Spherical Fuzzy Decision-Making Approach Integrating Delphi and TOPSIS for Package Tour Provider Selection

The spherical fuzzy sets were recently developed among various fuzzy sets to handle the hesitancy representation issue in multiple criteria decision-making (MCDM) problems, where experts provide information about attributes in the form of spherical fuzzy numbers using linguistic variables. The main purpose of this study is to develop a novel approach integrating Delphi Technique for Order of Preference by Similarity to Ideal Solution based on spherical fuzzy sets (SF-Delphi and SF-TOPSIS). First, the SF-Delphi technique is suggested to derive a valid set of critical criteria based on qualitative information and linguistic preferences. Second, the SF-TOPSIS approach is utilized to rank alternatives based on different spherical fuzzy aggregating operators. Hence, to validate the effectiveness of the proposed methodology, an empirical case study of package tour provider selection is given. Seventeen critical criteria related to four main dimensions (price, service quality, information and technology, and location) were shortlisted and validated from literature and expert opinions. Ten potential package tour providers from Vietnam were ranked in this study. A comparative analysis was conducted to check the proposed methodology’s robustness and validity. The results indicated that the novel SF-Delphi technique may become very helpful for dealing with critical factors, and SF-TOPSIS could be applied to decision problems in uncertain data environments. Furthermore, this research’s findings imply that tour operators should emphasize the most critical attributes to increase the appeal and competitiveness of their package tour products.