Comprehensively describes the deeper mathematical aspects of fuzzy sets, particularly those aspects which are category-theoretic in nature. Divided into four parts, this book contains bibliography, indices, and long chapters, which make it suitable as a text for advanced graduate students.

Part II refines and works within non-model-theoretic approaches to fuzzy sets, giving a full account of the use of categorical methods to describe fuzzy topology from the structure-theoretic, category-theoretic, and point-set lattice-theoretic viewpoints. Explored in detail are set functors, topological constructs, convergence, and the relationship between locales, fuzzy topologies, and functor categories. Part III addresses issues related to Part I and II, including pointless geometry, fuzzy paths and relational databases, fuzzy points and locales, sobriety and Urysohn Lemmas, and the relationship between the Helly space and the fuzzy unit interval. The fourth part consists of several appendices: round tables and open questions, a comprehensive bibliography, and two extensive indices.