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This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces.Key Features:- Complete state of the art of the importance of triangular norms in various mathematical fields- 16 self-contained chapters with extensive bibliographies cover bot

Fuzzy sets. --- Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Sets, Fuzzy --- Fuzzy mathematics --- Set theory

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This book presents an up-to-date account of research in important topics of fuzzy group theory. The book concentrates on the theoretical aspects of fuzzy subgroups of a group. It also includes applications to some abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. The notions of ascending series and descending series of fuzzy subgroups are used to define nilpotency of a fuzzy subgroup. Fuzzy subgroups of Hamiltonian, solvable, P-Hall, and nilpotent groups are discussed. Construction of free fuzzy subgroups is determined. Numerical invariants of fuzzy subgroups of Abelian groups are developed. The problem in group theory of obtaining conditions under which a group can be expressed as a direct product of its normal subgroups is considered. The number of fuzzy subgroups (up to an equivalence relation) of certain finite Abelian groups is determined. Methods for deriving fuzzy theorems from crisp ones are presented and the embedding of lattices of fuzzy subgroups into lattices of crisp groups is discussed. Deriving membership functions from similarity relations is considered. The material presented in this book makes it a good reference for graduate students and researchers working in fuzzy group theory.

Fuzzy sets. --- Group theory. --- Ensembles flous --- Groupes, Théorie des --- Engineering. --- Artificial intelligence. --- Systems and Information Theory in Engineering. --- Artificial Intelligence (incl. Robotics). --- Group Theory and Generalizations. --- Fuzzy sets --- Computer Science --- Algebra --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Théorie des groupes --- Sets, Fuzzy --- Groups, Theory of --- Substitutions (Mathematics) --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Construction --- Computer science. --- Computers. --- Complexity, Computational. --- Computer Science. --- Theory of Computation. --- Complexity. --- Information theory. --- Artificial Intelligence. --- Industrial arts --- Technology --- Communication theory --- Communication --- Cybernetics --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computational complexity. --- Complexity, Computational --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace

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This basic textbook gives an easily accessible introduction to Fuzzy theory and its applications. It provides basic and concrete concepts of the field in a self-contained, condensed and understandable style. This "First Course on Fuzzy Theory and Applications" includes numerous examples, descriptive illustrations and figures of the basic concepts, as well as exercises at the end of each chapter. The author has long time experience in teaching on fuzzy theory and its applications and continuously developed and summarized his didactic lecture notes into this book. This book can be used in introductory graduate and undergraduate courses in Fuzziness and Soft Computing and is recommendable to students, scientists, engineers, or professionals in the field for self-study.

Fuzzy sets. --- Fuzzy logic. --- Fuzzy systems. --- Ensembles flous --- Logique floue --- Systèmes flous --- Fuzzy sets --- Fuzzy logic --- Fuzzy systems --- Algebra --- Applied Mathematics --- Civil Engineering --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Systems, Fuzzy --- Nonlinear logic --- Sets, Fuzzy --- Computer science. --- Artificial intelligence. --- Applied mathematics. --- Engineering mathematics. --- Probabilities. --- Vibration. --- Dynamical systems. --- Dynamics. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Appl.Mathematics/Computational Methods of Engineering. --- Vibration, Dynamical Systems, Control. --- Applications of Mathematics. --- Probability Theory and Stochastic Processes. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical analysis --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Informatics --- Science --- System analysis --- Fuzzy mathematics --- Logic, Symbolic and mathematical --- Set theory --- Mathematics. --- Distribution (Probability theory. --- Artificial Intelligence. --- Mathematical and Computational Engineering. --- Math --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities