# An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Linguistic Term Set

**Example**

**1.**

**Definition**

**1.**

#### 2.2. Hesitant Fuzzy Linguistic Term Set

**Definition**

**2.**

**Example**

**2.**

**Definition**

**3.**

**Example**

**3.**

#### 2.3. Probabilistic Linguistic Term Set

**Definition**

**4.**

**Example**

**4.**

#### 2.4. Dempster–Shafer Evidence Theory

**Definition**

**5.**

**Definition**

**6.**

#### 2.5. D Number Theory

**Definition**

**7.**

**Property**

**1.**

**Example**

**5.**

**Example**

**6.**

**Property**

**2.**

**Example**

**7.**

## 3. Proposed Method

## 4. Case Study and Discussion

#### 4.1. Case Study

#### 4.2. Discussion

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kowalski-Trakofler, K.M.; Vaught, C.; Scharf, T. Judgment and decision-making under stress: An overview for emergency managers. Int. J. Emerg. Manag.
**2003**, 1, 278–289. [Google Scholar] [CrossRef] - Yu, L.; Lai, K.K. A distance-based group decision-making methodology for multi-person multi-criteria emergency decision support. Decis. Support Syst.
**2011**, 51, 307–315. [Google Scholar] [CrossRef] - Li, P.; Wei, C. An emergency decision-making method based on DS evidence theory for probabilistic linguistic term sets. Int. J. Disaster Risk Reduct.
**2019**, 37, 101178. [Google Scholar] [CrossRef] - Peterson, E.W.; Grot, R.A. Rapid Fire Emergency Response for Minimizing Human Casualties within a Facility. U.S. Patent 6,496,110, 17 December 2002. [Google Scholar]
- Levy, J.K.; Hartmann, J.; Li, K.W.; An, Y.; Asgary, A. Multi-criteria decision support systems for flood hazard mitigation and emergency response in urban watersheds. J. Am. Water Resour. Assoc.
**2007**, 43, 346–358. [Google Scholar] [CrossRef] - Cheng, F.F.; Dong, X.M.; Wang, S.Y. Emergency management of Yushu earthquake tests the Wenchuan experience. J. Evid.-Based Med.
**2010**, 10, 157–162. [Google Scholar] - Guo, D.; Liu, J.; Jiang, G. The mechanism of the emergency rescue response during coal mine gas explosion. J. China Coal Soc.
**2006**, 31, 697–700. [Google Scholar] - Zhou, L.; Wu, X.; Xu, Z.; Fujita, H. Emergency decision-making for natural disasters: An overview. Int. J. Disaster Risk Reduct.
**2018**, 27, 567–576. [Google Scholar] [CrossRef] - Liu, X.; Xu, Y.; Ge, Y.; Zhang, W.; Herrera, F. A group decision-making approach considering self-confidence behaviors and its application in environmental pollution emergency management. Int. J. Environ. Res. Public Health
**2019**, 16, 385. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Keshavarz Ghorabaee, M.; Amiri, M.; Zavadskas, E.K.; Antucheviciene, J. Supplier evaluation and selection in fuzzy environments: A review of MADM approaches. Econ. Res.-Ekon. Istraživanja
**2017**, 30, 1073–1118. [Google Scholar] [CrossRef] - Liao, H.; Wu, X.; Mi, X.; Herrera, F. An integrated method for cognitive complex multiple experts multiple criteria decision-making based on ELECTRE III with weighted Borda rule. Omega
**2019**. [Google Scholar] [CrossRef] - Fei, L.; Deng, Y. Multi-criteria decision-making in Pythagorean fuzzy environment. Appl. Intell.
**2020**, 50, 537–561. [Google Scholar] [CrossRef] - Janis, I.L.; Mann, L. Emergency decision-making: A theoretical analysis of responses to disaster warnings. J. Hum. Stress
**1977**, 3, 35–48. [Google Scholar] [CrossRef] [PubMed] - Li, M.Y.; Cao, P.P. Extended TODIM method for multi-attribute risk decision-making problems in emergency response. Comput. Ind. Eng.
**2018**, 135, 1286–1293. [Google Scholar] [CrossRef] - Xu, Z.; Liu, Y.; Xuan, J.; Chen, H.; Mei, L. Crowdsourcing based social media data analysis of urban emergency events. Multimed. Tools Appl.
**2017**, 76, 11567–11584. [Google Scholar] [CrossRef] - Kaye, W.E.; Orr, M.F.; Wattigney, W.A. Surveillance of hazardous substance emergency events: Identifying areas for public health prevention. Int. J. Hyg. Environ. Health
**2005**, 208, 37–44. [Google Scholar] [CrossRef] [PubMed] - Dubois, D.; Prade, H. Operations on fuzzy numbers. Int. J. Syst. Sci.
**1978**, 9, 613–626. [Google Scholar] [CrossRef] - Dutta, P. Modeling of variability and uncertainty in human health risk assessment. MethodsX
**2017**, 4, 76–85. [Google Scholar] [CrossRef] - Dutta, P.; Hazarika, G. Construction of families of probability boxes and corresponding membership functions at different fractiles. Expert Syst.
**2017**, 34, e12202. [Google Scholar] [CrossRef] - Xiao, F. A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans. Syst. Man Cybern. Syst.
**2019**. [Google Scholar] [CrossRef] - Jiang, W.; Cao, Y.; Deng, X. A novel Z-network model based on Bayesian network and Z-number. IEEE Trans. Fuzzy Syst.
**2019**, 2019. [Google Scholar] [CrossRef] - Li, Y.; Garg, H.; Deng, Y. A new uncertainty measure of discrete Z-numbers. Int. J. Fuzzy Syst.
**2020**, 22. [Google Scholar] [CrossRef] - Xu, Z.; Xia, M. On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst.
**2011**, 26, 410–425. [Google Scholar] [CrossRef] - Cao, Z.; Lin, C.T. Inherent fuzzy entropy for the improvement of EEG complexity evaluation. IEEE Trans. Fuzzy Syst.
**2018**, 26, 1032–1035. [Google Scholar] [CrossRef] [Green Version] - Cao, Z.; Lin, C.T.; Lai, K.L.; Ko, L.W.; King, J.T.; Liao, K.K.; Fuh, J.L.; Wang, S.J. Extraction of SSVEPs-based inherent fuzzy entropy using a wearable headband EEG in migraine patients. IEEE Trans. Fuzzy Syst.
**2019**. [Google Scholar] [CrossRef] [Green Version] - Herrera, F.; Herrera-Viedma, E. Linguistic decision analysis: Steps for solving decision problems under linguistic information. Fuzzy Sets Syst.
**2000**, 115, 67–82. [Google Scholar] [CrossRef] - Kang, B.; Deng, Y. The maximum Deng entropy. IEEE Access
**2019**, 7, 120758–120765. [Google Scholar] [CrossRef] - Gao, X.; Deng, Y. The Pseudo-Pascal triangle of maximum Deng entropy. Int. J. Comput. Commun. Control
**2020**, 15, 1006. [Google Scholar] [CrossRef] [Green Version] - Seiti, H.; Hafezalkotob, A. Developing the R-TOPSIS methodology for risk-based preventive maintenance planning: A case study in rolling mill company. Comput. Ind. Eng.
**2019**, 128, 622–636. [Google Scholar] [CrossRef] - Loia, V.; Orciuoli, F. Understanding the composition and evolution of terrorist group networks: A rough set approach. Future Gener. Comput. Syst.
**2019**, 101, 983–992. [Google Scholar] [CrossRef] - Wang, H.; He, S.; Pan, X.; Li, C. Shadowed sets-based linguistic term modeling and its application in multi-attribute decision-making. Symmetry
**2018**, 10, 688. [Google Scholar] [CrossRef] [Green Version] - Malik, M.; Bashir, Z.; Rashid, T.; Ali, J. Probabilistic hesitant intuitionistic linguistic term sets in multi-attribute group decision-making. Symmetry
**2018**, 10, 392. [Google Scholar] [CrossRef] [Green Version] - Zhang, S.; Gao, H.; Wei, G.; Wei, Y.; Wei, C. Evaluation based on distance from average solution method for multiple criteria group decision-making under picture 2-tuple linguistic environment. Mathematics
**2019**, 7, 243. [Google Scholar] [CrossRef] [Green Version] - Herrera, F.; Herrera-Viedma, E.; Verdegay, J.L. A sequential selection process in group decision-making with a linguistic assessment approach. Inf. Sci.
**1995**, 85, 223–239. [Google Scholar] [CrossRef] - Delgado, M.; Verdegay, J.L.; Vila, M. Linguistic decision-making models. Int. J. Intell. Syst.
**1992**, 7, 479–492. [Google Scholar] [CrossRef] - Rodriguez, R.M.; Martinez, L.; Herrera, F. Hesitant fuzzy linguistic term sets for decision-making. IEEE Trans. Fuzzy Syst.
**2011**, 20, 109–119. [Google Scholar] [CrossRef] - Tang, M.; Liao, H.; Li, Z.; Xu, Z. Nature disaster risk evaluation with a group decision-making method based on incomplete hesitant fuzzy linguistic preference relations. Int. J. Environ. Res. Public Health
**2018**, 15, 751. [Google Scholar] [CrossRef] [Green Version] - Wei, C.; Rodríguez, R.M.; Li, P. Note on entropies of hesitant fuzzy linguistic term sets and their applications. Inf. Sci.
**2020**, 512, 352–368. [Google Scholar] [CrossRef] - Feng, X.; Zhang, L.; Wei, C. The consistency measures and priority weights of hesitant fuzzy linguistic preference relations. Appl. Soft Comput.
**2018**, 65, 79–90. [Google Scholar] [CrossRef] - Wang, H. Extended hesitant fuzzy linguistic term sets and their aggregation in group decision-making. Int. J. Comput. Intell. Syst.
**2015**, 8, 14–33. [Google Scholar] [CrossRef] - Pang, Q.; Wang, H.; Xu, Z. Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci.
**2016**, 369, 128–143. [Google Scholar] [CrossRef] - Lin, M.; Chen, Z.; Liao, H.; Xu, Z. ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing. Nonlinear Dyn.
**2019**, 96, 2125–2143. [Google Scholar] [CrossRef] - Song, Y.; Li, G. A large-scale group decision-making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection. J. Oper. Res. Soc.
**2019**, 70, 827–841. [Google Scholar] [CrossRef] - Zhang, Y.; Xu, Z.; Wang, H.; Liao, H. Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput.
**2016**, 49, 817–833. [Google Scholar] [CrossRef] - Peng, H.; Zhang, H.; Wang, J. Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information. Int. J. Hosp. Manag.
**2018**, 68, 124–138. [Google Scholar] [CrossRef] - Gao, J.; Xu, Z.; Liang, Z.; Liao, H. Expected consistency-based emergency decision-making with incomplete probabilistic linguistic preference relations. Knowl.-Based Syst.
**2019**, 176, 15–28. [Google Scholar] [CrossRef] - Tang, M.; Long, Y.; Liao, H.; Xu, Z. Inclusion measures of probabilistic linguistic term sets and their application in classifying cities in the Economic Zone of Chengdu Plain. Appl. Soft Comput.
**2019**, 82. [Google Scholar] [CrossRef] - Wu, X.; Liao, H.; Xu, Z.; Hafezalkotob, A.; Herrera, F. Probabilistic linguistic MULTIMOORA: A multicriteria decision-making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Trans. Fuzzy Syst.
**2018**, 26, 3688–3702. [Google Scholar] [CrossRef] - Wu, X.; Liao, H. A consensus-based probabilistic linguistic gained and lost dominance score method. Eur. J. Oper. Res.
**2019**, 272, 1017–1027. [Google Scholar] [CrossRef] - Jiang, L.; Liao, H. Mixed fuzzy least absolute regression analysis with quantitative and probabilistic linguistic information. Fuzzy Sets Syst.
**2019**. [Google Scholar] [CrossRef] - Dempster, A.P. Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat.
**1967**, 38, 325–339. [Google Scholar] [CrossRef] - Shafer, G. A Mathematical Theory of Evidence; Princeton University Press: Princeton, NJ, USA, 1976; Volume 1. [Google Scholar]
- Yuan, R.; Tang, M.; Wang, H.; Li, H. A reliability analysis method of accelerated performance degradation based on Bayesian strategy. IEEE Access
**2019**, 7, 169047–169054. [Google Scholar] [CrossRef] - Xiao, F. Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inf. Fusion
**2019**, 46, 23–32. [Google Scholar] [CrossRef] - Xiao, F. A new divergence measure for belief functions in D-S evidence theory for multisensor data fusion. Inf. Sci.
**2019**, 514, 462–483. [Google Scholar] [CrossRef] - Pan, L.; Deng, Y. An association coefficient of belief function and its application in target recognition system. Int. J. Intell. Syst.
**2020**, 35, 85–104. [Google Scholar] [CrossRef] - Jiang, W.; Huang, C.; Deng, X. A new probability transformation method based on a correlation coefficient of belief functions. Int. J. Intell. Syst.
**2019**, 34, 1337–1347. [Google Scholar] [CrossRef] - Pan, Y.; Zhang, L.; Li, Z.; Ding, L. Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and DS evidence theory. IEEE Trans. Fuzzy Syst.
**2019**. [Google Scholar] [CrossRef] - Xiao, F. EFMCDM: Evidential fuzzy multicriteria decision-making based on belief entropy. IEEE Trans. Fuzzy Syst.
**2019**. [Google Scholar] [CrossRef] - Sun, C.; Li, S.; Deng, Y. Determining weights in multi-criteria decision-making based on negation of probability distribution under uncertain environment. Mathematics
**2020**, 8, 191. [Google Scholar] [CrossRef] [Green Version] - Meng, D.; Li, Y.; Zhu, S.P.; Hu, Z.; Xie, T.; Fan, Z. Collaborative maritime design using sequential optimisation and reliability assessment. Proc. Inst. Civ. Eng.-Marit. Eng.
**2020**. [Google Scholar] [CrossRef] - Liu, W.; Wang, T.; Zang, T.; Huang, Z.; Wang, J.; Huang, T.; Wei, X.; Li, C. A fault diagnosis method for power transmission networks based on spiking neural P systems with self-updating rules considering biological apoptosis mechanism. Complexity
**2020**, 2020, 2462647. [Google Scholar] [CrossRef] [Green Version] - Li, H.; Yuan, R.; Fu, J. A reliability modeling for multi-component systems considering random shocks and multistate degradation. IEEE Access
**2019**, 7, 168805–168814. [Google Scholar] [CrossRef] - Meng, D.; Liu, M.; Yang, S.; Zhang, H.; Ding, R. A fluid–structure analysis approach and its application in the uncertainty-based multidisciplinary design and optimization for blades. Adv. Mech. Eng.
**2018**, 10. [Google Scholar] [CrossRef] [Green Version] - Zhou, L.; Xiao, F. DCM: D number extended cognitive map: Application on location selection in SCM. Int. J. Comput. Commun. Control
**2019**, 14, 753–771. [Google Scholar] - Zhao, J.; Deng, Y. Performer selection in human reliability analysis: D numbers approach. Int. J. Comput. Commun. Control
**2019**, 14, 437–452. [Google Scholar] [CrossRef] [Green Version] - Xiao, F. A novel multi-criteria decision-making method for assessing health-care waste treatment technologies based on D numbers. Eng. Appl. Artif. Intell.
**2018**, 71, 216–225. [Google Scholar] [CrossRef] - Lin, S.; Li, C.; Xu, F.; Liu, D.; Liu, J. Risk identification and analysis for new energy power system in China based on D numbers and decision-making trial and evaluation laboratory (DEMATEL). J. Clean. Prod.
**2018**, 180, 81–96. [Google Scholar] [CrossRef] - Liu, B.; Deng, Y. Risk evaluation in failure mode and effects analysis based on D numbers theory. Int. J. Comput. Commun. Control
**2019**, 14, 672–691. [Google Scholar] - Deng, X.; Jiang, W. Evaluating green supply chain management practices under fuzzy environment: A novel method based on D number theory. Int. J. Fuzzy Syst.
**2019**, 21, 1389–1402. [Google Scholar] [CrossRef] - Shankar, R.; Choudhary, D.; Jharkharia, S. An integrated risk assessment model: A case of sustainable freight transportation systems. Transp. Res. Part D Transp. Environ.
**2018**, 63, 662–676. [Google Scholar] [CrossRef] - Wang, N.; Wei, D. A modified D numbers methodology for environmental impact assessment. Technol. Econ. Dev. Econ.
**2018**, 24, 653–669. [Google Scholar] [CrossRef] - Wang, N.; Liu, X.; Wei, D. A modified D numbers’ integration for multiple attributes decision making. Int. J. Fuzzy Syst.
**2018**, 20, 104–115. [Google Scholar] [CrossRef] - Xiao, F. A multiple-criteria decision-making method based on D numbers and belief entropy. Int. J. Fuzzy Syst.
**2019**, 21, 1144–1153. [Google Scholar] [CrossRef] - Liu, P.; Zhang, X. A multicriteria decision-making approach with linguistic D numbers based on the choquet integral. Cogn. Comput.
**2019**. [Google Scholar] [CrossRef] - Li, X.; Chen, X. D-intuitionistic hesitant fuzzy sets and their application in multiple attribute decision-making. Cogn. Comput.
**2018**, 10, 496–505. [Google Scholar] [CrossRef] - Chen, L.; Yu, H. Emergency alternative selection based on an E-IFWA approach. IEEE Access
**2019**, 7, 44431–44440. [Google Scholar] [CrossRef] - Peng, X.; Garg, H. Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure. Comput. Ind. Eng.
**2018**, 119, 439–452. [Google Scholar] [CrossRef] - Gao, J.; Xu, Z.; Ren, P.; Liao, H. An emergency decision-making method based on the multiplicative consistency of probabilistic linguistic preference relations. Int. J. Mach. Learn. Cybern.
**2019**, 10, 1613–1629. [Google Scholar] [CrossRef] - Ju, Y.; Wang, A. Emergency alternative evaluation under group decision-makers: A method of incorporating DS/AHP with extended TOPSIS. Expert Syst. Appl.
**2012**, 39, 1315–1323. [Google Scholar] [CrossRef] - Xu, Z. Deviation measures of linguistic preference relations in group decision-making. Omega
**2005**, 33, 249–254. [Google Scholar] [CrossRef] - Kennes, R.; Smets, P. Fast algorithms for Dempster–Shafer theory. In Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, France, 2–6 July 1990; Springer: Berlin/Heidelberg, Germany, 1990; pp. 14–23. [Google Scholar]
- Yang, J.; Lin, Y.; Hong, L.; Zetao, L. Improved method to D-S evidence theory based on weight and matrix. Comput. Eng. Appl.
**2012**, 48, 150–153. [Google Scholar] - Zadeh, L.A. A simple view of the Dempster–Shafer theory of evidence and its implication for the rule of combination. AI Mag.
**1986**, 7, 85. [Google Scholar] - Zhang, X.; Xing, X. Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability
**2017**, 9, 1231. [Google Scholar] [CrossRef] [Green Version]

Mutually Exclusive | Completeness Constraint | Independence Constraint | Computational Complexity | One-vote-veto | |
---|---|---|---|---|---|

D-S theory | Must be | Must be | Must be | O(${m}^{n}$) | Exists |

D number | Not necessary | Not necessary | Not necessary | O(mn) | Does not exist |

Experts | ${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | Experts | ${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ||
---|---|---|---|---|---|---|---|---|---|

${E}_{1}$ | ${T}_{1}$ | F | VH | F | ${E}_{2}$ | ${T}_{1}$ | F | VH | L |

${T}_{2}$ | VH | - | H | ${T}_{2}$ | VH | F | H | ||

${T}_{3}$ | H | H | VH | ${T}_{3}$ | H | H | VH | ||

${T}_{4}$ | VH | VL | H | ${T}_{4}$ | VH | VL | H | ||

${E}_{3}$ | ${T}_{1}$ | F | VH | L | ${E}_{4}$ | ${T}_{1}$ | F | VH | L |

${T}_{2}$ | VH | F | VH | ${T}_{2}$ | P | F | VH | ||

${T}_{3}$ | H | H | VH | ${T}_{3}$ | H | H | VH | ||

${T}_{4}$ | VH | VL | H | ${T}_{4}$ | VH | VL | H | ||

${E}_{5}$ | ${T}_{1}$ | H | VH | L | ${E}_{6}$ | ${T}_{1}$ | H | VH | L |

${T}_{2}$ | P | F | VH | ${T}_{2}$ | P | F | VH | ||

${T}_{3}$ | H | H | VH | ${T}_{3}$ | H | VH | VH | ||

${T}_{4}$ | - | L | H | ${T}_{4}$ | P | F | H | ||

${E}_{7}$ | ${T}_{1}$ | H | VH | L | ${E}_{8}$ | ${T}_{1}$ | H | VH | L |

${T}_{2}$ | P | F | P | ${T}_{2}$ | P | - | P | ||

${T}_{3}$ | H | VH | P | ${T}_{3}$ | H | VH | P | ||

${T}_{4}$ | P | F | H | ${T}_{4}$ | P | H | H | ||

${E}_{9}$ | ${T}_{1}$ | H | VH | F | ${E}_{10}$ | ${T}_{1}$ | H | VH | L |

${T}_{2}$ | P | F | P | ${T}_{2}$ | P | F | P | ||

${T}_{3}$ | H | VH | P | ${T}_{3}$ | H | VH | P | ||

${T}_{4}$ | - | H | H | ${T}_{4}$ | P | H | - |

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

${T}_{1}$ | $\{({s}_{0},0.4),({s}_{1},0.6)\}$ | $\left\{({s}_{2},1)\right\}$ | $\{({s}_{-}1,0.8),({s}_{0},0.2)\}$ |

${T}_{2}$ | $\{({s}_{2},0.3),({s}_{3},0.7)\}$ | $\left\{({s}_{0},0.8)\right\}$ | $\{({s}_{1},0.2),({s}_{2},0.4),({s}_{3},0.4)\}$ |

${T}_{3}$ | $\left\{({s}_{1},1.0)\right\}$ | $\{({s}_{1},0.5),({s}_{2},0.5)\}$ | $\{({s}_{2},0.6),({s}_{3},0.4)\}$ |

${T}_{4}$ | $\{({s}_{2},0.4),({s}_{3},0.4)\}$ | $\{({s}_{-}2,0.4),({s}_{-}1,0.1),({s}_{0},0.2),({s}_{1},0.3)\}$ | $\left\{({s}_{1},0.9)\right\}$ |

${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{a}}_{3}$ | ${\mathit{a}}_{4}$ | |
---|---|---|---|---|

${x}_{1}$ | $\{({s}_{3},0.4),({s}_{4},0.6)\}$ | $\{({s}_{2},0.2),({s}_{4},0.8)\}$ | $\{({s}_{3},0.2),({s}_{4},0.8)\}$ | $\{({s}_{3},0.4),({s}_{5},0.6)\}$ |

${x}_{2}$ | $\{({s}_{5},0.2),({s}_{3},0.8)\}$ | $\{({s}_{2},0.2),({s}_{3},0.4),({s}_{4},0.2)\}$ | $\{({s}_{1},0.2),({s}_{2},0.4),({s}_{3},0.2)\}$ | $\{({s}_{3},0.8),({s}_{4},0.2)\}$ |

${x}_{3}$ | $\{({s}_{3},0.6),({s}_{4},0.4)\}$ | $\{({s}_{3},0.6),({s}_{4},0.2)\}$ | $\{({s}_{3},0.2),({s}_{4},0.2),({s}_{5},0.2)\}$ | $\{({s}_{4},0.8),({s}_{6},0.2)\}$ |

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**MDPI and ACS Style**

Mo, H.
An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory. *Symmetry* **2020**, *12*, 380.
https://doi.org/10.3390/sym12030380

**AMA Style**

Mo H.
An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory. *Symmetry*. 2020; 12(3):380.
https://doi.org/10.3390/sym12030380

**Chicago/Turabian Style**

Mo, Hongming.
2020. "An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory" *Symmetry* 12, no. 3: 380.
https://doi.org/10.3390/sym12030380