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Author: Phil Diamond
Publisher: World Scientific
ISBN: 9789810217310
Category : Mathematics
Languages : en
Pages : 192
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Book Description
The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.
Author: Phil Diamond
Publisher: World Scientific
ISBN: 9789810217310
Category : Mathematics
Languages : en
Pages : 192
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Book Description
The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.
Author: M.Vasuky
Publisher: Shanlax Publications
ISBN: 9389658101
Category : Mathematics
Languages : en
Pages : 66
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Book Description
The various uncertainties arise in complicated problems in Economics, Engineering, Environmental Science, Medical Science and Social Science. The methods of classical Mathematics may not be successfully used to solve them. Mathematical theories such as probability theory, fuzzy set theory and rough set theory were established by researchers to model uncertainties appearing in the above fields. But all these theories have their own difficulties. To overcome these difficulties, In 1999 Molodstov[7] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties. As the problem of setting the membership function does not arise in soft set theory, it can be easily applied to many different fields. In 2003, Maji.et.al.[5] studied some operations on the soft set theory. In 2009, M.I.Ali et.al.[1] studied some new operations on soft sets and its applications. In 2013, Sujoy Das et.al.[11] proposed soft metric space. In 2015, Thangaraj Beaula et.al.,[12] established the fuzzy soft metric spaces. In chapter 1, the basic definitions, examples, properties and theorems are given which are used for throughout the dissertation. In chapter 2, we defined Fuzzy soft metric space with suitable illustrations. We proved arbitrary union of fuzzy soft open set is fuzzy soft open set and the intersection of finite number of fuzzy soft open set is fuzzy soft open set. In chapter 3, Cauchy sequence are defined. First category, second category, dense, nowhere dense are all defined with suitable illustrations. We established Cantor intersection theorem on complete fuzzy soft metric space and also we proved Baires category theorem on fuzzy soft metric space. In chapter 4, fuzzy soft open cover, fuzzy soft compact set and fuzzy soft totally bounded set are defined. We proved some important theorems. Also we defined Bolzano Weirstress property and based on this we proved theorem namely fuzzy soft metric space becomes fuzzy soft sequentially compact if and only if fuzzy soft metric space has the property Bolzano Weirstrass. In chapter 5, we defined convex fuzzy soft metric space. Also we defined self mapping, fixed point and convergence of convex fuzzy soft metric space. Using these all we proved fixed point theorem on convex fuzzy soft metric space.
Author: Linqiang Pan
Publisher: Springer
ISBN: 3662450496
Category : Computers
Languages : en
Pages : 672
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Book Description
This book constitutes the proceedings of the 9th International Conference on Bio-inspired Computing: Theories and Applications, BIC-TA 2014, held in Wuhan, China, in October 2014. The 109 revised full papers presented were carefully reviewed and selected from 204 submissions. The papers focus on four main topics, namely evolutionary computing, neural computing, DNA computing, and membrane computing.
Author: E. Chandrasekaran
Publisher: John Wiley & Sons
ISBN: 1119760453
Category : Computers
Languages : en
Pages : 482
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Book Description
FUZZY INTELLIGENT SYSTEMS A comprehensive guide to Expert Systems and Fuzzy Logic that is the backbone of artificial intelligence. The objective in writing the book is to foster advancements in the field and help disseminate results concerning recent applications and case studies in the areas of fuzzy logic, intelligent systems, and web-based applications among working professionals and those in education and research covering a broad cross section of technical disciplines. Fuzzy Intelligent Systems: Methodologies, Techniques, and Applications comprises state-of-the-art chapters detailing how expert systems are built and how the fuzzy logic resembling human reasoning, powers them. Engineers, both current and future, need systematic training in the analytic theory and rigorous design of fuzzy control systems to keep up with and advance the rapidly evolving field of applied control technologies. As a consequence, expert systems with fuzzy logic capabilities make for a more versatile and innovative handling of problems. This book showcases the combination of fuzzy logic and neural networks known as a neuro-fuzzy system, which results in a hybrid intelligent system by combining a human-like reasoning style of neural networks. Audience Researchers and students in computer science, Internet of Things, artificial intelligence, machine learning, big data analytics and information and communication technology-related fields. Students will gain a thorough understanding of fuzzy control systems theory by mastering its contents.
Author: Dhananjay Gopal
Publisher: CRC Press
ISBN: 1003812783
Category : Mathematics
Languages : en
Pages : 193
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Book Description
This book not only presents essential material to understand fuzzy metric fixed point theory, but also enables the readers to appreciate the recent advancements made in this direction. It contains seven chapters on different topics in fuzzy metric fixed point theory. These chapters cover a good range of interesting topics such as con- vergence problems in fuzzy metrics, fixed figure problems, and applications of fuzzy metrics. The main focus is to unpack a number of diverse aspects of fuzzy metric fixed point theory and its applications in an understandable way so that it could help and motivate young graduates to explore new avenues of research to extend this flourishing area in different directions. The discussion on fixed figure problems and fuzzy contractive fixed point theorems and their different generalizations invites active researchers in this field to develop a new branch of fixed point theory. Features: Explore the latest research and developments in fuzzy metric fixed point theory. Describes applications of fuzzy metrics to colour image processing. Covers new topics on fuzzy fixed figure problems. Filled with examples and open problems. This book serves as a reference book for scientific investigators who want to analyze a simple and direct presentation of the fundamentals of the theory of fuzzy metric fixed point and its applications. It may also be used as a textbook for postgraduate and research students who try to derive future research scope in this area.
Author: Dhananjay Gopal
Publisher: CRC Press
ISBN: 1000087999
Category : Mathematics
Languages : en
Pages : 303
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Book Description
This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications. Some of the noteworthy features of this book include · Diagrammatic illustrations that encourage readers to think geometrically · Focus on systematic strategy to generate ideas for the proofs of theorems · A wealth of remarks, observations along with a variety of exercises · Historical notes and brief biographies appearing throughout the text
Author: Said Melliani
Publisher: Springer Nature
ISBN: 3030539296
Category : Technology & Engineering
Languages : en
Pages : 285
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Book Description
This book provides an overview of the state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. Covering topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods for differential equations, it discusses applications such as fuzzy real-time scheduling, intelligent control, diagnostics and time series prediction. The book features selected contributions presented at the 6th international congress of the Moroccan Applied Mathematics Society, which took place at Sultan Moulay Slimane University Beni Mellal, Morocco, from 7 to 9 November 2019.
Author: Ulrich Höhle
Publisher: Springer Science & Business Media
ISBN: 1461550793
Category : Mathematics
Languages : en
Pages : 722
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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: Yeol Je Cho
Publisher: Springer
ISBN: 3319935011
Category : Mathematics
Languages : en
Pages : 410
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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: Necip ŞIMŞEK
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book Description
In this paper, we introduce the neutrosophic cantractive and neutrosophic mapping. We establish some results on fixed points of a neutrosophic mapping.
