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Multi-valued and fuzzy logics provide mathematical and computational tools for handling imperfect information and decision-making with rational collective reasoning and irrational individual judgements. The suggested implementation of multi-valued logics is based on the uninorm and absorbing norm with generating functions defined by probability distributions. Natural extensions of these logics result in non-commutative and non-distributive logics. In addition to Boolean truth values, these logics handle subjective truth and false values and model irrational decisions. Dynamics of decision-making are specified by the subjective Markov process and learning – by neural network with extended Tsetlin neurons. Application of the suggested methods is illustrated by modelling of irrational economic decisions and biased reasoning in the wisdom-of-the-crowd method, and by control of mobile robots and navigation of their groups. Topics and features: Bridges the gap between fuzzy and probability methods Includes examples in the field of machine-learning and robots’ control Defines formal models of subjective judgements and decision-making Presents practical techniques for solving non-probabilistic decision-making problems Initiates further research in non-commutative and non-distributive logics The book forms a basis for theoretical studies and practice of decision-making under uncertainty and will be useful for computer scientists and mathematicians interested in multi-valued and fuzzy logic, as well as for engineers working in the field of data mining and data analysis. Dr. Evgeny Kagan is with the Faculty of Engineering, Ariel University, Israel; Dr. Alexander Rybalov is with the LAMBDA Laboratory, Tel-Aviv University, Israel; and Prof. Ronald Yager is with the Machine Learning Institute, Yona College, New York, USA.

Computer science. --- Algebraic logic. --- Computer science --- Mathematical statistics. --- Computer Science Logic and Foundations of Programming. --- Algebraic Logic. --- Probability and Statistics in Computer Science. --- Mathematics.

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This handy reference book detailing the intricacies of R updates the popular first edition by adding R version 3.4 and 3.5 features. Starting with the basic structure of R, the book takes you on a journey through the terminology used in R and the syntax required to make R work. You will find looking up the correct form for an expression quick and easy. Some of the new material includes information on RStudio, S4 syntax, working with character strings, and an example using the Twitter API. With a copy of the R Quick Syntax Reference in hand, you will find that you are able to use the multitude of functions available in R and are even able to write your own functions to explore and analyze data. You will: Discover the modes and classes of R objects and how to use them Use both packaged and user-created functions in R Import/export data and create new data objects in R Create descriptive functions and manipulate objects in R Take advantage of flow control and conditional statements Work with packages such as base, stats, and graphics.

Programming languages (Electronic computers) --- Artificial intelligence. --- Mathematical statistics. --- Big data. --- Computer programming. --- R (Computer program language). --- Programming Languages, Compilers, Interpreters. --- Artificial Intelligence. --- Probability and Statistics in Computer Science. --- Big Data. --- Programming Techniques.

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Algorithms. --- Computer science. --- Computer science—Mathematics. --- Mathematical statistics. --- Discrete mathematics. --- Probabilities. --- Theory of Computation. --- Probability and Statistics in Computer Science. --- Discrete Mathematics in Computer Science. --- Probability Theory. --- Algorithms --- Stochastic approximation --- Computer science --- Mathematics

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Übung macht bekanntlich den Meister. In der Mathematik gilt dieses alte Sprichwort auch heute noch uneingeschränkt! Eine Fülle erprobter studienbegleitender Übungsaufgaben zur Vorlesung "Mathematik für Informatiker" helfen dem Studenten, sein mathematisches Rüstzeug zu erneuern, zu optimieren und sich unter anderem damit bestens für Klausuren vorzubereiten. Im Gegensatz zu vielen anderen Übungsbüchern zu Mathematik werden hier nicht nur Ergebnisse oder bestenfalls Lösungsskizzen gegeben. Vielmehr werden Musteraufgaben vom ersten Ansatz bis zum Ergebnis vollständig durchgerechnet und schrittweise erklärt. Beispiele und Java-Applets erläutern dabei prinzipielle Methoden, die zur Lösung der Aufgaben angewendet werden. Das Übungsbuch und das Lehrbuch Wolff/Hauck/Küchlin: Mathematik für BioInformatiker sind aufeinander abgestimmt. Die Java-Applets sind unter der URL http://min.informatik.uni-tuebingen.de zu finden.

Philology. --- Linguistics. --- Computer science. --- Computer science—Mathematics. --- Mathematical statistics. --- Mathematical analysis. --- Analysis (Mathematics). --- Combinatorics. --- Language and Literature. --- Computer Science, general. --- Discrete Mathematics in Computer Science. --- Probability and Statistics in Computer Science. --- Analysis. --- Combinatorial analysis.

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Dynamische Systeme stellen einen unverzichtbaren Bestandteil mathematischer Modellbildung für Anwendungen aller Art dar, angefangen von Physik über Biologie bis hin zur Informatik. Dieser Band führt in diese Theorie ein und beschreibt Methoden und Dynamiken, wie sie für eine systematische Modellbildung auch in den Anwendungen notwendig erscheinen. Wesentliche Grundzüge der Theorie werden beispielhaft im ersten Kapitel erläutert. Es schließt sich eine Einführung in niedrig-dimensionale Dynamiken an (u.a. rationale Funktionen), gefolgt von topologischer Dynamik (z.B. Attraktoren, Entropie und chaotisches Verhalten), differenzierbarer Dynamik (z.B. Liapunoff-Exponenten, Strukturstabilität und Hyperbolizität), Ergodentheorie (z.B. Ergodensätze, invariante Masse, Konservativität) und schließlich thermodynamischer Formalismus (z.B. Gibbs-Theorie, Zetafunktionen).

Mathematical analysis. --- Analysis (Mathematics). --- Computers. --- Mathematical physics. --- Dynamics. --- Ergodic theory. --- Physics. --- Mathematical statistics. --- Analysis. --- Theory of Computation. --- Theoretical, Mathematical and Computational Physics. --- Dynamical Systems and Ergodic Theory. --- Mathematical Methods in Physics. --- Probability and Statistics in Computer Science.