## 1 Introduction
[19] believe that combining fuzzy sets with the AHP approach is a reasonable reflection of the actual situation. They used the FAHP method to address supplier selection issues. [PERSON] et al. [20] believe that combining AHP and fuzzy sets can achieve more flexible judgments and handle complex decision-making problems, especially in managing multiple evaluation criteria and processing both qualitative and quantitative information. [PERSON] et al. [21] believe that the traditional analytic hierarchy process cannot fully reflect human thinking methods and that incorporating fuzzy information can enhance the judgment of decision makers. Due to its enhanced capability in handling fuzzy semantic information compared to traditional AHP approaches, FAHP finds widespread application in addressing decision-making issues across different fields, such as material circularity in building construction [22], safety zone site selection problem [23], risk assessment of coal mine gas explosions [24], stock portfolio selection [25], and soil conservation [26]. Traditional MCDM methods often rely on a single arithmetic model for solving decision-making problems. [PERSON] et al. [27] combined the concept of the WSM and the WPM to develop the weighted aggregated sum product assessment (WASPAS) approach. The WASPAS approach provides more accurate results than WSM and WPM and allows for adjusting the lambda (\(\lambda\)) value for different problems and situations. By employing different combinations of WSM and WPM and utilizing different lambda (\(\lambda\)) values to represent the expert's preference parameters, the WASPAS approach determines the total relative importance of different alternatives [28]. Due to its straightforward calculation process and accurate results, the WASPAS approach has gained significant attention from decision makers across various sectors of society, establishing itself as an effective decision-making tool [29]. To date, the WASPAS approach has been successfully applied in addressing decision-making issues across different fields, such as marine risk assessment [30], supply chain network design [31], urban transportation [32], wastewater reuse applications [33], and solar water heating systems [34]. Recently, [PERSON] and [PERSON] [35] employed the entropy-based WASPAS approach to conduct a geoheitage assessment of the Karcal Mountains. While the method introduced by [PERSON] and [PERSON] [35] effectively determines the priority values of geological sites, enhancing the accuracy of decision-making results, this method cannot handle fuzzy and incomplete expert-provided information. In response to the limitations of traditional Internet platform selection approaches, this study combined the FAHP approach and the WASPAS approach to handle Internet platform selection problems within an incomplete information environment. Moreover, the proposed approach employed data-filling techniques to handle incomplete expert-provided information, making the calculation results more reasonable and aligned with real-world situations. The theoretical and practical contributions of the proposed novel fuzzy analytic hierarchy process-based method are as follows: First, it can simultaneously handle quantitative and qualitative information. Second, it can process fuzzy semantic messages provided by experts. Third, it can simultaneously consider the characteristics of two arithmetic models. Fourth, it can effectively process incomplete information. Fifth, it evaluates the relative importance of evaluation criteria through pairwise comparisons. The remainder of this article is organized as follows. Section 2 briefly introduces the basic definitions and calculation rules of WSM, WPM, FAHP, and WASPAS approaches. Section 3 proposes a novel FAHP-based approach to handle Internet platform selection problems within an incomplete information environment.