

${c}_{8}$ | 0.143 | 0.154 | 0.136 | 0.133 | 0.134 | 0.153 | 0.146 | 0.466 | 0.534 | 0.335 | 0.337 | 0.328 |

${c}_{9}$ | 0.146 | 0.154 | 0.136 | 0.133 | 0.132 | 0.152 | 0.147 | 0.502 | 0.498 | 0.337 | 0.336 | 0.327 |

${c}_{10}$ | 0.146 | 0.154 | 0.133 | 0.134 | 0.133 | 0.152 | 0.147 | 0.478 | 0.522 | 0.323 | 0.348 | 0.329 |

${c}_{11}$ | 0.146 | 0.154 | 0.135 | 0.132 | 0.133 | 0.151 | 0.148 | 0.484 | 0.516 | 0.344 | 0.318 | 0.338 |

${c}_{12}$ | 0.145 | 0.157 | 0.133 | 0.132 | 0.133 | 0.153 | 0.148 | 0.486 | 0.514 | 0.346 | 0.344 | 0.310 |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | 0.137 | 0.146 | 0.147 | 0.146 | 0.147 | 0.148 | 0.147 | 0.143 | 0.146 | 0.146 | 0.146 | 0.145 |

${c}_{2}$ | 0.156 | 0.145 | 0.155 | 0.154 | 0.154 | 0.156 | 0.154 | 0.154 | 0.154 | 0.154 | 0.154 | 0.157 |

${c}_{3}$ | 0.138 | 0.134 | 0.128 | 0.139 | 0.138 | 0.135 | 0.138 | 0.136 | 0.136 | 0.133 | 0.135 | 0.133 |

${c}_{4}$ | 0.137 | 0.135 | 0.135 | 0.127 | 0.136 | 0.137 | 0.136 | 0.133 | 0.133 | 0.134 | 0.132 | 0.132 |

${c}_{5}$ | 0.131 | 0.135 | 0.133 | 0.131 | 0.124 | 0.134 | 0.135 | 0.134 | 0.132 | 0.133 | 0.133 | 0.133 |

${c}_{6}$ | 0.155 | 0.155 | 0.154 | 0.154 | 0.152 | 0.143 | 0.153 | 0.153 | 0.152 | 0.152 | 0.151 | 0.153 |

${c}_{7}$ | 0.147 | 0.149 | 0.148 | 0.149 | 0.149 | 0.147 | 0.137 | 0.146 | 0.147 | 0.147 | 0.148 | 0.148 |

${c}_{8}$ | 0.481 | 0.479 | 0.480 | 0.484 | 0.479 | 0.487 | 0.482 | 0.466 | 0.502 | 0.478 | 0.484 | 0.486 |

${c}_{9}$ | 0.519 | 0.521 | 0.520 | 0.516 | 0.521 | 0.513 | 0.518 | 0.534 | 0.498 | 0.522 | 0.516 | 0.514 |

${c}_{10}$ | 0.336 | 0.336 | 0.338 | 0.336 | 0.336 | 0.338 | 0.337 | 0.335 | 0.337 | 0.323 | 0.344 | 0.346 |

${c}_{11}$ | 0.336 | 0.336 | 0.333 | 0.335 | 0.336 | 0.335 | 0.335 | 0.337 | 0.336 | 0.348 | 0.318 | 0.344 |

${c}_{12}$ | 0.328 | 0.328 | 0.329 | 0.328 | 0.328 | 0.327 | 0.328 | 0.328 | 0.327 | 0.329 | 0.338 | 0.310 |

${\mathit{D}}_{1}$ | ${\mathit{D}}_{2}$ | ${\mathit{D}}_{3}$ | |
---|---|---|---|

${D}_{1}$ | 0.29 | 0.36 | 0.35 |

${D}_{2}$ | 0.35 | 0.27 | 0.38 |

${D}_{3}$ | 0.36 | 0.36 | 0.28 |

${\mathit{c}}_{1}$ | ${\mathit{c}}_{2}$ | ${\mathit{c}}_{3}$ | ${\mathit{c}}_{4}$ | ${\mathit{c}}_{5}$ | ${\mathit{c}}_{6}$ | ${\mathit{c}}_{7}$ | ${\mathit{c}}_{8}$ | ${\mathit{c}}_{9}$ | ${\mathit{c}}_{10}$ | ${\mathit{c}}_{11}$ | ${\mathit{c}}_{12}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${c}_{1}$ | 0.041 | 0.044 | 0.044 | 0.044 | 0.044 | 0.044 | 0.044 | 0.052 | 0.053 | 0.051 | 0.051 | 0.051 |

${c}_{2}$ | 0.047 | 0.043 | 0.046 | 0.046 | 0.046 | 0.047 | 0.046 | 0.055 | 0.055 | 0.054 | 0.054 | 0.055 |

${c}_{3}$ | 0.041 | 0.040 | 0.038 | 0.042 | 0.041 | 0.041 | 0.041 | 0.049 | 0.049 | 0.046 | 0.047 | 0.046 |

${c}_{4}$ | 0.041 | 0.040 | 0.041 | 0.038 | 0.041 | 0.041 | 0.041 | 0.048 | 0.048 | 0.047 | 0.046 | 0.046 |

${c}_{5}$ | 0.039 | 0.041 | 0.040 | 0.039 | 0.037 | 0.040 | 0.041 | 0.048 | 0.048 | 0.047 | 0.046 | 0.047 |

${c}_{6}$ | 0.046 | 0.047 | 0.046 | 0.046 | 0.046 | 0.043 | 0.046 | 0.055 | 0.055 | 0.053 | 0.053 | 0.053 |

${c}_{7}$ | 0.044 | 0.045 | 0.044 | 0.045 | 0.045 | 0.044 | 0.041 | 0.053 | 0.053 | 0.052 | 0.052 | 0.052 |

${c}_{8}$ | 0.159 | 0.158 | 0.158 | 0.160 | 0.158 | 0.161 | 0.159 | 0.121 | 0.131 | 0.172 | 0.174 | 0.175 |

${c}_{9}$ | 0.171 | 0.172 | 0.172 | 0.170 | 0.172 | 0.169 | 0.171 | 0.139 | 0.129 | 0.188 | 0.186 | 0.185 |

${c}_{10}$ | 0.124 | 0.124 | 0.125 | 0.124 | 0.124 | 0.125 | 0.125 | 0.127 | 0.128 | 0.094 | 0.100 | 0.100 |

${c}_{11}$ | 0.124 | 0.124 | 0.123 | 0.124 | 0.124 | 0.124 | 0.124 | 0.128 | 0.128 | 0.101 | 0.092 | 0.100 |

${c}_{12}$ | 0.121 | 0.121 | 0.122 | 0.121 | 0.121 | 0.121 | 0.121 | 0.125 | 0.124 | 0.095 | 0.098 | 0.090 |

c_{1} | c_{2} | c_{3} | c_{4} | c_{5} | c_{6} | c_{7} | c_{8} | c_{9} | c_{10} | c_{11} | c_{12} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

c_{1} | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 | 0.049 |

c_{2} | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 | 0.052 |

c_{3} | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 |

c_{4} | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 |

c_{5} | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 | 0.045 |

c_{6} | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 | 0.051 |

c_{7} | 0.050 | 0.049 | 0.049 | 0.049 | 0.049 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.049 | 0.050 |

c_{8} | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 | 0.153 |

c_{9} | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 | 0.164 |

c_{10} | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 |

c_{11} | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 | 0.116 |

c_{12} | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 | 0.113 |

Dimensions/Factors | Local Weights | Global Weights |
---|---|---|

Natural factors | 0.336 | |

Wave and current (c_{1}) | 0.145 | 0.049 |

Sediment transport (c_{2}) | 0.153 | 0.052 |

Storm surge (c_{3}) | 0.136 | 0.045 |

Tidal range (c_{4}) | 0.135 | 0.045 |

Global warming (c_{5}) | 0.132 | 0.045 |

Beach profile and stability (c_{6}) | 0.152 | 0.051 |

Sea level rise (c_{7}) | 0.146 | 0.05 |