Introduction to Lattice Algebra

""This book gives the first comprehensive introduction to lattice algebra from the point of view of applications in image analysis and artificial neural networks. . . .] Roughly half of the book is devoted to the detailed mathematical description of lattice semi-rings and lattice semi-fields, which are put into the foundation of lattice-based vector spaces. The second half is then devoted to applications of this toolbox to artificial intelligence with a focus on pattern recognition. Throughout the book, many examples and exercises are given. Solutions to the exercises are provided on an associated website. The authors give a self-contained account of algebraic concepts that allow researchers and students with a computer science background to learn the necessary mathematics."" – MAA Reviews ""In this mathematically rigorous book, the esoteric domain of Lattice Theory which has fascinated mathematicians for decades jumps to the frontline of Artificial Intelligence, touching the most exciting topics of this era with a fresh alternative view"" – Professor Manuel Grana, Catedrático de Universidad ""Introduction to Lattice Algebra by G. X. Ritter and G. Urcid is a self-contained first of its kind book. It can be used as an excellent supplementary resource for any course in artificial intelligence with a focus on pattern recognition and artificial neural networks."" – Dr. Humberto Sossa, CIC-IPN ""This one-of-a-kind textbook presents the authors' perspective on the vast and growing area of lattice computing. This self-contained textbook, that includes a large number of exercises, will not only appeal to researchers and practitioners, but also to graduate and advanced undergraduate students in pure and applied mathematics, computer science, and engineering. Therefore, this book will serve as one of the principal reference for the graduate course on lattice computing that we are offering at our university as well as similar courses throughout the world. The readers may find some of the innovative applications of lattice computing methods such as the ones in hyperspectral and color image analysis to be especially interesting."" – Peter Sussner, University of Campinas ""This is an introduction textbook to lattice algebra with applications in AI written by knowledgeable researchers-teachers. It focuses on two subjects, first, lattice algebra and, second, the practical applications of lattice algebra with emphasis on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. More specifically, the first four chapters of this book present basic lattice theory, whereas the remaining chapters concentrate on applications of lattice algebra often in image processing and image analysis. Following its formal introduction in mathematics more than a century ago, with the proliferation of computers, the employment of lattice theory keeps extending in practical applications, e.g. in computer science for knowledge representation, in engineering for modeling, in logic /reasoning for sophisticated decision-making , planning, etc. With this textbook the authors convey their valuable expertise to students of lattice algebra in selected information processing applications. Furthermore, the authors consider the potential of cross-fertilization with alternative approaches in information processing based on lattice theory. For all the aforementioned reasons the ""Introduction to Lattice Algebra with Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks"" by Gerhard X. Ritter and Gonzalo Urcid, is a cornerstone book for students as well as for researchers with interests in information processing applications based on lattice theory."" – Professor Vassilis G. Kaburlasos, International Hellenic University ""Exceptionally well organized and presented, Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks by the team of Gerhard X. Ritter and Gonzalo Urcid is an ideal textbook and should be considered as an essential, core addition to professional, college, and university library Abstract Algebra, Graph Theory, and Computer Vision/Pattern Recognition collections and supplemental curriculum studies reading lists."" – Midwest Books Review