The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where elements belong to the set with a certain membership value (called the fuzzy value). This paper combines fuzzy data with relational algebra to provide the mathematical foundation for a fuzzy database querying language, describing various useful operations in the language of linear algebra and multiset operations, in addition to rigorously proving key identities.

翻译：人工智能的日益兴起使得像ChatGPT这样的计算机程序中不精确语言的使用更加突出。模糊逻辑通过引入模糊集的概念来处理这种不精确语言，其中元素以一定的隶属度值（称为模糊值）属于该集合。本文将模糊数据与关系代数相结合，为模糊数据库查询语言提供数学基础，除了严格证明关键恒等式外，还以线性代数和多重集操作的语言描述了各种有用的操作。