The Arithmetic Of Z Numbers
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Arithmetic Of Z Numbers The Theory And Applications
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Author : Rafik Aziz Aliev
language : en
Publisher: World Scientific
Release Date : 2015-05-08
Arithmetic Of Z Numbers The Theory And Applications written by Rafik Aziz Aliev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-08 with Computers categories.
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.
The Arithmetic Of Z Numbers
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Author : R. A. Aliev
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015
The Arithmetic Of Z Numbers written by R. A. Aliev and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Fuzzy arithmetic categories.
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.
13th International Conference On Theory And Application Of Fuzzy Systems And Soft Computing Icafs 2018
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Author : Rafik A. Aliev
language : en
Publisher: Springer
Release Date : 2018-12-28
13th International Conference On Theory And Application Of Fuzzy Systems And Soft Computing Icafs 2018 written by Rafik A. Aliev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-28 with Technology & Engineering categories.
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.
A Conversational Introduction To Algebraic Number Theory
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Author : Paul Pollack
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-01
A Conversational Introduction To Algebraic Number Theory written by Paul Pollack and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-01 with Mathematics categories.
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Complex Numbers From A To Z
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-08
Complex Numbers From A To Z written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-08 with Mathematics categories.
* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory
Interval Valued Intuitionistic Fuzzy Sets
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Author : Krassimir T. Atanassov
language : en
Publisher: Springer Nature
Release Date : 2019-09-21
Interval Valued Intuitionistic Fuzzy Sets written by Krassimir T. Atanassov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-21 with Technology & Engineering categories.
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.
Progress In Intelligent Decision Science
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Author : Tofigh Allahviranloo
language : en
Publisher: Springer Nature
Release Date : 2021-01-29
Progress In Intelligent Decision Science written by Tofigh Allahviranloo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-29 with Technology & Engineering categories.
This book contains the topics of artificial intelligence and deep learning that do have much application in real-life problems. The concept of uncertainty has long been used in applied science, especially decision making and a logical decision must be made in the field of uncertainty or in the real-life environment that is formed and combined with vague concepts and data. The chapters of this book are connected to the new concepts and aspects of decision making with uncertainty. Besides, other chapters are involved with the concept of data mining and decision making under uncertain computations.
Recent Developments In Fuzzy Logic And Fuzzy Sets
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Author : Shahnaz N. Shahbazova
language : en
Publisher: Springer Nature
Release Date : 2020-03-05
Recent Developments In Fuzzy Logic And Fuzzy Sets written by Shahnaz N. Shahbazova and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-05 with Technology & Engineering categories.
This book provides a timely and comprehensive overview of current theories and methods in fuzzy logic, as well as relevant applications in a variety of fields of science and technology. Dedicated to Lotfi A. Zadeh on his one year death anniversary, the book goes beyond a pure commemorative text. Yet, it offers a fresh perspective on a number of relevant topics, such as computing with words, theory of perceptions, possibility theory, and decision-making in a fuzzy environment. Written by Zadeh’s closest colleagues and friends, the different chapters are intended both as a timely reference guide and a source of inspiration for scientists, developers and researchers who have been dealing with fuzzy sets or would like to learn more about their potential for their future research.
Number Theory In Function Fields
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Author : Michael Rosen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Number Theory In Function Fields written by Michael Rosen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con sidering finite algebraic extensions K of Q, which are called algebraic num ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K.
10th International Conference On Theory And Application Of Soft Computing Computing With Words And Perceptions Icsccw 2019
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Author : Rafik A. Aliev
language : en
Publisher: Springer Nature
Release Date : 2019-11-19
10th International Conference On Theory And Application Of Soft Computing Computing With Words And Perceptions Icsccw 2019 written by Rafik A. Aliev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-19 with Technology & Engineering categories.
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.