The truth value algebra of type-2 fuzzy sets : order convolutions of functions on the unit interval

This mongraph is on the topic of type-2 fuzzy sets from a mathematical as opposed to an engineering perspective. It will be of interest to mathematicians who work in fields related to fuzzy sets as well as those who work with universal algebra. Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explores the fundamental properties of this algebra and the role of these properties in applications. Accessible to anyone with a standard undergraduate mathematics background, this self-contained book offers several options for a one- or two-semester course. It covers topics increasingly used in fuzzy set theory, such as lattice theory, analysis, category theory, and universal algebra. The book discusses the basics of the type-2 truth value algebra, its subalgebra of convex normal functions, and their applications. It also examines the truth value algebra from a more algebraic and axiomatic view Content: The algebra of truth values -- Properties of the type-2 truth value algebra -- Subalgebras of the type-2 truth value algebra -- Automorphisms -- T-norms and T-conorms -- Convex normal functions -- Varieties related to M -- Type-2 fuzzy sets and bichains -- Categories of fuzzy relations -- The finite case.