## 1 Introduction  
The number of online communities has grown rapidly, producing a wealth of information [1; 2]. Among these communities, the collaborative tagging system (CTS) has empowered users to voluntarily form various communities to exchange their interests and materials [3; 4]. The primary role of CTS is to provide a straightforward and collaborative way to assign labels to internet resources through tags. Sites representative of CTS include social bookmarking (e.g., Margarin), image sharing (e.g., Instagram), picture sharing (e.g., Flickr), and citation sharing (e.g., CiteULike). This study focuses on social bookmarking sites that have been in use for a relatively long time. Users bookmark websites (resources) by assigning tags. From the data obtained from CTS, various collaborative schemes can be enhanced to offer advanced personalized services. Collaborative filtering (CF) has emerged as a leading algorithm in the domain of recommendation systems [5]. CF provides a way to deliver personalized recommendations and possesses a benefit over content-based filtering, as it can sift through various types of items ranging from text and music to videos and photos [6]. In this study, we selectively chose two factors, tag and time, to identify users' preferences and calculate the similarity between users. Tags offer a semantic insight, encapsulating users' perceptions and categorizations of content and giving depth to our understanding of user preferences. Conversely, the temporal dynamics provided by \"time\" capture the ever-evolving nature of user interactions, adding breadth by revealing the patterns and nuances of content consumption. While individual studies have explored these factors independently [7; 8; 9], their synergistic combination is relatively uncharted, representing a promising frontier in personalizing recommendations. By integrating the semantic richness of tags with the dynamic insights of time, our study endeavors to craft a more holistic, nuanced, and responsive recommendation model. Generally, a user assigns one or more tags to bookmark a resource in social bookmarking sites. Consequently, these sites can collect much more tag information than resources. If a user uses \"tag 1\" once and \"tag 2\" ten times, it can be inferred that the user's preference for \"tag 2\" is greater than \"tag 1\". Moreover, time information is critical for deciphering someone's interests. If a user used \"tag 1\" one year ago and \"tag 2\" yesterday, it can be deduced that the user's current interest lies with \"tag 2\" rather than \"tag 1\". Leveraging the data from CTS is essential in order to discern a user's prevailing interests and enhance the precision of tailored recommendations. This research introduces a CF model structured in three phases: weight formulation, calculation of user similarity, and resource suggestion. Three methods were devised for weight determination utilizing tag and time data. First, tag-specific weight is allocated to every resource grounded on tag details. Next, time-oriented weighting determines the weight for each resource, reflecting the moment at which a user marked the resource. Finally, the hybrid weight approach assigns a weight to every resource using a combined measure of both tag and time data. This study contributes to the literature on personalized recommendations for CTS in several specific ways. Firstly, it considers tag and time information to identify users' preferences and designs a computational method to provide customized recommendations for CTS users. Secondly, time is reflected on a cardinal scale to measure users' interests more accurately. Thirdly, it calculates users' similarities by using each preference vector of the user, which varies according to the type of weight. Finally, it offers detailed experimental evaluations with actual big data. The findings from this research clearly indicate that the introduced methodology offers a significant improvement in the quality of recommendations.