## 1 Introduction  
Advancements in science and technology and social changes have propelled the Internet to serve as a medium for information dissemination and global interconnectedness. It overcomes geographical restrictions, enabling seamless communication and sharing across nations while promoting broader opportunities for business cooperation. However, choosing an Internet platform is crucial to obtaining accurate and useful information. Smart choices foster effective information sharing and communication and help reduce misunderstandings, improve project development efficiency, and optimize resource management. However, caution must be exercised regarding the potential risks posed by the Internet. The process of Internet platform selection involves considering factors such as credibility, efficiency, reliability, and cost. Different Internet platforms possess unique characteristics and advantages; choosing the appropriate Internet platform is a complex multi-criteria decision-making (MCDM) problem. However, traditional Internet platform selection methods have shortcomings, including the inability to handle quantitative and qualitative information problems, the incapacity to handle expert-provided fuzzy information, reliance solely on a single arithmetic model for decision-making problems, and the inability to handle incomplete information provided by experts. [PERSON] et al. [1] used the AHP method to determine the relative weights of five assessment criteria (reliability, security, business, mobility, and heterogeneity) for handling Internet of Things process selection. [PERSON] et al. [2] combined the AHP method with the simple additive weighting method to address IoT application system selection problems. However, the methods proposed by both [PERSON] et al. [1] and [PERSON] et al. [2] cannot handle the fuzzy information provided by experts, nor can they process incomplete expert-provided information. The widely used weighted sum model (WSM) and weighted product model (WPM) approach, characterized by its simple mathematical calculations and ease of understanding, is one of the most commonly applied methods to resolve various MCDM issues. However, this approach cannot process qualitative, incomplete, and fuzzy expert-provided information, leading to challenges in selecting an Internet platform. To simultaneously handle both quantitative and qualitative information and consider the hierarchical structure of the assessment criteria, [PERSON] [3] proposed the analytical hierarchy process (AHP) method. This method uses paired comparisons of different criteria to handle quantitative and qualitative information in decision making [4]. Over time, the AHP approach has been extended to address diverse decision-making challenges across various fields, such as sustainable forest management [5], military simulation training systems [6], solid waste management [7], wind farm site selection [8], ecotourism suitability [9], and food safety [10]. To address the complexities of MCDM problems involving fuzzy semantics, [PERSON] [11] introduced the concept of a fuzzy set, which employs membership degrees to represent human cognitive information. Today, numerous scholars have expanded fuzzy sets to solve decision-making problems involving various forms of semantic information, such as intuitionistic fuzzy information [12], picture fuzzy information [13], neutrosophtic fuzzy information [14; 15], Pythagorean fuzzy information [16], spherical fuzzy information [17], and hesitant fuzzy linguistic information [18]. Building upon the concept of the AHP approach and integrating the benefits of fuzzy sets, the fuzzy analytic hierarchy process (FAHP) approach establishes a hierarchical structure to calculate the relative weights of different criteria and utilizes fuzzy sets to handle natural language information from experts. Since subjective judgments in pairwise comparisons of evaluation criteria may contain inaccurate information, [PERSON] et al.