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The Recommendation Method for Hotel Selection Under Traveller Preference Characteristics: A Cloud-Based Multi-Criteria Group Decision Support Model

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.

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Acknowledgement

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

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Correspondence to Jian-qiang Wang.

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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

\({{c}}_{1}\) \({{c}}_{2}\) \({{c}}_{3}\)
\((0.920,0.058,0.022)\) \((0.950,0.032,0.018)\) \((0.854,0.086,0.060)\)
\((0.844,0.092,0.064)\) \((0.890,0.062,0.048)\) \((0.832,0.096,0.072)\)
\((0.834,0.110,0.056)\) \((0.938,0.044,0.018)\) \((0.858,0.088,0.054)\)
\((0.908,0.070,0.022)\) \((0.948,0.042,0.010)\) \((0.910,0.056,0.034)\)
\((0.964,0.016,0.020)\) \((0.964,0.026,0.010)\) \((0.860,0.104,0.036)\)
\({{c}}_{4}\) \({{c}}_{5}\) \({{c}}_{6}\)
\((0.916,0.050,0.034)\) \((0.734,0.166,0.100)\) \((0.882,0.066,0.052)\)
\((0.890,0.084,0.026)\) \((0.710,0.180,0.110)\) \((0.852,0.080,0.068)\)
\((0.912,0.058,0.030)\) \((0.790,0.144,0.066)\) \((0.848,0.084,0.068)\)
\((0.884,0.068,0.048)\) \((0.762,0.132,0.106)\) \((0.882,0.056,0.062)\)
\((0.920,0.046,0.034)\) \((0.836,0.124,0.040)\) \((0.936,0.044,0.020)\)

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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

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Keywords

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