Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general.

Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and – depending on the student’s major – can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines.


  • Filled with instructive examples and exercises to help build understanding
  • Suitable for researchers, professionals and students, both in mathematics and computer science
    • Contains numerous exercises.

    chapter Chapter 1|35 pages

    Elements of Algebra

    chapter Chapter 2|45 pages

    Pertinent Properties of Euclidean Space

    chapter Chapter 3|29 pages

    Lattice Theory

    chapter Chapter 4|59 pages

    Lattice Algebra

    chapter Chapter 5|60 pages

    Matrix-Based Lattice Associative Memories

    chapter Chapter 6|36 pages

    Extreme Points of Data Sets

    chapter Chapter 7|49 pages

    Image Unmixing and Segmentation

    chapter Chapter 8|22 pages

    Lattice-Based Biomimetic Neural Networks

    chapter Chapter 9|45 pages

    Learning in Biomimetic Neural Networks

    chapter |2 pages