Download or read book Arithmetic Of Z numbers The Theory And Applications written by Rafik Aziz Aliev and published by World Scientific. This book was released on 2015-05-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world information is imperfect and is usually described in natural language (NL). Moreover, this information is often partially reliable and a degree of reliability is also expressed in NL. In view of this, the concept of a Z-number is a more adequate concept for the description of real-world information. The main critical problem that naturally arises in processing Z-numbers-based information is the computation with Z-numbers. Nowadays, there is no arithmetic of Z-numbers suggested in existing literature.This book is the first to present a comprehensive and self-contained theory of Z-arithmetic and its applications. Many of the concepts and techniques described in the book, with carefully worked-out examples, are original and appear in the literature for the first time.The book will be helpful for professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics.
Download or read book Number Theory and Geometry An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2019-03-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Download or read book 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing ICAFS 2020 written by Rafik A. Aliev and published by Springer Nature. This book was released on 2021-01-04 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 14th International Conference on Applications of Fuzzy Systems, Soft Computing, and Artificial Intelligence Tools, ICAFS-2020, held in Budva, Montenegro, on August 27–28, 2020. It includes contributions from diverse areas of fuzzy systems, soft computing, AI tools such as uncertain computation, decision making under imperfect information, deep learning and others. The topics of the papers include theory and application of soft computing, neuro-fuzzy technology, intelligent control, deep learning–machine learning, fuzzy logic in data analytics, evolutionary computing, fuzzy logic and artificial intelligence in engineering, social sciences, business, economics, material sciences and others.
Download or read book 10th International Conference on Theory and Application of Soft Computing Computing with Words and Perceptions ICSCCW 2019 written by Rafik A. Aliev and published by Springer Nature. This book was released on 2019-11-19 with total page 997 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 10th Conference on Theory and Applications of Soft Computing, Computing with Words and Perceptions, ICSCCW 2019, held in Prague, Czech Republic, on August 27–28, 2019. It includes contributions from diverse areas of soft computing and computing with words, such as uncertain computation, decision-making under imperfect information, neuro-fuzzy approaches, deep learning, natural language processing, and others. The topics of the papers include theory and applications of soft computing, information granulation, computing with words, computing with perceptions, image processing with soft computing, probabilistic reasoning, intelligent control, machine learning, fuzzy logic in data analytics and data mining, evolutionary computing, chaotic systems, soft computing in business, economics and finance, fuzzy logic and soft computing in earth sciences, fuzzy logic and soft computing in engineering, fuzzy logic and soft computing in material sciences, soft computing in medicine, biomedical engineering, and pharmaceutical sciences. Showcasing new ideas in the field of theories of soft computing and computing with words and their applications in economics, business, industry, education, medicine, earth sciences, and other fields, it promotes the development and implementation of these paradigms in various real-world contexts. This book is a useful guide for academics, practitioners and graduates.
Download or read book 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing ICAFS 2018 written by Rafik A. Aliev and published by Springer. This book was released on 2018-12-28 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 13th International Conference on Application of Fuzzy Systems and Soft Computing (ICAFS 2018), held in Warsaw, Poland on August 27–28, 2018. It includes contributions from diverse areas of soft computing such as uncertain computation, Z-information processing, neuro-fuzzy approaches, evolutionary computing and others. The topics of the papers include theory of uncertainty computation; theory and application of soft computing; decision theory with imperfect information; neuro-fuzzy technology; image processing with soft computing; intelligent control; machine learning; fuzzy logic in data analytics and data mining; evolutionary computing; chaotic systems; soft computing in business, economics and finance; fuzzy logic and soft computing in the earth sciences; fuzzy logic and soft computing in engineering; soft computing in medicine, biomedical engineering and the pharmaceutical sciences; and probabilistic and statistical reasoning in the social and educational sciences. The book covers new ideas from theoretical and practical perspectives in economics, business, industry, education, medicine, the earth sciences and other fields. In addition to promoting the development and application of soft computing methods in various real-life fields, it offers a useful guide for academics, practitioners, and graduates in fuzzy logic and soft computing fields.
Download or read book Decision Theory With Imperfect Information written by Aliev Rafig Aziz and published by World Scientific. This book was released on 2014-08-08 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every day decision making in complex human-centric systems are characterized by imperfect decision-relevant information. The principal problems with the existing decision theories are that they do not have capability to deal with situations in which probabilities and events are imprecise. In this book, we describe a new theory of decision making with imperfect information. The aim is to shift the foundation of decision analysis and economic behavior from the realm bivalent logic to the realm fuzzy logic and Z-restriction, from external modeling of behavioral decisions to the framework of combined states.This book will be helpful for professionals, academics, managers and graduate students in fuzzy logic, decision sciences, artificial intelligence, mathematical economics, and computational economics.
Download or read book 11th International Conference on Theory and Application of Soft Computing Computing with Words and Perceptions and Artificial Intelligence ICSCCW 2021 written by Rafik A. Aliev and published by Springer Nature. This book was released on 2022-01-04 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of the 11th Conference on Theory and Applications of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence, ICSCCW-2021, held in Antalya, Turkey, on August 23–24, 2021. The general scope of the book covers uncertain computation, decision making under imperfect information, neuro-fuzzy approaches, natural language processing, and other areas. The topics of the papers include theory and application of soft computing, computing with words, image processing with soft computing, intelligent control, machine learning, fuzzy logic in data mining, soft computing in business, economics, engineering, material sciences, biomedical engineering, and health care. This book is a useful guide for academics, practitioners, and graduates in fields of soft computing and computing with words. It allows for increasing of interest in development and applying of these paradigms in various real-life fields.
Download or read book 16th International Conference on Applications of Fuzzy Systems Soft Computing and Artificial Intelligence Tools ICAFS 2023 written by Rafik A. Aliev and published by Springer Nature. This book was released on with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Number Theory and Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-09-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.
Download or read book Applications of Number Theory to Numerical Analysis written by S. K. Zaremba and published by Academic Press. This book was released on 2014-05-10 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.
Download or read book Lectures on Number Theory written by Peter Gustav Lejeune Dirichlet and published by American Mathematical Soc.. This book was released on 1999 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.
Download or read book Discrete Mathematics and Its Applications written by Kenneth H. Rosen and published by . This book was released on 2007 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The companion Web site -- To the student -- The foundations : logic, sets, and functions -- The fundamentals : algorithms, the integers, and matrices -- Mathematical reasoning -- Counting -- Advanced counting techniques -- Relations -- Graphs -- Trees -- Boolean algebra -- Modeling computation
Download or read book 15th International Conference on Applications of Fuzzy Systems Soft Computing and Artificial Intelligence Tools ICAFS 2022 written by R. A. Aliev and published by Springer Nature. This book was released on 2023-02-28 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general scope of the book covers diverse areas of fuzzy systems, soft computing, AI tools such as uncertain computation, decision-making under imperfect information, deep learning, and others. The topics of the papers include theory and application of Soft Computing, Neuro-Fuzzy Technology, Intelligent Control, Deep Learning-Machine Learning, Fuzzy Logic in Data Analytics, Evolutionary Computing, Fuzzy logic and Artificial Intelligence in Engineering, Social Sciences, Business, Economics, Material Sciences, and others.This book presents the proceedings of the 16th International Conference on Applications of Fuzzy Systems, Soft Computing, and Artificial Intelligence Tools, ICAFS-2022, held in Budva, Montenegro, on August 26-27, 2022. This is a useful guide for academics, practitioners, and graduates in fields of fuzzy logic and soft computing. It allows for increasing of interest in development and applying of these paradigms in various real-life fields.
Download or read book Interval Valued Intuitionistic Fuzzy Sets written by Krassimir T. Atanassov and published by Springer Nature. This book was released on 2019-09-21 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers a comprehensive survey of interval-valued intuitionistic fuzzy sets. It reports on cutting-edge research carried out by the founder of the intuitionistic fuzzy sets, Prof. Krassimir Atanassov, giving a special emphasis to the practical applications of this extension. A few interesting case studies, such as in the area of data mining, decision making and pattern recognition, among others, are discussed in detail. The book offers the first comprehensive guide on interval-valued intuitionistic fuzzy sets. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. The book is a valuable reference resource for graduate students and researchers alike.
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2016-08-16 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.
Download or read book Arithmetic Tales written by Olivier Bordellès and published by Springer Nature. This book was released on 2020-11-26 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Download or read book Discrete Geometric Analysis written by Motoko Kotani and published by American Mathematical Soc.. This book was released on 2004 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collects papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. This book covers topics that center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects.
