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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.
List of contents
Neural Computation.- Granular Enhancement of Fuzzy ART/SOM Neural Classifiers Based on Lattice Theory.- Learning in Lattice Neural Networks that Employ Dendritic Computing.- Orthonormal Basis Lattice Neural Networks.- Generalized Lattices Express Parallel Distributed Concept Learning.- Mathematical Morphology Applications.- Noise Masking for Pattern Recall Using a Single Lattice Matrix Associative Memory.- Convex Coordinates From Lattice Independent Sets for Visual Pattern Recognition.- A Lattice-Based Approach to Mathematical Morphology for Greyscale and Colour Images.- Morphological and Certain Fuzzy Morphological Associative Memories for Classification and Prediction.- Machine Learning Applications.- The Fuzzy Lattice Reasoning (FLR) Classifier for Mining Environmental Data.- Machine Learning Techniques for Environmental Data Estimation.- Application of Fuzzy Lattice Neurocomputing (FLN) in Ocean Satellite Images for Pattern Recognition.- Genetically Engineered ART Architectures.- Fuzzy Lattice Reasoning (FLR) Classification Using Similarity Measures.- Logic and Inference.- Fuzzy Prolog: Default Values to Represent Missing Information.- Valuations on Lattices: Fuzzification and its Implications.- L-fuzzy Sets and Intuitionistic Fuzzy Sets.- A Family of Multi-valued t-norms and t-conorms.- The Construction of Fuzzy-valued t-norms and t-conorms.
Summary
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.
