Fuzzy Operator Theory in Mathematical Analysis PDF Download

Author: Yeol Je Cho
Publisher: Springer
ISBN: 3319935011
Category : Mathematics
Languages : en
Pages : 411

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Book Description
This self-contained monograph presents an overview of fuzzy operator theory in mathematical analysis. Concepts, principles, methods, techniques, and applications of fuzzy operator theory are unified in this book to provide an introduction to graduate students and researchers in mathematics, applied sciences, physics, engineering, optimization, and operations research. New approaches to fuzzy operator theory and fixed point theory with applications to fuzzy metric spaces, fuzzy normed spaces, partially ordered fuzzy metric spaces, fuzzy normed algebras, and non-Archimedean fuzzy metric spaces are presented. Surveys are provided on: Basic theory of fuzzy metric and normed spaces and its topology, fuzzy normed and Banach spaces, linear operators, fundamental theorems (open mapping and closed graph), applications of contractions and fixed point theory, approximation theory and best proximity theory, fuzzy metric type space, topology and applications.

Author: Ulrich Höhle
Publisher: Springer Science & Business Media
ISBN: 9780792383888
Category : Business & Economics
Languages : en
Pages : 732

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Book Description
Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.

Author: John N. Mordeson
Publisher: Physica
ISBN: 3790818089
Category : Mathematics
Languages : en
Pages : 319

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Book Description
In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor "and", sup for "or") to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper "Fuzzy groups", which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.

Author: Sribatsa Nanda
Publisher: Alpha Science Int'l Ltd.
ISBN: 9788173195976
Category : Computers
Languages : en
Pages : 268

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Book Description
Intends to serve as an introduction to the knowledge in various areas like Fuzzy Topological spaces, Operator Theory, Variational Inequalities, and Number Theory and more. This book includes articles on Fuzzy functions, applications of Functional Analysis and Complementarity problems provide applications of classical areas.

Author: Reza Saadati
Publisher: Academic Press
ISBN: 0081009550
Category : Mathematics
Languages : en
Pages : 84

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Book Description
Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. - Explores random differentiation and random integral equations - Delves into the study of random operator theory - Discusses the concept of random Banach algebras and its applications

Author: Ali Aral
Publisher: Springer Science & Business Media
ISBN: 1461469465
Category : Mathematics
Languages : en
Pages : 275

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Book Description
The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. ​​This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain​ forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.

Author: Ronald R. Yager
Publisher: Springer Science & Business Media
ISBN: 3642179096
Category : Mathematics
Languages : en
Pages : 300

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Book Description
This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology. Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management.

Author: Naokant Deo
Publisher: Springer Nature
ISBN: 9811511535
Category : Mathematics
Languages : en
Pages : 262

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Book Description
This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as operator theory, approximation theory, fixed-point theory, holomorphic functions, summability theory, and analytic functions. It is a valuable resource for students as well as researchers in mathematical sciences.

Author: E.I. Gordon
Publisher: Springer Science & Business Media
ISBN: 9781402007385
Category : Mathematics
Languages : en
Pages : 442

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Book Description
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0

Author: Library of Congress
Publisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1512

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Book Description