A number of di?erent instruments for design can be uni?ed in the context of lattice theory towards cross-fertilization By“latticetheory”[1]wemean,equivalently,eitherapartialordering relation [2,3]ora couple of binary algebraic operations [3, 4]. There is a growing interest in computational intelligence based on lattice theory. A number of researchers are currently active developing lattice theory based models and techniques in engineering, computer and information s- ences, applied mathematics, and other scienti?c endeavours. Some of these models and techniques are presented here. However, currently, lattice theory is not part of the mainstream of com- tationalintelligence.Amajorreasonforthisisthe“learningcurve”associated with novel notions and tools. Moreover, practitioners of lattice theory, in s- ci?c domains of interest, frequently develop their own tools and/or practices without being aware of valuable contributions made by colleagues. Hence, (potentially) useful work may be ignored, or duplicated. Yet, other times, di?erent authors may introduce a con?icting terminology. The compilation of this book is an initiative towards proliferating est- lished knowledge in the hope to further expand it, soundly. There was a critical mass of people and ideas engaged to produce this book. Around two thirds of this book’s chapters are substantial enhancements of preliminary works presented lately in a three-part special session entitled “Computational Intelligence Based on Lattice Theory” organized in the c- text of the World Congress in Computational Intelligence (WCCI), FUZZ- IEEE program, July 16-21, 2006 in Vancouver, BC, Canada. The remaining book chapters are novel contributions by other researchers.
The emergence of lattice theory within the field of computational intelligence (CI) is partially due to its proven effectiveness in neural computation. Moreover, lattice theory has the potential to unify a number of diverse concepts and aid in the cross-fertilization of both tools and ideas within the numerous subfields of CI. The compilation of this eighteen-chapter book is an initiative towards proliferating established knowledge in the hope to further expand it. This edited book is a balanced synthesis of four parts emphasizing, in turn, neural computation, mathematical morphology, machine learning, and (fuzzy) inference/logic. The articles here demonstrate how lattice theory may suggest viable alternatives in practical clustering, classification, pattern analysis, and regression applications.
