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The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field.

Computer Science --- Engineering & Applied Sciences --- Engineering. --- Algebra. --- Ordered algebraic structures. --- Mathematical logic. --- Computational intelligence. --- Computational Intelligence. --- Mathematical Logic and Foundations. --- Order, Lattices, Ordered Algebraic Structures. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Mathematical analysis --- Construction --- Industrial arts --- Technology --- Logic, Symbolic and mathematical. --- Fuzzy sets. --- Artificial intelligence. --- Computer science. --- 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 --- Sets, Fuzzy --- Fuzzy mathematics --- Informatics --- Science

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The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field.

Mathematical logic --- Ordered algebraic structures --- Algebra --- Applied physical engineering --- Artificial intelligence. Robotics. Simulation. Graphics --- neuronale netwerken --- algebra --- fuzzy logic --- cybernetica --- wiskunde --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- logica --- AI (artificiële intelligentie)

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This book collects the abstracts of the contributions presented at AGOP 2017, the 9th International Summer School on Aggregation Operators. The conference took place in Skövde (Sweden) in June 2017. Contributions include works from theory and fundamentals of aggregation functions to their use in applications. Aggregation functions are usually defined as those functions that are monotonic and that satisfy the unanimity condition. In particular settings these conditions are relaxed. Aggregation functions are used for data fusion and decision making. Examples of these functions include means, t-norms and t-conorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals).

Aggregation operators. --- Numerical aggregation operators --- Engineering. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- 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 --- Construction --- Industrial arts --- Technology --- Operator theory --- Artificial Intelligence.

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Triangular norms were first used in the context of probabilistic metric spaces in order to extend the triangle inequality from classical metric spaces to this more general case. The theory of triangular norms has two roots, viz., specific functional equations and the theory of special topological semigroups. These are discussed in Part I. Part II of the book surveys several applied fields in which triangular norms play a significant part: probabilistic metric spaces, aggregation operators, many-valued logics, fuzzy logics, sets and control, and non-additive measures together with their corresponding integrals. Part I is self contained, including all proofs, and gives many graphical illustrations. The review in Part II shows the importance if triangular norms in the field concerned, providing a well-balanced picture of theory and applications.

Triangular norms.

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Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio, bipolar). It is an ideal introduction for graduate students and a unique resource for researchers.

Aggregation operators --- Numerical functions. --- Aggregation operators. --- wiskundige functies --- Numerical functions --- Functions, Numerical --- Numerical aggregation operators --- Operator theory