A formal algebra is essential for applying standard database-style query optimization to XML queries. A significant number of spatiotemporal applications necessitate the efficient management of (fuzzy) spatiotemporal data, which is pertinent to both academic research and industrial practices. The adaptability of a semi-structured fuzzy spatiotemporal data model, derived from general data models in XML, spatiotemporal data models in XML, and fuzzy data models in XML, is fundamental to the effective management of fuzzy spatiotemporal data. Additionally, XML is inherently suited for the integration and exchange of data from diverse sources, making it a logical choice for modeling. Although fuzzy theory and fuzzy mathematical programming have been established, researches on fuzzy spatiotemporal data have only recently emerged and warrants further investigation. In the context of spatiotemporal data represented in XML, there are ongoing efforts to amalgamate spatial and temporal attributes within a unified framework and to analyze spatiotemporal data in XML. For instance, Huang et al. propose a methodology for representing and querying spatiotemporal data in XML. Liu and Wan introduce a feature-based spatiotemporal data model and utilize a Native XML Database for the storage of spatiotemporal data. Furthermore, Franceschet et al. present a translation algorithm that converts spatiotemporal conceptual schemas into XML schemas, along with a framework that facilitates the validation of XML documents containing spatiotemporal information against these conceptual schemas. In addition, Bai et al. propose a fuzzy spatiotemporal XML data model; however, it does not accommodate algebraic operations.