Fuzzy signatures have been used for various applications, including medical diagnosis, communication of robots based on intention guessing, and residential building evaluation. However, there exist many questions about this research topic which have not been addressed in the literature. One of the most important aims is to formally define a family of fuzzy signatures from which an algebraic structure can be obtained allowing to make computations among fuzzy signatures. This paper studies this family and defines suitable meet and join operators satisfying the properties of a lattice as an algebraic structure. A partial ordering relation, the least and greatest elements are also defined on the family of fuzzy signatures. As a consequence, fuzzy signatures can be used as truth values of fuzzy sets, which provides a great level of representativity, completely different from the interval-valued and type-2 fuzzy sets, among others.