Streamlining apartment provider evaluation: A spherical fuzzy multi-criteria decision-making model

In the context of the thriving real estate market in developing countries like Vietnam, understanding consumer preferences and effectively addressing them through a comprehensive multi-criteria decision-making (MCDM) framework is paramount for real estate providers. This study presents a two-stage MCDM model that integrates the Delphi technique and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) based on Spherical Fuzzy Sets (SFSs). Initially, the SF-Delphi technique validates critical criteria influencing customers' apartment selection in Vietnam. Secondly, the SF-TOPSIS method evaluates the top ten apartment providers. To ensure robustness and validity, a comparative analysis compares the results with those from the Intuitionistic Fuzzy TOPSIS (IF-TOPSIS) and Fuzzy TOPSIS (F-TOPSIS) methods. Subsequently, five rank correlation coefficients (Spearman, Kendall, Goodman-Kruskal, Weighted rank measure of correlation, Weighted Similarity) are used to assess the relationships between various TOPSIS techniques applied to apartment suppliers in Vietnam. The correlation coefficients demonstrate strong agreement among the TOPSIS methods, with the smallest coefficient being 0.7778, surpassing the threshold of 0.7. This high level of consistency confirms the efficacy of the proposed TOPSIS approach with different Fuzzy Sets in reliably evaluating customers' preferences for apartment suppliers. Notably, the legal aspect's prominence underscores its critical role in shaping customer choices, emphasizing the significance of considering legal factors in the context of apartment supply and demand in Vietnam. Furthermore, using SFSs makes this approach particularly suited to capture consumer perceptions within the dynamic and uncertain business environment characterized by volatility, uncertainty, complexity, and ambiguity (VUCA).