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Crisp and Soft Computing with Hypercubical Calculus: New Approaches to Modeling in Cognitive Science and Technology with Parity Logic, Fuzzy Logic, and Evolutionary Computing - Softcover
Synopsis
Introduction: Parity Logic. Fuzzy Logic. Evolutionary Computing.- Parity Logic: Mathematical Foundations of Parity Logic: The Space Betan 0 (0,1)n. Fundamental Properties of XOR. Foundations of Generalized XOR. Motions, Inner Products, and Genitons.- Binary Signal Analysis in Parity Logic: Standard Function Systems. Towards the Binary Counterpart of Fourier Analysis and the Role of Paritons. Analytical Signal Representations. Shegalkin- and Langlet Transforms.- Modeling Perception and Action in Parity Logic: The Nature of Efficient Action. The Conjugacy of Perception and Action. Intrinsic Measurement Bases. Conclusions.- Parity Logic Engines and Excitable Media: From Feedback Machines to Parity Logic Engines. Parity Logic Engines. Excitable Media and Paritons. Towards Artificial Retina Modeling with Fanions. Conclusions.- Transdisciplinary Perspectives of Parity Logic: The Scope of Parity Integration. Perspectives of Applied Parity Logic.- Fuzzy Logic: Mathematical Foundations of Fuzzy Logic: The Space In = (0,1)n. Conceptual and Computational Foundations. Emergent Meaning, Fuzzy Entropy, and Subsethood. Generalized Fuzzy Inner- and Outer Products.- Causal Modeling with Fuzzy Cognitive Maps: On the History of Cognitive Maps. Fuzzy Cognitive Maps and Causal Reasoning. Formal Properties of Causal Algebra. Constructing and Aggregating FCMs. Real and Virtual Worlds FCMs. Continuous FCMs and Methodological Issues. Conclusions.- Evolutionary Computing: Foundations of Evolutionary Computing: Scientific Modeling from Scratch. Parity Integration in Evolutionary Computation. Algorithmic Compression through Langlet Transforms. N-fold Symmetry Operators and Autogenetic Growth. Parity Logic Engines and Evolutionary Computing. Conclusions.- Fundamentals of Autogenetic Algorithms: A Conceptual Framework of Evolutionary Computing. Theoretical Foundations of Genetic and Autogenetic Algorithms. Computational Foundations of GAs and AGAs. Uni- and Multivariate Search with GAs and AGAs. Multivariate Search in Face Space. Conclusions.
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