## Abstract

The research provides a multi-criteria group decision support model for hotel selection according to traveller preference characteristics. Specifically, the study attempts to identify characteristic preferences among travellers through online reviews and then generate recommendation lists under these characteristics. Utilizing a sample of 48,756 online reviews on TripAdvisor.com, the research exploits natural language processing to acquire high-frequency feature words and employs these features to group online reviews for filtering unrelated ones. Subsequently, online reviews and fuzzy theory are combined to develop a decision support model, by utilising the information of user ratings and text comments. In addition, the related extension of the theoretic knowledge is presented. The findings demonstrate that, hotel quality varies under different characteristics and a comprehensive evaluation of hotels would encounter difficulty meeting travellers’ demands, and the proposed model exhibits great performance in addressing this condition. The study can enable travellers to make a satisfactory hotel selection that matches their expectation to a high degree and also provides implications for hoteliers to understand tourist preferences and for tourism websites to optimize management strategies.

This is a preview of subscription content, access via your institution.

## References

Ahani A, Nilashi M, Ibrahim O, Sanzogni L, Weaven S (2019) Market segmentation and travel choice prediction in Spa hotels through TripAdvisor’s online reviews. Int J Hosp Manag 80:52–77

Akram M, Arshad M (2019) A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making. Group Decis Negot 28(3):565–584

An X, Wang Z, Li H, Ding J (2018) Project delivery system selection with interval-valued intuitionistic fuzzy set group decision-making method. Group Decis Negot 27(4):689–707

Bao G, Lian X, He M, Wang L (2010) Improved two-tuple linguistic representation model based on new linguistic evaluation scale. Control Decis 25(5):780–784

Brunelli M (2019) A study on the anonymity of pairwise comparisons in group decision making. Eur J Oper Res 279(2):502–510

Chang W, Fu C, Feng N, Yang S (2020) Multi-criteria group decision making with various ordinal assessments. Group Decis Negot. https://doi.org/10.1007/s10726-020-09677-z

Chang Y-C, Ku C-H, Chen C-H (2019) Social media analytics: Extracting and visualizing Hilton hotel ratings and reviews from TripAdvisor. Int J Inf Manage 48:263–279

Chen S, Wang J, Wang T (2019) Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator. Comput Appl Math 38(2):88

Cheng S-H (2018) Autocratic decision making using group recommendations based on hesitant fuzzy sets for green hotels selection and bidders selection. Inf Sci 467:604–617

Dong Y, Zha Q, Zhang H, Kou G, Fujita H, Chiclana F, Herrera-Viedma E (2018) Consensus reaching in social network group decision making: Research paradigms and challenges. Knowl-Based Syst 162:3–13

Du Y-W, Shan Y-K (2020) A dynamic intelligent recommendation method based on the analytical ER rule for evaluating product ideas in large-scale group decision-making. Group Decis Negot. https://doi.org/10.1007/s10726-020-09687-x

Gao B, Li X, Liu S, Fang D (2018) How power distance affects online hotel ratings: The positive moderating roles of hotel chain and reviewers’ travel experience. Tour Manage 65:176–186

Guo Y, Barnes SJ, Jia Q (2017) Mining meaning from online ratings and reviews: Tourist satisfaction analysis using latent dirichlet allocation. Tour Manage 59:467–483

Herrera F, Herrera Viedma E, Martı́nez, L. (2000) A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst 114(1):43–58

Hou Z, Cui F, Meng Y, Lian T, Yu C (2019) Opinion mining from online travel reviews: A comparative analysis of Chinese major OTAs using semantic association analysis. Tour Manage 74:276–289

Hu N, Zhang T, Gao B, Bose I (2019) What do hotel customers complain about? Text analysis using structural topic model. Tour Manage 72:417–426

Jia F, Liu Y, Wang X (2019) An extended MABAC method for multi-criteria group decision making based on intuitionistic fuzzy rough numbers. Expert Syst Appl 127:241–255

Kwok PK, Lau HYK (2019) Hotel selection using a modified TOPSIS-based decision support algorithm. Decis Support Syst 120:95–105

Li D, Liu C, Gan W (2009) A new cognitive model: cloud model. Int J Intell Syst 24(3):357–375

Ma Z, Zhu J, Ponnambalam K, Zhang S (2019) A clustering method for large-scale group decision-making with multi-stage hesitant fuzzy linguistic terms. Inf Fus 50:231–250

Mishra AR, Rani P (2018) Interval-valued intuitionistic fuzzy WASPAS method: Application in reservoir flood control management policy. Group Decis Negot 27(6):1047–1078

Nie R-X, Tian Z-P, Wang J-Q, Chin KS (2020) Hotel selection driven by online textual reviews: Applying a semantic partitioned sentiment dictionary and evidence theory. Int J Hosp Manag 88:102495

Nilashi M, Ibrahim O, Yadegaridehkordi E, Samad S, Akbari E, Alizadeh A (2018) Travelers decision making using online review in social network sites: a case on TripAdvisor. J Comput Sci 28:168–179

Ostovare M, Shahraki MR (2019) Evaluation of hotel websites using the multicriteria analysis of PROMETHEE and GAIA: evidence from the five-star hotels of Mashhad. Tourism Manag Perspect 30:107–116

Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci 369:128–143

Peng H, Wang J (2020) Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information. Fuzzy Optim Decis Making. https://doi.org/10.1007/s10700-020-09330-z

Peng H, Zhang H, Wang J (2018) Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information. Int J Hosp Manag 68:124–138

Radojevic T, Stanisic N, Stanic N, Davidson R (2018) The effects of traveling for business on customer satisfaction with hotel services. Tour Manage 67:326–341

Ramanathan U (2017) Role of social media in retail network operations and marketing to enhance customer satisfaction. Int J Oper Prod Manag 37(1):105–123

Sánchez-Franco MJ, Navarro-García A, Rondán-Cataluña FJ (2019) A naive Bayes strategy for classifying customer satisfaction: A study based on online reviews of hospitality services. J Bus Res 101:499–506

Sharifi S (2019) Examining the impacts of positive and negative online consumer reviews on behavioral intentions: Role of need for cognitive closure and satisfaction guarantees. J Hosp Market Manag 28(4):397–426

Shen J, Ma MD, Xiang R, Lu Q, Vallejos EP, Xu G, Huang C-R, Long Y (2020) Dual memory network model for sentiment analysis of review text. Knowl-Based Syst 188:105004

Shin S, Chung N, Xiang Z, Koo C (2019) Assessing the impact of textual content concreteness on helpfulness in online travel reviews. J Travel Res 58(4):579–593

Tang M, Zhou X, Liao H, Xu J, Fujita H, Herrera F (2019) Ordinal consensus measure with objective threshold for heterogeneous large-scale group decision making. Knowl-Based Syst 180:62–74

Tavana M, Zandi F, Katehakis MN (2013) A hybrid fuzzy group ANP-TOPSIS framework for assessment of e-government readiness from a CiRM perspective. Inf Manag 50(7):383–397

Tian Z, Nie R, Wang J (2019) Social network analysis-based consensus-supporting framework for large-scale group decision-making with incomplete interval type-2 fuzzy information. Inf Sci 502:446–471

Tian Z, Wang J, Wang J, Zhang H (2017) Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis Negot 26(3):597–627

Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323

Vinzenz F (2019) The added value of rating pictograms for sustainable hotels in classified ads. Tourism Manag Perspect 29:56–65

Wang J, Wu J, Wang J, Zhang H, Chen X (2014) Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf Sci 288:55–72

Wang JQ, Peng JJ, Zhang HY, Liu T, Chen XH (2015) An uncertain linguistic multi-criteria group decision-making method based on a cloud model. Group Decis Negot 24(1):171–192

Wang L, Wang X, Peng J, Wang J (2020) The differences in hotel selection among various types of travellers: A comparative analysis with a useful bounded rationality behavioural decision support model. Tour Manage 76:103961

Wang X, Wang J, Zhang H (2019) Distance-based multicriteria group decision-making approach with probabilistic linguistic term sets. Expert Syst 36(2):e12352

Wu T, Liu X, Liu F (2018) The solution for fuzzy large-scale group decision making problems combining internal preference information and external social network structures. Soft Comput 23(18):9025–9043

Xiang Z, Du Q, Ma Y, Fan W (2017) A comparative analysis of major online review platforms: Implications for social media analytics in hospitality and tourism. Tour Manage 58:51–65

Xu Z (2008) Group decision making based on multiple types of linguistic preference relations. Inf Sci 178(2):452–467

Xu Z, Zhou W (2017) Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optim Decis Making 16(4):481–503

Yan G, Jia S, Ding J, Xu X, Pang Y (2019) A time series forecasting based on cloud model similarity measurement. Soft Comput 23(14):5443–5454

Yu S, Wang J, Wang J, Li L (2018) A multi-criteria decision-making model for hotel selection with linguistic distribution assessments. Appl Soft Comput 67:741–755

Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

Zhang C-X, Zhao M, Cai M-Y, Xiao Q-R (2020) Multi-stage multi-attribute decision making method based on online reviews for hotel selection considering the aspirations with different development speeds. Comput Ind Eng 143:106421

Zhang C, Zhang H, Wang J (2018) Personalized restaurant recommendation method combining group correlations and customer preferences. Inf Sci 454–455:128–143

Zhang H, Ji P, Wang J, Chen X (2017) A novel decision support model for satisfactory restaurants utilizing social information: A case study of TripAdvisor.com. Tour Manage 59:281–297

Zhang Y, Xu Z, Liao H (2019) Water security evaluation based on the TODIM method with probabilistic linguistic term sets. Soft Comput 23(15):6215–6230

## Acknowledgement

This work was supported by the National Natural Science Foundation of China (No. 71871228).

## Author information

### Affiliations

### Corresponding author

## Additional information

### Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Appendices

### Appendix A

Group 1
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.83} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.63} \right),s_{3} \left( {0.20} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.73} \right),s_{3} \left( {0.13} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.56} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.16} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.83} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.85} \right),s_{3} \left( {0.11} \right),s_{2} \left( {0.02} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.20} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.60} \right),s_{3} \left( {0.26} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.72} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.58} \right),s_{3} \left( {0.24} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.74} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.02} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.73} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.53} \right),s_{3} \left( {0.33} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.01} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(s_{4} \left( {0.44} \right),s_{3} \left( {0.31} \right),s_{2} \left( {0.17} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.75} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.39} \right),s_{3} \left( {0.35} \right),s_{2} \left( {0.17} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.67} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.01} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.46} \right),s_{3} \left( {0.34} \right),s_{2} \left( {0.13} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.69} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.03} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.46} \right),s_{3} \left( {0.32} \right),s_{2} \left( {0.13} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.04} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.49} \right),s_{3} \left( {0.35} \right),s_{2} \left( {0.12} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.80} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

Group 2
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(s_{4} \left( {0.75} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.85} \right),s_{3} \left( {0.11} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.66} \right),s_{3} \left( {0.21} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.10} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.62} \right),s_{3} \left( {0.22} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.81} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.84} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.04} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.85} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.01} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.02} \right),s_{1} \left( {0.01} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.22} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.78} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.61} \right),s_{3} \left( {0.25} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.74} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.63} \right),s_{3} \left( {0.21} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.75} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.02} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.78} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.74} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.55} \right),s_{3} \left( {0.33} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.71} \right),s_{3} \left( {0.22} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\({{a}}_{1}\) | \(s_{4} \left( {0.47} \right),s_{3} \left( {0.31} \right),s_{2} \left( {0.14} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.13} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) |

\({{a}}_{2}\) | \(s_{4} \left( {0.43} \right),s_{3} \left( {0.34} \right),s_{2} \left( {0.15} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.66} \right),s_{3} \left( {0.21} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) |

\({{a}}_{3}\) | \(s_{4} \left( {0.49} \right),s_{3} \left( {0.32} \right),s_{2} \left( {0.13} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.72} \right),s_{3} \left( {0.13} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.04} \right)\) |

\({{{a}}}_{4}\) | \(s_{4} \left( {0.48} \right),s_{3} \left( {0.31} \right),s_{2} \left( {0.12} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.11} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.03} \right)\) |

\({{{a}}}_{5}\) | \(s_{4} \left( {0.51} \right),s_{3} \left( {0.35} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.83} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

Group 3
| ||

\({{c}}_{1}\) | \({{c}}_{2}\) | |

\({{a}}_{1}\) | \(s_{4} \left( {0.73} \right),s_{3} \left( {0.22} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.86} \right),s_{3} \left( {0.10} \right),s_{2} \left( {0.02} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\({{a}}_{2}\) | \(s_{4} \left( {0.62} \right),s_{3} \left( {0.24} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.78} \right),s_{3} \left( {0.11} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) |

\({{a}}_{3}\) | \(s_{4} \left( {0.60} \right),s_{3} \left( {0.24} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right)\) |

\({{a}}_{4}\) | \(s_{4} \left( {0.70} \right),s_{3} \left( {0.22} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.81} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right)\) |

\({{a}}_{5}\) | \(s_{4} \left( {0.85} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.01} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(s_{4} \left( {0.64} \right),s_{3} \left( {0.20} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.60} \right),s_{3} \left( {0.27} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.73} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.71} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.73} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.75} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.72} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.53} \right),s_{3} \left( {0.34} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.70} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(s_{4} \left( {0.47} \right),s_{3} \left( {0.32} \right),s_{2} \left( {0.14} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.02} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.39} \right),s_{3} \left( {0.38} \right),s_{2} \left( {0.15} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.65} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.44} \right),s_{3} \left( {0.35} \right),s_{2} \left( {0.16} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.03} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.43} \right),s_{3} \left( {0.35} \right),s_{2} \left( {0.14} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.75} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.02} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.49} \right),s_{3} \left( {0.36} \right),s_{2} \left( {0.12} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.81} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right)\) |

Group 4
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.85} \right),s_{3} \left( {0.11} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.64} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.10} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.01} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.80} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.24} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.83} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.84} \right),s_{3} \left( {0.13} \right),s_{2} \left( {0.01} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.02} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(s_{4} \left( {0.65} \right),s_{3} \left( {0.20} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.78} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.04} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.02} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.59} \right),s_{3} \left( {0.27} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.72} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.67} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.72} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.54} \right),s_{3} \left( {0.34} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.69} \right),s_{3} \left( {0.23} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.03} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(s_{4} \left( {0.45} \right),s_{3} \left( {0.32} \right),s_{2} \left( {0.15} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.14} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.39} \right),s_{3} \left( {0.34} \right),s_{2} \left( {0.18} \right),s_{1} \left( {0.06} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.64} \right),s_{3} \left( {0.21} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.02} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.45} \right),s_{3} \left( {0.33} \right),s_{2} \left( {0.15} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.69} \right),s_{3} \left( {0.15} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.03} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.51} \right),s_{3} \left( {0.30} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.05} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.77} \right),s_{3} \left( {0.12} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.03} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.51} \right),s_{3} \left( {0.35} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.82} \right),s_{3} \left( {0.13} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

Group 5
| ||

\({c}_{1}\) | \({c}_{2}\) | |

\({{{a}}}_{1}\) | \({s}_{4}\left(0.72\right),{s}_{3}\left(0.11\right),{s}_{2}\left(0.14\right),{s}_{1}\left(0.02\right),{s}_{0}\left(0.01\right)\) | \({s}_{4}\left(0.76\right),{s}_{3}\left(0.16\right),{s}_{2}\left(0.05\right),{s}_{1}\left(0.01\right),{s}_{0}\left(0.02\right)\) |

\({{{a}}}_{2}\) | \({s}_{4}\left(0.60\right),{s}_{3}\left(0.25\right),{s}_{2}\left(0.11\right),{s}_{1}\left(0.03\right),{s}_{0}\left(0.01\right)\) | \({s}_{4}\left(0.81\right),{s}_{3}\left(0.13\right),{s}_{2}\left(0.04\right),{s}_{1}\left(0.02\right)\) |

\({{{a}}}_{3}\) | \({s}_{4}\left(0.61\right),{s}_{3}\left(0.23\right),{s}_{2}\left(0.10\right),{s}_{1}\left(0.04\right),{s}_{0}\left(0.02\right)\) | \({s}_{4}\left(0.77\right),{s}_{3}\left(0.15\right),{s}_{2}\left(0.05\right),{s}_{1}\left(0.01\right),{s}_{0}\left(0.02\right)\) |

\({{{a}}}_{4}\) | \({s}_{4}\left(0.58\right),{s}_{3}\left(0.30\right),{s}_{2}\left(0.09\right),{s}_{1}\left(0.02\right),{s}_{0}\left(0.01\right)\) | \(s_{4} \left( {0.76} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.06} \right),s_{0} \left( {0.01} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.79} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.69} \right),s_{3} \left( {0.26} \right),s_{2} \left( {0.03} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.01} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(s_{4} \left( {0.55} \right),s_{3} \left( {0.25} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.06} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.67} \right),s_{3} \left( {0.21} \right),s_{2} \left( {0.07} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.43} \right),s_{3} \left( {0.28} \right),s_{2} \left( {0.15} \right),s_{1} \left( {0.10} \right),s_{0} \left( {0.04} \right)\) | \(s_{4} \left( {0.59} \right),s_{3} \left( {0.25} \right),s_{2} \left( {0.12} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.02} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.70} \right),s_{3} \left( {0.17} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.01} \right)\) | \(s_{4} \left( {0.70} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.06} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.03} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.68} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.02} \right)\) | \(s_{4} \left( {0.61} \right),s_{3} \left( {0.21} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.06} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.43} \right),s_{3} \left( {0.38} \right),s_{2} \left( {0.13} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.63} \right),s_{3} \left( {0.28} \right),s_{2} \left( {0.05} \right),s_{1} \left( {0.04} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(s_{4} \left( {0.27} \right),s_{3} \left( {0.31} \right),s_{2} \left( {0.23} \right),s_{1} \left( {0.12} \right),s_{0} \left( {0.07} \right)\) | \(s_{4} \left( {0.64} \right),s_{3} \left( {0.16} \right),s_{2} \left( {0.11} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.05} \right)\) |

\(a_{2}\) | \(s_{4} \left( {0.25} \right),s_{3} \left( {0.29} \right),s_{2} \left( {0.25} \right),s_{1} \left( {0.12} \right),s_{0} \left( {0.09} \right)\) | \(s_{4} \left( {0.62} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.10} \right),s_{1} \left( {0.07} \right),s_{0} \left( {0.03} \right)\) |

\(a_{3}\) | \(s_{4} \left( {0.45} \right),s_{3} \left( {0.32} \right),s_{2} \left( {0.15} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.06} \right)\) | \(s_{4} \left( {0.62} \right),s_{3} \left( {0.22} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.03} \right),s_{0} \left( {0.04} \right)\) |

\(a_{4}\) | \(s_{4} \left( {0.32} \right),s_{3} \left( {0.33} \right),s_{2} \left( {0.17} \right),s_{1} \left( {0.08} \right),s_{0} \left( {0.10} \right)\) | \(s_{4} \left( {0.65} \right),s_{3} \left( {0.18} \right),s_{2} \left( {0.09} \right),s_{1} \left( {0.02} \right),s_{0} \left( {0.06} \right)\) |

\(a_{5}\) | \(s_{4} \left( {0.44} \right),s_{3} \left( {0.33} \right),s_{2} \left( {0.16} \right),s_{1} \left( {0.04} \right),s_{0} \left( {0.03} \right)\) | \(s_{4} \left( {0.70} \right),s_{3} \left( {0.19} \right),s_{2} \left( {0.08} \right),s_{1} \left( {0.01} \right),s_{0} \left( {0.02} \right)\) |

### Appendix B

Group 1
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(\left( {0.0016,0.0457,0.6937,0.7821,0.0100,0.0003} \right)\) | \(\left( {0.0017,0.0487,0.7421,0.8372,0.0072,0.0002} \right)\) |

\(a_{2}\) | \(\left( {0.0013,0.0384,0.5753,0.6474,0.0132,0.0005} \right)\) | \(\left( {0.0015,0.0434,0.6577,0.7416,0.0087,0.0003} \right)\) |

\(a_{3}\) | \(\left( {0.0013,0.0356,0.5263,0.5908,0.0157,0.0006} \right)\) | \(\left( {0.0016,0.0466,0.7092,0.7998,0.0087,0.0003} \right)\) |

\(a_{4}\) | \(\left( {0.0015,0.0416,0.6266,0.7055,0.0140,0.0005} \right)\) | \(\left( {0.0017,0.0486,0.7403,0.8352,0.0073,0.0003} \right)\) |

\(a_{5}\) | \(\left( {0.0017,0.0497,0.7568,0.8538,0.0078,0.0003} \right)\) | \(\left( {0.0016,0.0458,0.6946,0.7830,0.0109,0.0004} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(\left( {0.0014,0.0409,0.6161,0.6939,0.0126,0.0004} \right)\) | \(\left( {0.0016,0.0448,0.6800,0.7667,0.0097,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0013,0.0375,0.5590,0.6285,0.0159,0.0006} \right)\) | \(\left( {0.0015,0.0430,0.6513,0.7340,0.0113,0.0004} \right)\) |

\(a_{3}\) | \(\left( {0.0013,0.0364,0.5425,0.6099,0.0151,0.0005} \right)\) | \(\left( {0.0015,0.0440,0.6676,0.7526,0.0105,0.0004} \right)\) |

\(a_{4}\) | \(\left( {0.0016,0.0449,0.6815,0.7684,0.0095,0.0003} \right)\) | \(\left( {0.0015,0.0434,0.6581,0.7419,0.0101,0.0004} \right)\) |

\(a_{5}\) | \(\left( {0.0013,0.0353,0.5177,0.5800,0.0199,0.0007} \right)\) | \(\left( {0.0015,0.0415,0.6259,0.7048,0.0138,0.0005} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(\left( {0.0011,0.0313,0.4468,0.4987,0.0202,0.0007} \right)\) | \(\left( {0.0015,0.0441,0.6697,0.7552,0.0090,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0011,0.0303,0.4242,0.4717,0.0223,0.0008} \right)\) | \(\left( {0.0014,0.0401,0.6039,0.6803,0.0120,0.0004} \right)\) |

\(a_{3}\) | \(\left( {0.0012,0.0327,0.4719,0.5273,0.0209,0.0007} \right)\) | \(\left( {0.0014,0.0413,0.6243,0.7036,0.0103,0.0004} \right)\) |

\(a_{4}\) | \(\left( {0.0011,0.0320,0.4614,0.5160,0.0198,0.0007} \right)\) | \(\left( {0.0016,0.0450,0.6849,0.7725,0.0080,0.0003} \right)\) |

\(a_{5}\) | \(\left( {0.0012,0.0340,0.4925,0.5507,0.0212,0.0007} \right)\) | \(\left( {0.0016,0.0471,0.7163,0.8080,0.0082,0.0003} \right)\) |

Group 2
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(\left( {0.0016,0.0447,0.6779,0.7641,0.0114,0.0004} \right)\) | \(\left( {0.0017,0.0494,0.7527,0.8493,0.0066,0.0002} \right)\) |

\(a_{2}\) | \(\left( {0.0014,0.0402,0.6056,0.6821,0.0129,0.0004} \right)\) | \(\left( {0.0016,0.0451,0.6862,0.7740,0.0073,0.0003} \right)\) |

\(a_{3}\) | \(\left( {0.0013,0.0385,0.5759,0.6480,0.0139,0.0005} \right)\) | \(\left( {0.0016,0.0474,0.7211,0.8133,0.0082,0.0003} \right)\) |

\(a_{4}\) | \(\left( {0.0015,0.0418,0.6288,0.7079,0.0141,0.0005} \right)\) | \(\left( {0.0017,0.0489,0.7454,0.8410,0.0071,0.0002} \right)\) |

\(a_{5}\) | \(\left( {0.0017,0.0499,0.7608,0.8583,0.0077,0.0003} \right)\) | \(\left( {0.0016,0.0465,0.7068,0.7969,0.0105,0.0004} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(\left( {0.0014,0.0413,0.6235,0.7022,0.0130,0.0005} \right)\) | \(\left( {0.0016,0.0458,0.6954,0.7843,0.0091,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0013,0.0382,0.5704,0.6415,0.0153,0.0005} \right)\) | \(\left( {0.0015,0.0438,0.6633,0.7476,0.0107,0.0004} \right)\) |

\(a_{3}\) | \(\left( {0.0013,0.0385,0.5777,0.6503,0.0132,0.0005} \right)\) | \(\left( {0.0015,0.0447,0.6781,0.7645,0.0101,0.0004} \right)\) |

\(a_{4}\) | \(\left( {0.0016,0.0457,0.6948,0.7835,0.0091,0.0003} \right)\) | \(\left( {0.0015,0.0440,0.6676,0.7526,0.0101,0.0004} \right)\) |

\(a_{5}\) | \(\left( {0.0013,0.0364,0.5362 ,0.6013,0.0194,0.0007} \right)\) | \(\left( {0.0015,0.0426,0.6433,0.7247,0.0132,0.0005} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(\left( {0.0012,0.0326,0.4717,0.5275,0.0195,0.0007} \right)\) | \(\left( {0.0016,0.0455,0.6913,0.7798,0.0081,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0011,0.0312,0.4444,0.4956,0.0212,0.0007} \right)\) | \(\left( {0.0014,0.0402,0.6056,0.6821,0.0128,0.0004} \right)\) |

\(a_{3}\) | \(\left( {0.0012,0.0333,0.4840,0.5414,0.0200,0.0007} \right)\) | \(\left( {0.0015,0.0424,0.6432,0.7253,0.0091,0.0003} \right)\) |

\(a_{4}\) | \(\left( {0.0012,0.0327,0.4755,0.5323,0.0192,0.0007} \right)\) | \(\left( {0.0016,0.0463,0.7045,0.7947,0.0071,0.0002} \right)\) |

\(a_{5}\) | \(\left( {0.0013,0.0350,0.5097,0.5705,0.0209,0.0007} \right)\) | \(\left( {0.0017,0.0487,0.7423,0.8374,0.0070,0.0002} \right)\) |

Group 3
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(\left( {0.0015,0.0438,0.6627,0.7466,0.0131,0.0005} \right)\) | \(\left( {0.0017,0.0502,0.7649,0.8630,0.0060,0.0002} \right)\) |

\(a_{2}\) | \(\left( {0.0013,0.0383,0.5725,0.6443,0.0144,0.0005} \right)\) | \(\left( {0.0016,0.0456,0.6938,0.7826,0.0072,0.0003} \right)\) |

\(a_{3}\) | \(\left( {0.0013,0.0374,0.5577,0.6272,0.0149,0.0005} \right)\) | \(\left( {0.0016,0.0464,0.7058,0.7959,0.0093,0.0003} \right)\) |

\(a_{4}\) | \(\left( {0.0015,0.0423,0.6382,0.7188,0.0130,0.0005} \right)\) | \(\left( {0.0016,0.0475,0.7229,0.8154,0.0084,0.0003} \right)\) |

\(a_{5}\) | \(\left( {0.0017,0.0504,0.7689,0.8674,0.0071,0.0002} \right)\) | \(\left( {0.0016,0.0459,0.6957,0.7843,0.0113,0.0004} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(\left( {0.0014,0.0387,0.5810,0.6541,0.0129,0.0005} \right)\) | \(\left( {0.0016,0.0454,0.6893,0.7773,0.0091,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0014,0.0384,0.5647,0.6333,0.0184,0.0007} \right)\) | \(\left( {0.0015,0.0435,0.6603,0.7442,0.0106,0.0004} \right)\) |

\(a_{3}\) | \(\left( {0.0015,0.0424,0.6422,0.7237,0.0115,0.0004} \right)\) | \(\left( {0.0015,0.0434,0.6573,0.7408,0.0113,0.0004} \right)\) |

\(a_{4}\) | \(\left( {0.0015,0.0445,0.6750,0.7611,0.0099,0.0003} \right)\) | \(\left( {0.0015,0.0428,0.6481,0.7304,0.0112,0.0004} \right)\) |

\(a_{5}\) | \(\left( {0.0013,0.0357,0.5235,0.5865,0.0203,0.0007} \right)\) | \(\left( {0.0015,0.0421,0.6346,0.7147,0.0137,0.0005} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(\left( {0.0012,0.0325,0.4686,0.5237,0.0203,0.0007} \right)\) | \(\left( {0.0015,0.0447,0.6791,0.7657,0.0092,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0011,0.0312,0.4336,0.4814,0.0240,0.0008} \right)\) | \(\left( {0.0014,0.0395,0.5937,0.6683,0.0139,0.0005} \right)\) |

\(a_{3}\) | \(\left( {0.0012,0.0322,0.4593,0.5122,0.0218,0.0008} \right)\) | \(\left( {0.0014,0.0410,0.6191,0.6976,0.0112,0.0004} \right)\) |

\(a_{4}\) | \(\left( {0.0011,0.0316,0.4495,0.5014,0.0215,0.0008} \right)\) | \(\left( {0.0015,0.0444,0.6740,0.7601,0.0092,0.0003} \right)\) |

\(a_{5}\) | \(\left( {0.0012,0.0342,0.4942,0.5524,0.0218,0.0008} \right)\) | \(\left( {0.0016,0.0473,0.7205,0.8126,0.0084,0.0003} \right)\) |

Group 4
| ||

\(c_{1}\) | \(c_{2}\) | |

\(a_{1}\) | \(\left( {0.0016,0.0451,0.6838,0.7708,0.0108,0.0004} \right)\) | \(\left( {0.0017,0.0498,0.7598,0.8572,0.0063,0.0002} \right)\) |

\(a_{2}\) | \(\left( {0.0013,0.0386,0.5796,0.6528,0.0117,0.0004} \right)\) | \(\left( {0.0016,0.0463,0.7045,0.7947,0.0070,0.0003} \right)\) |

\(a_{3}\) | \(\left( {0.0014,0.0412,0.6219,0.7007,0.0116,0.0004} \right)\) | \(\left( {0.0016,0.0472,0.7184,0.8103,0.0082,0.0003} \right)\) |

\(a_{4}\) | \(\left( {0.0015,0.0415,0.6252,0.7038,0.0143,0.0005} \right)\) | \(\left( {0.0017,0.0487,0.7413,0.8363,0.0074,0.0003} \right)\) |

\(a_{5}\) | \(\left( {0.0017,0.0497,0.7571,0.8541,0.0080,0.0003} \right)\) | \(\left( {0.0016,0.0465,0.7060,0.7960,0.0108,0.0004} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\(a_{1}\) | \(\left( {0.0014,0.0395,0.5943,0.6692,0.0129,0.0005} \right)\) | \(\left( {0.0016,0.0457,0.6942,0.7828,0.0091,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0013,0.0371,0.5520,0.6203,0.0164,0.0006} \right)\) | \(\left( {0.0015,0.0430,0.6509,0.7335,0.0112,0.0004} \right)\) |

\(a_{3}\) | \(\left( {0.0014,0.0405,0.6109,0.6882,0.0119,0.0004} \right)\) | \(\left( {0.0016,0.0448,0.6802,0.7670,0.0098,0.0003} \right)\) |

\(a_{4}\) | \(\left( {0.0016,0.0449,0.6810,0.7679,0.0097,0.0003} \right)\) | \(\left( {0.0015,0.0427,0.6466,0.7289,0.0107,0.0004} \right)\) |

\(a_{5}\) | \(\left( {0.0013,0.0361,0.5293,0.5931,0.0204,0.0007} \right)\) | \(\left( {0.0015,0.0418,0.6298,0.7092,0.0139,0.0005} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\(a_{1}\) | \(\left( {0.0012,0.0321,0.4601,0.5139,0.0203,0.0007} \right)\) | \(\left( {0.0016,0.0451,0.6861,0.7738,0.0086,0.0003} \right)\) |

\(a_{2}\) | \(\left( {0.0011,0.0301,0.4205,0.4675,0.0219,0.0008} \right)\) | \(\left( {0.0014,0.0391,0.5876,0.6616,0.0132,0.0005} \right)\) |

\({{a}}_{3}\) | \(\left( {0.0012,0.0324,0.4661,0.5206,0.0207,0.0007} \right)\) | \(\left( {0.0014,0.0410,0.6201,0.6989,0.0103,0.0004} \right)\) |

\({{a}}_{4}\) | \(\left( {0.0012,0.0345,0.5016,0.5616,0.0201,0.0007} \right)\) | \(\left( {0.0016,0.0452,0.6881,0.7761,0.0079,0.0003} \right)\) |

\({{a}}_{5}\) | \(\left( {0.0012,0.0347,0.5049,0.5649,0.0210,0.0007} \right)\) | \(\left( {0.0017,0.0479,0.7296,0.8231,0.0077,0.0003} \right)\) |

Group 5
| ||

\({{c}}_{1}\) | \({{c}}_{2}\) | |

\({{a}}_{1}\) | \(\left( {0.0015,0.0427,0.6447,0.7265,0.0097,0.0004} \right)\) | \(\left( {0.0016,0.0451,0.6847,0.7720,0.0096,0.0003} \right)\) |

\({{a}}_{2}\) | \(\left( {0.0013,0.0375,0.5595,0.6289,0.0156,0.0005} \right)\) | \(\left( {0.0016,0.0473,0.7199,0.8120,0.0077,0.0003} \right)\) |

\({{a}}_{3}\) | \(\left( {0.0013,0.0374,0.5589,0.6287,0.0144,0.0005} \right)\) | \(\left( {0.0016,0.0457,0.6938,0.7824,0.0091,0.0003} \right)\) |

\({{a}}_{4}\) | \(\left( {0.0013,0.0375,0.5560,0.6243,0.0178,0.0006} \right)\) | \(\left( {0.0016,0.0449,0.6818,0.7687,0.0103,0.0004} \right)\) |

\({{a}}_{5}\) | \(\left( {0.0016,0.0469,0.7122,0.8030,0.0103,0.0004} \right)\) | \(\left( {0.0015,0.0421,0.6937,0.7127,0.0152,0.0005} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\({{a}}_{1}\) | \(\left( {0.0012,0.0350,0.5174,0.5812,0.0158,0.0006} \right)\) | \(\left( {0.0014,0.0405,0.6111,0.6882,0.0131,0.0005} \right)\) |

\({{a}}_{2}\) | \(\left( {0.0011,0.0303,0.4296,0.4803,0.0188,0.0007} \right)\) | \(\left( {0.0013,0.0369,0.5496,0.6176,0.0156,0.0006} \right)\) |

\({{a}}_{3}\) | \(\left( {0.0015,0.0420,0.6340,0.7143,0.0112,0.0004} \right)\) | \(\left( {0.0015,0.0421,0.6372,0.7180,0.0117,0.0004} \right)\) |

\({{a}}_{4}\) | \(\left( {0.0014,0.0410,0.6188,0.6971,0.0119,0.0004} \right)\) | \(\left( {0.0013,0.0373,0.5591,0.6292,0.0137,0.0005} \right)\) |

\({{a}}_{5}\) | \(\left( {0.0012,0.0322,0.4573,0.5095,0.0232,0.0008} \right)\) | \(\left( {0.0014,0.0391,0.5848,0.6577,0.0163,0.0006} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\({{a}}_{1}\) | \(\left( {0.0010,0.0260,0.3331,0.3662,0.0227,0.0008} \right)\) | \(\left( {0.0013,0.0385,0.5791,0.6523,0.0115,0.0004} \right)\) |

\({{a}}_{2}\) | \(\left( {0.0009,0.0253,0.3178,0.3487,0.0225,0.0008} \right)\) | \(\left( {0.0013,0.0377,0.5657,0.6370,0.0124,0.0004} \right)\) |

\({{a}}_{3}\) | \(\left( {0.0011,0.0317,0.4565,0.5099,0.0204,0.0007} \right)\) | \(\left( {0.0013,0.0382,0.5730,0.6449,0.0136,0.0005} \right)\) |

\({{a}}_{4}\) | \(\left( {0.0010,0.0268,0.3649,0.4045,0.0221,0.0008} \right)\) | \(\left( {0.0014,0.0390,0.5885,0.6629,0.0118,0.0004} \right)\) |

\({{a}}_{5}\) | \(\left( {0.0011,0.0315,0.4495,0.5015,0.0208,0.0007} \right)\) | \(\left( {0.0015,0.0421,0.6356,0.7161,0.0119,0.0004} \right)\) |

### Appendix C

\({{c}}_{1}\) | \({{c}}_{2}\) | |

\({{a}}_{1}\) | \(s_{4} \left( {0.746} \right),s_{3} \left( {0.174} \right),s_{2} \left( {0.058} \right),s_{1} \left( {0.012} \right),s_{0} \left( {0.010} \right)\) | \(s_{4} \left( {0.830} \right),s_{3} \left( {0.120} \right),s_{2} \left( {0.032} \right),s_{1} \left( {0.010} \right),s_{0} \left( {0.008} \right)\) |

\({{a}}_{2}\) | \(s_{4} \left( {0.630} \right),s_{3} \left( {0.214} \right),s_{2} \left( {0.092} \right),s_{1} \left( {0.042} \right),s_{0} \left( {0.022} \right)\) | \(s_{4} \left( {0.776} \right),s_{3} \left( {0.114} \right),s_{2} \left( {0.062} \right),s_{1} \left( {0.034} \right),s_{0} \left( {0.014} \right)\) |

\({{a}}_{3}\) | \(s_{4} \left( {0.614} \right),s_{3} \left( {0.220} \right),s_{2} \left( {0.110} \right),s_{1} \left( {0.040} \right),s_{0} \left( {0.016} \right)\) | \(s_{4} \left( {0.792} \right),s_{3} \left( {0.146} \right),s_{2} \left( {0.044} \right),s_{1} \left( {0.010} \right),s_{0} \left( {0.008} \right)\) |

\({{a}}_{4}\) | \(s_{4} \left( {0.664} \right),s_{3} \left( {0.244} \right),s_{2} \left( {0.070} \right),s_{1} \left( {0.012} \right),s_{0} \left( {0.010} \right)\) | \(s_{4} \left( {0.814} \right),s_{3} \left( {0.134} \right),s_{2} \left( {0.042} \right),s_{1} \left( {0.060} \right),s_{0} \left( {0.004} \right)\) |

\({{a}}_{5}\) | \(s_{4} \left( {0.836} \right),s_{3} \left( {0.128} \right),s_{2} \left( {0.016} \right),s_{1} \left( {0.010} \right),s_{0} \left( {0.010} \right)\) | \(s_{4} \left( {0.762} \right),s_{3} \left( {0.202} \right),s_{2} \left( {0.026} \right),s_{1} \left( {0.008} \right),s_{0} \left( {0.002} \right)\) |

\({{c}}_{3}\) | \({{c}}_{4}\) | |

\({{a}}_{1}\) | \(s_{4} \left( {0.640} \right),s_{3} \left( {0.214} \right),s_{2} \left( {0.086} \right),s_{1} \left( {0.044} \right),s_{0} \left( {0.016} \right)\) | \(s_{4} \left( {0.752} \right),s_{3} \left( {0.164} \right),s_{2} \left( {0.050} \right),s_{1} \left( {0.016} \right),s_{0} \left( {0.018} \right)\) |

\({{a}}_{2}\) | \(s_{4} \left( {0.566} \right),s_{3} \left( {0.266} \right),s_{2} \left( {0.096} \right),s_{1} \left( {0.050} \right),s_{0} \left( {0.022} \right)\) | \(s_{4} \left( {0.700} \right),s_{3} \left( {0.190} \right),s_{2} \left( {0.084} \right),s_{1} \left( {0.014} \right),s_{0} \left( {0.012} \right)\) |

\({{a}}_{3}\) | \(s_{4} \left( {0.658} \right),s_{3} \left( {0.200} \right),s_{2} \left( {0.088} \right),s_{1} \left( {0.034} \right),s_{0} \left( {0.020} \right)\) | \(s_{4} \left( {0.736} \right),s_{3} \left( {0.176} \right),s_{2} \left( {0.058} \right),s_{1} \left( {0.012} \right),s_{0} \left( {0.018} \right)\) |

\({{a}}_{4}\) | \(s_{4} \left( {0.746} \right),s_{3} \left( {0.164} \right),s_{2} \left( {0.056} \right),s_{1} \left( {0.020} \right),s_{0} \left( {0.014} \right)\) | \(s_{4} \left( {0.704} \right),s_{3} \left( {0.180} \right),s_{2} \left( {0.068} \right),s_{1} \left( {0.018} \right),s_{0} \left( {0.030} \right)\) |

\({{a}}_{5}\) | \(s_{4} \left( {0.516} \right),s_{3} \left( {0.344} \right),s_{2} \left( {0.104} \right),s_{1} \left( {0.022} \right),s_{0} \left( {0.014} \right)\) | \(s_{4} \left( {0.682} \right),s_{3} \left( {0.238} \right),s_{2} \left( {0.046} \right),s_{1} \left( {0.028} \right),s_{0} \left( {0.006} \right)\) |

\({{c}}_{5}\) | \({{c}}_{6}\) | |

\({{a}}_{1}\) | \(s_{4} \left( {0.420} \right),s_{3} \left( {0.314} \right),s_{2} \left( {0.166} \right),s_{1} \left( {0.062} \right),s_{0} \left( {0.038} \right)\) | \(s_{4} \left( {0.738} \right),s_{3} \left( {0.144} \right),s_{2} \left( {0.066} \right),s_{1} \left( {0.022} \right),s_{0} \left( {0.030} \right)\) |

\({{a}}_{2}\) | \(s_{4} \left( {0.370} \right),s_{3} \left( {0.340} \right),s_{2} \left( {0.180} \right),s_{1} \left( {0.066} \right),s_{0} \left( {0.044} \right)\) | \(s_{4} \left( {0.648} \right),s_{3} \left( {0.204} \right),s_{2} \left( {0.080} \right),s_{1} \left( {0.048} \right),s_{0} \left( {0.020} \right)\) |

\({{a}}_{3}\) | \(s_{4} \left( {0.458} \right),s_{3} \left( {0.332} \right),s_{2} \left( {0.145} \right),s_{1} \left( {0.024} \right),s_{0} \left( {0.042} \right)\) | \(s_{4} \left( {0.680} \right),s_{3} \left( {0.168} \right),s_{2} \left( {0.084} \right),s_{1} \left( {0.034} \right),s_{0} \left( {0.034} \right)\) |

\({{a}}_{4}\) | \(s_{4} \left( {0.440} \right),s_{3} \left( {0.320} \right),s_{2} \left( {0.132} \right),s_{1} \left( {0.056} \right),s_{0} \left( {0.050} \right)\) | \(s_{4} \left( {0.746} \right),s_{3} \left( {0.136} \right),s_{2} \left( {0.056} \right),s_{1} \left( {0.026} \right),s_{0} \left( {0.036} \right)\) |

\({{a}}_{5}\) | \(s_{4} \left( {0.488} \right),s_{3} \left( {0.348} \right),s_{2} \left( {0.124} \right),s_{1} \left( {0.024} \right),s_{0} \left( {0.016} \right)\) | \(s_{4} \left( {0.792} \right),s_{3} \left( {0.144} \right),s_{2} \left( {0.044} \right),s_{1} \left( {0.010} \right),s_{0} \left( {0.010} \right)\) |

### Appendix D

\({{c}}_{1}\) | \({{c}}_{2}\) | \({{c}}_{3}\) |

\((0.920,0.058,0.022)\) | \((0.950,0.032,0.018)\) | \((0.854,0.086,0.060)\) |

\((0.844,0.092,0.064)\) | \((0.890,0.062,0.048)\) | \((0.832,0.096,0.072)\) |

\((0.834,0.110,0.056)\) | \((0.938,0.044,0.018)\) | \((0.858,0.088,0.054)\) |

\((0.908,0.070,0.022)\) | \((0.948,0.042,0.010)\) | \((0.910,0.056,0.034)\) |

\((0.964,0.016,0.020)\) | \((0.964,0.026,0.010)\) | \((0.860,0.104,0.036)\) |

\({{c}}_{4}\) | \({{c}}_{5}\) | \({{c}}_{6}\) |

\((0.916,0.050,0.034)\) | \((0.734,0.166,0.100)\) | \((0.882,0.066,0.052)\) |

\((0.890,0.084,0.026)\) | \((0.710,0.180,0.110)\) | \((0.852,0.080,0.068)\) |

\((0.912,0.058,0.030)\) | \((0.790,0.144,0.066)\) | \((0.848,0.084,0.068)\) |

\((0.884,0.068,0.048)\) | \((0.762,0.132,0.106)\) | \((0.882,0.056,0.062)\) |

\((0.920,0.046,0.034)\) | \((0.836,0.124,0.040)\) | \((0.936,0.044,0.020)\) |

## Rights and permissions

## About this article

### Cite this article

Wang, Xk., Wang, Sh., Zhang, Hy. *et al.* The Recommendation Method for Hotel Selection Under Traveller Preference Characteristics: A Cloud-Based Multi-Criteria Group Decision Support Model.
*Group Decis Negot* (2021). https://doi.org/10.1007/s10726-021-09735-0

Accepted:

Published:

### Keywords

- Multi-criteria group decision making
- Online reviews
- Linguistic variables
- PLTSs
- Extended cloud models