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. The book will make connections to logic, but will focus on truth value algebras which is fundamental to the subject. The underlying principles of this book will lead to connections with many other fields of mathematics like lattice theory, topological algebras, complex algebras and category theory. A major feature of this book will be the emphasis on applications as the subalgebra of rmal convex functions will be covered.
John Harding is a professor in the Department of Mathematical Sciences at New Mexico State University. He is the author/coauthor of roughly 70 papers, president of the International Quantum Structures Association, and member of the editorial board of Order and the advisory board of Mathematica Slovaca. His research focuses on order theory and its applications, particularly applications to topology and logic, the foundations of quantum mechanics, completions, and fuzzy sets. He earned his Ph.D. in mathematics from McMaster University. Carol Walker was a professor in the Department of Mathematical Sciences at New Mexico State University before retiring in 1996. She was department head for 14 years and associate dean of arts and sciences and director of the Arts and Sciences Research Center for three years. She is the author/coauthor of more than 35 papers as well as several textbooks and technical manuals. Her research focuses on algebra, including abelian group theory, applications of category theory to abelian groups and modules, and algebraic aspects of the mathematics of fuzzy sets. She earned her Ph.D. in mathematics from New Mexico State University. Elbert Walker was a professor in the Department of Mathematical Sciences at New Mexico State University before retiring in 1987. He then worked at the U.S. National Science Foundation for two years. He is the author/coauthor of about 95 research papers and several books. His research interests include abelian group theory, statistics, and the mathematics of fuzzy sets and fuzzy logic. He earned his Ph.D. in mathematics from the University of Kansas.