Axiomatic Fuzzy Set Theory and Its Applications PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Axiomatic Fuzzy Set Theory and Its Applications PDF full book. Access full book title Axiomatic Fuzzy Set Theory and Its Applications by Xiaodong Liu. Download full books in PDF and EPUB format.
Author: Xiaodong Liu
Publisher: Springer Science & Business Media
ISBN: 3642004016
Category : Mathematics
Languages : en
Pages : 522
Get Book Here
Book Description
It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.
Author: Xiaodong Liu
Publisher: Springer Science & Business Media
ISBN: 3642004016
Category : Mathematics
Languages : en
Pages : 522
Get Book Here
Book Description
It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.
Author: Baoding Liu
Publisher: Springer
ISBN: 3540731652
Category : Technology & Engineering
Languages : en
Pages : 263
Get Book Here
Book Description
This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.
Author: Hans-Jürgen Zimmermann
Publisher: Springer Science & Business Media
ISBN: 9401587027
Category : Mathematics
Languages : en
Pages : 441
Get Book Here
Book Description
Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.
Author: Bernadette Bouchon
Publisher: Springer Science & Business Media
ISBN: 3642107265
Category : Computers
Languages : en
Pages : 272
Get Book Here
Book Description
This book draws on papers presented at the 2008 Conference on Information Processing and Management of Uncertainty (IPMU), held in Málaga, Spain. The conference brought together some of the world’s leading experts in the study of uncertainty.
Author: Xiaoxia Huang
Publisher: Springer
ISBN: 3642112145
Category : Computers
Languages : en
Pages : 188
Get Book Here
Book Description
The most salient feature of security returns is uncertainty. The purpose of the book is to provide systematically a quantitative method for analyzing return and risk of a portfolio investment in di?erent kinds of uncertainty and present the ways for striking a balance between investment return and risk such that an optimal portfolio can be obtained. In classical portfolio theory, security returns were assumed to be random variables, and probability theory was the main mathematical tool for h- dling uncertainty in the past. However,the world is complex and uncertainty is varied. Randomnessis nottheonly typeofuncertaintyinreality,especially when human factors are included. Security market, one of the most complex marketsintheworld,containsalmostallkindsofuncertainty. Thesecurity- turns are sensitive to various factors including economic, social, political and very importantly, people’s psychological factors. Therefore, other than strict probability method, scholars have proposed some other approaches including imprecise probability, possibility, and interval set methods, etc. , to deal with uncertaintyinportfolioselectionsince1990’s. Inthisbook,wewantto addto thetools existingin sciencesomenewandunorthodoxapproachesforanal- ing uncertainty of portfolio returns. When security returns are fuzzy, we use credibility which has self-duality property as the basic measure and employ credibilitytheorytohelpmakeselectiondecisionsuchthatthedecisionresult will be consistent with the laws of contradiction and excluded middle. Being awarethat one tool is not enough for solving complex practical problems, we further employ uncertain measure and uncertainty theory to help select an optimal portfolio when security returns behave neither randomly nor fuzzily. One core of portfolio selection is to ?nd a quantitative risk de?nition of a portfolio investment.
Author: Dan E. Tamir
Publisher: Springer
ISBN: 3319196839
Category : Technology & Engineering
Languages : en
Pages : 679
Get Book Here
Book Description
This book presents a comprehensive report on the evolution of Fuzzy Logic since its formulation in Lotfi Zadeh’s seminal paper on “fuzzy sets,” published in 1965. In addition, it features a stimulating sampling from the broad field of research and development inspired by Zadeh’s paper. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Conceived by the editors as an academic celebration of the fifty years’ anniversary of the 1965 paper, this work is a must-have for students and researchers willing to get an inspiring picture of the potentialities, limitations, achievements and accomplishments of Fuzzy Logic-based systems.
Author: Ulrich Höhle
Publisher: Springer Science & Business Media
ISBN: 9780792383888
Category : Business & Economics
Languages : en
Pages : 732
Get Book Here
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: Zongmin Ma
Publisher: Springer Science & Business Media
ISBN: 3642140092
Category : Computers
Languages : en
Pages : 353
Get Book Here
Book Description
This book covers in a great depth the fast growing topic of techniques, tools and applications of soft computing in XML data management. It is shown how XML data management (like model, query, integration) can be covered with a soft computing focus. This book aims to provide a single account of current studies in soft computing approaches to XML data management. The objective of the book is to provide the state of the art information to researchers, practitioners, and graduate students of the Web intelligence, and at the same time serving the information technology professional faced with non-traditional applications that make the application of conventional approaches difficult or impossible.
Author: Cengiz Kahraman
Publisher: Springer Science & Business Media
ISBN: 3642120512
Category : Business & Economics
Languages : en
Pages : 566
Get Book Here
Book Description
Production engineering and management involve a series of planning and control activities in a production system. A production system can be as small as a shop with only one machine or as big as a global operation including many manufacturing plants, distribution centers, and retail locations in multiple continents. The product of a production system can also vary in complexity based on the material used, technology employed, etc. Every product, whether a pencil or an airplane, is produced in a system which depends on good management to be successful. Production management has been at the center of industrial engineering and management science disciplines since the industrial revolution. The tools and techniques of production management have been so successful that they have been adopted to various service industries, as well. The book is intended to be a valuable resource to undergraduate and graduate students interested in the applications of production management under fuzziness. The chapters represent all areas of production management and are organized to reflect the natural order of production management tasks. In all chapters, special attention is given to applicability and wherever possible, numerical examples are presented. While the reader is expected to have a fairly good understanding of the fuzzy logic, the book provides the necessary notation and preliminary knowledge needed in each chapter.
Author: Robert Jeansoulin
Publisher: Springer Science & Business Media
ISBN: 3642147542
Category : Mathematics
Languages : en
Pages : 380
Get Book Here
Book Description
Spatial information is pervaded by uncertainty. Indeed, geographical data is often obtained by an imperfect interpretation of remote sensing images, while people attach ill-defined or ambiguous labels to places and their properties. As another example, medical images are often the result of measurements by imprecise sensors (e.g. MRI scans). Moreover, by processing spatial information in real-world applications, additional uncertainty is introduced, e.g. due to the use of interpolation/extrapolation techniques or to conflicts that are detected in an information fusion step. To the best of our knowledge, this book presents the first overview of spatial uncertainty which goes beyond the setting of geographical information systems. Uncertainty issues are especially addressed from a representation and reasoning point of view. In particular, the book consists of 14 chapters, which are clustered around three central topics. The first of these topics is about the uncertainty in meaning of linguistic descriptions of spatial scenes. Second, the issue of reasoning about spatial relations and dealing with inconsistency in information merging is studied. Finally, interpolation and prediction of spatial phenomena are investigated, both at the methodological level and from an application-oriented perspective. The concept of uncertainty by itself is understood in a broad sense, including both quantitative and more qualitative approaches, dealing with variability, epistemic uncertainty, as well as with vagueness of terms.
