Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information. Key Features: Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data. Describes methods of increasing importance with applications in areas such as environmental statistics and social science. Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples. Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data. This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.
Decision making by the aircrafts services of the international airport, which provides for intensive traffic of aircraft and their ground handling, becomes a very topical issue. If earlier it was believed that the intensity is provided only by the number of runways, nowadays a large accumulation of aircraft on the airport platform-field creates equally complex difficulties in comparison with aircraft take-offs and landings. Solving such problems with the use of «crisp methods» of queuing theory gives little. This article deals with modern «fuzzy methods» based on simulation modeling and fuzzy logic.
Logic concepts are more mainstream than you may realize. There’s logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you’re a college student of a student of life. You’ll find out about: Formal Logic Syllogisms Constructing proofs and refutations Propositional and predicate logic Modal and fuzzy logic Symbolic logic Deductive and inductive reasoning Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.
Autonomous Learning Systems is the result of over a decade of focused research and studies in this emerging area which spans a number of well-known and well-established disciplines that include machine learning, system identification, data mining, fuzzy logic, neural networks, neuro-fuzzy systems, control theory and pattern recognition. The evolution of these systems has been both industry-driven with an increasing demand from sectors such as defence and security, aerospace and advanced process industries, bio-medicine and intelligent transportation, as well as research-driven – there is a strong trend of innovation of all of the above well-established research disciplines that is linked to their on-line and real-time application; their adaptability and flexibility. Providing an introduction to the key technologies, detailed technical explanations of the methodology, and an illustration of the practical relevance of the approach with a wide range of applications, this book addresses the challenges of autonomous learning systems with a systematic approach that lays the foundations for a fast growing area of research that will underpin a range of technological applications vital to both industry and society. Key features: Presents the subject systematically from explaining the fundamentals to illustrating the proposed approach with numerous applications. Covers a wide range of applications in fields including unmanned vehicles/robotics, oil refineries, chemical industry, evolving user behaviour and activity recognition. Reviews traditional fields including clustering, classification, control, fault detection and anomaly detection, filtering and estimation through the prism of evolving and autonomously learning mechanisms. Accompanied by a website hosting additional material, including the software toolbox and lecture notes. Autonomous Learning Systems provides a ‘one-stop shop’ on the subject for academics, students, researchers and practicing engineers. It is also a valuable reference for Government agencies and software developers.
Explains for the first time how «computing with words» can aid in making subjective judgments Lotfi Zadeh, the father of fuzzy logic, coined the phrase «computing with words» (CWW) to describe a methodology in which the objects of computation are words and propositions drawn from a natural language. Perceptual Computing explains how to implement CWW to aid in the important area of making subjective judgments, using a methodology that leads to an interactive device—a «Perceptual Computer»—that propagates random and linguistic uncertainties into the subjective judgment in a way that can be modeled and observed by the judgment maker. This book focuses on the three components of a Perceptual Computer—encoder, CWW engines, and decoder—and then provides detailed applications for each. It uses interval type-2 fuzzy sets (IT2 FSs) and fuzzy logic as the mathematical vehicle for perceptual computing, because such fuzzy sets can model first-order linguistic uncertainties whereas the usual kind of fuzzy sets cannot. Drawing upon the work on subjective judgments that Jerry Mendel and his students completed over the past decade, Perceptual Computing shows readers how to: Map word-data with its inherent uncertainties into an IT2 FS that captures these uncertainties Use uncertainty measures to quantify linguistic uncertainties Compare IT2 FSs by using similarity and rank Compute the subsethood of one IT2 FS in another such set Aggregate disparate data, ranging from numbers to uniformly weighted intervals to nonuniformly weighted intervals to words Aggregate multiple-fired IF-THEN rules so that the integrity of word IT2 FS models is preserved Free MATLAB-based software is also available online so readers can apply the methodology of perceptual computing immediately, and even try to improve upon it. Perceptual Computing is an important go-to for researchers and students in the fields of artificial intelligence and fuzzy logic, as well as for operations researchers, decision makers, psychologists, computer scientists, and computational intelligence experts.
Discover the latest models and methods for robotic microassembly from around the world This book presents and analyzes new and emerging models and methods developed around the world for robotic microassembly, a new and innovative way to produce better microsystems. By exploring everything from the physics of micromanipulation to microassembly to microhandling, it provides the first complete overview and review of this rapidly growing field. Robotic Microassembly is divided into three parts: Part One: Modeling of the Microworld Part Two: Handling Strategies Part Three: Robotic and Microassembly Together, these three parts feature eight chapters contributed by eight different authors. The authors, internationally recognized experts in the field of robotic microassembly, represent research laboratories in Asia, Europe, and North America. As a result, readers get a remarkable perspective on different approaches to robotic microassembly from around the world. Examples provided throughout the chapters help readers better understand how these different approaches work in practice. References at the end of each chapter lead to the primary literature for further investigation of individual topics. Robotic microassembly offers a new, improved way to manufacture high-performance microelectro-mechanical systems (MEMS). Therefore, any professional or student involved in microrobotics, micromechatronics, self-assembly or MEMS will find plenty of novel ideas and methods in this book that set the stage for new approaches to design and build the next generation of MEMS and microproducts.
An enlightening introduction to the study of logic: its history, philosophical foundations, and formal structures Logic: Inquiry, Argument, and Order is the first book of its kind to frame the study of introductory logic in terms of problems connected to wider issues of knowledge and judgment that arise in the context of racial, cultural, and religious diversity. With its accessible style and integration of philosophical inquiry and real-life concerns, this book offers a novel approach to the theory of logic and its relevance to questions of meaning and value that arise in the world around us. The book poses four problems for logic: Is logic separate from experience? Does logic require dualisms? Can logic reconcile opposed ways of understanding the world? And when things are divided, does the boundary have a logic? The author begins the exploration of these questions with a discussion of the process of analyzing and constructing arguments. Using the logical theories of C. S. Peirce, John Dewey, and Josiah Royce to frame the investigation, subsequent chapters outline the process of inquiry, the concept of communicative action, the nature of validity, categorical reasoning through the theory of the syllogism, and inductive reasoning and probability. The book concludes with a presentation of modal logic, propositional logic, and quantification. Logic is presented as emerging from the activities of inquiry and communication, allowing readers to understand even the most difficult aspects of formal logic as straightforward developments of the process of anticipating and taking action. Numerous practice problems use arguments related to issues of diversity and social theory, and the book introduces methods of proving validity that include Venn diagrams, natural deduction, and the method of tableaux. Logic: Inquiry, Argument, and Order is an ideal book for courses on philosophical methods and critical reasoning at the upper-undergraduate and graduate levels. It is also an insightful reference for anyone who would like to explore a cross-cultural approach to the topic of logic.
Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout various media (books, journal articles, webpages, etc.), the diffuse nature of these sources is problematic and logic as a topic benefits from a unified approach. Logic for Computer Science and Artificial Intelligence utilizes this format, surveying the tableaux, resolution, Davis and Putnam methods, logic programming, as well as for example unification and subsumption. For non-classical logics, the translation method is detailed. Logic for Computer Science and Artificial Intelligence is the classroom-tested result of several years of teaching at Grenoble INP (Ensimag). It is conceived to allow self-instruction for a beginner with basic knowledge in Mathematics and Computer Science, but is also highly suitable for use in traditional courses. The reader is guided by clearly motivated concepts, introductions, historical remarks, side notes concerning connections with other disciplines, and numerous exercises, complete with detailed solutions, The title provides the reader with the tools needed to arrive naturally at practical implementations of the concepts and techniques discussed, allowing for the design of algorithms to solve problems.