An original, systematic-solution approach to uncertain nonlinear systems control and modeling using fuzzy equations and fuzzy differential equations There are various numerical and analytical approaches to the modeling and control of uncertain nonlinear systems. Fuzzy logic theory is an increasingly popular method used to solve inconvenience problems in nonlinear modeling. Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z-Number presents a structured approach to the control and modeling of uncertain nonlinear systems in industry using fuzzy equations and fuzzy differential equations. The first major work to explore methods based on neural networks and Bernstein neural networks, this innovative volume provides a framework for control and modeling of uncertain nonlinear systems with applications to industry. Readers learn how to use fuzzy techniques to solve scientific and engineering problems and understand intelligent control design and applications. The text assembles the results of four years of research on control of uncertain nonlinear systems with dual fuzzy equations, fuzzy modeling for uncertain nonlinear systems with fuzzy equations, the numerical solution of fuzzy equations with Z-numbers, and the numerical solution of fuzzy differential equations with Z-numbers. Using clear and accessible language to explain concepts and principles applicable to real-world scenarios, this book: Presents the modeling and control of uncertain nonlinear systems with fuzzy equations and fuzzy differential equations Includes an overview of uncertain nonlinear systems for non-specialists Teaches readers to use simulation, modeling and verification skills valuable for scientific research and engineering systems development Reinforces comprehension with illustrations, tables, examples, and simulations Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z-Number is suitable as a textbook for advanced students, academic and industrial researchers, and practitioners in fields of systems engineering, learning control systems, neural networks, computational intelligence, and fuzzy logic control.

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory. The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's theorem, and Black's median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard-Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu's degree of similarity of two fuzzy choice functions.

On the basis of fuzzy sets and some of their relevant generalizations, this book systematically presents the fundamental principles and applications of group decision making under different scenarios of preference relations. By using intuitionistic knowledge as the field of discourse, this work investigates by utilizing innovative research means the fundamental principles and methods of group decision making with various different intuitionistic preferences: Mathematical reasoning is employed to study the consistency of group decision making; Methods of fusing information are applied to look at the aggregation of multiple preferences; Techniques of soft computing and optimization are utilized to search for satisfactory decision alternatives. Each chapter follows the following structurally clear format of presentation: literature review, development of basic theory, verification and reasoning of principles , construction of models and computational schemes, and numerical examples, which cover such areas as technology, enterprise competitiveness, selection of airlines, experts decision making in weather-sensitive enterprises, etc. In terms of theoretical principles, this book can be used as a reference for researchers in the areas of management science, information science, systems engineering, operations research, and other relevant fields. It can also be employed as textbook for upper level undergraduate students and graduate students. In terms of applications, this book will be a good companion for all those decision makers in government, business, and technology areas.

This is the first book to provide a comprehensive and systematic introduction to the ranking methods for interval-valued intuitionistic fuzzy sets, multi-criteria decision-making methods with interval-valued intuitionistic fuzzy sets, and group decision-making methods with interval-valued intuitionistic fuzzy preference relations. Including numerous application examples and illustrations with tables and figures and presenting the authors' latest research developments, it is a valuable resource for researchers and professionals in the fields of fuzzy mathematics, operations research, information science, management science and decision analysis.

This book mainly introduces the latest development of generalized intuitionistic multiplicative fuzzy calculus and its application. The book pursues three major objectives: (1) to introduce the calculus models with concrete mathematical expressions for generalized intuitionistic multiplicative fuzzy information; (2) to introduce new information fusion methods based on the definite integral models; and (3) to clarify the involved approaches bymilitary case. The book is especially valuable for readers to understand how the theoretical framework of generalized intuitionistic multiplicative fuzzy calculus is constructed, not only discrete or continuous but also correlative (generalized) intuitionistic (multiplicative) fuzzy information is aggregated based on the definite integral models and the theory with a military practice is integrated, which would deepen the understanding and give researchers more inspiration in practical decision analysis under uncertainties.

This book presents the latest advances in applying fuzzy sets and operations research technology and methods. It is the first fuzzy mathematics textbook for students in high school and technical secondary schools. Part of Springer's book series: Advances in Intelligent and Soft Computing, it includes the 36 best papers from the Ninth International Conference on Fuzzy Information and Engineering (ICFIE2017), organized by the Fuzzy Information and Engineering Branch of Operations Research Society of China and Operations Research Society of Guangdong Province in China. Every paper has been carefully peer-reviewed by leading experts. The areas covered include 1. Fuzzy Measure and Integral; 2. Fuzzy Topology and Algebras; 3. Classification and Recognition; 4. Control and Fuzziness; 5. Extension of Fuzzy Set and System; 6. Operations Research and Management (OR); The book is suitable for college, masters and doctoral students; educators in universities, colleges, middle and primary schools teaching mathematics, fuzzy sets and systems, operations research, information and engineering, as well as management, control. Discussing case applications, it is also a valuable reference resource for professionals interested in theoretical and practical research.

These conference proceedings focus on the topics of data-driven decision-making, stochastic decision-making, fuzzy decision-making and their applications in real-life problems. Beijing University of Chemical Technology organized IFDS2016, the 4th International Forum on Decision Sciences, with the theme "Data-Driven Decision-Making." The proceedings collect 84 selected papers presenting cutting-edge modeling and solution methods and include numerous practical case studies, making it a valuable resource for students, researchers and practitioners working in the fields of decision science, operations research, management science and engineering.

Fuzzy set theory provides a framework for representing uncertainty. As increasing importance is being given to uncertainty management in intelligent systems, fuzzy inferencing procedures are vital. Using Fest (Fuzzy Expert System Tools), the authors focus on the parameters of fuzzy rule-based systems. The book then goes on to show how Fest can be used for inference of indistinct data and algorithmic descriptions. Divided into three parts, this comprehensive text covers the characteristics of expert systems and fuzzy sets theory, knowledge representation and the inference process. Features include:
* Incorporation of uncertainty management and fuzzy logic in soft expert systems
* Coverage of the processes of knowledge acquisition, representation, and generation
* Novel ideas in approaching fuzzy inferencing
* Notions pertaining to flexible grammar and the use of synonyms
Written by international experts, this is an invaluable reference for engineers and computer scientists working in the areas of expert systems, fuzzy logic systems and applications of fuzzy logic both in industry and academia. The accompanying disk will allow readers to practice the methods introduced and thus highlight the power of fuzzy logic when combined with expert system technology.

Fuzzy logic-based circuits are instrumental in computer hardware applications. Currently, they are widely relied upon to recognize gradual and relative properties in electronic and real data. This comprehensive edited volume focuses on 'fuzzy technology'. Presented in four clearly organized thematic sections, coverage includes fuzzy set theory, fuzzy logic control, examples of fuzzy logic implementations and finally examples of neuro-fuzzy hybrid systems and their applications, featuring explanation of classical fuzzy logic, fuzzy arithmetic operations, approximate reasoning and fuzzy control in terms of Boolean logic, set theory, and control theory; detailed discussion of digital and analog implementation of fuzzy logic discrete and VLSI circuits; coverage of fuzzy control-based systematic design methodology, and assessment of the compatibility of conventional control with crisp fuzzy control; an overview of the latest fuzzy logic digital and analog hardware applications including CMOS and CAD tools; and includes the chapter-by-chapter synopses and exercises. Written by a team of internationally renowned computer science specialists, this is a forward-looking account of the emergence of neuro-fuzzy systems. Professional computer scientists and engineers developing fuzzy logic applications will find this an invaluable reference. Researchers and students in the broad field of artificial intelligence will find this a source of inspiration.

On the basis of fuzzy sets and some of their relevant generalizations, this book systematically presents the fundamental principles and applications of group decision making under different scenarios of preference relations. By using intuitionistic knowledge as the field of discourse, this work investigates by utilizing innovative research means the fundamental principles and methods of group decision making with various different intuitionistic preferences: Mathematical reasoning is employed to study the consistency of group decision making; Methods of fusing information are applied to look at the aggregation of multiple preferences; Techniques of soft computing and optimization are utilized to search for satisfactory decision alternatives. Each chapter follows the following structurally clear format of presentation: literature review, development of basic theory, verification and reasoning of principles , construction of models and computational schemes, and numerical examples, which cover such areas as technology, enterprise competitiveness, selection of airlines, experts decision making in weather-sensitive enterprises, etc. In terms of theoretical principles, this book can be used as a reference for researchers in the areas of management science, information science, systems engineering, operations research, and other relevant fields. It can also be employed as textbook for upper level undergraduate students and graduate students. In terms of applications, this book will be a good companion for all those decision makers in government, business, and technology areas.

Great progresses have been made in the application of fuzzy set theory and fuzzy logic. Most remarkable area of application is 'fuzzy control', where fuzzy logic was first applied to plant control systems and its use is expanding to consumer products. Most of fuzzy control systems uses fuzzy inference with max-min or max-product composition, similar to the algorithm that first used by Mamdani in 1970s. Some algorithms are developed to refine fuzzy controls systems but the main part of algorithm stays the same. Triggered by the success of fuzzy control systems, other ways of applying fuzzy set theory are also investigated. They are usually referred to as 'fuzzy expert sys tems', and their purpose are to combine the idea of fuzzy theory with AI based approach toward knowledge processing. These approaches can be more generally viewed as 'fuzzy information processing', that is to bring fuzzy idea into informa tion processing systems."

The refereed proceedings of the 10th International Fuzzy Systems Association World Congress, IFSA 2003, held in June/July 2003 in Istanbul, Turkey. The 84 papers presented together with 5 invited papers were carefully reviewed and selected form 318 submissions. The papers address all current issues in the area and present the state of the art in fuzzy sets, fuzzy systems, and fuzzy logic and their applications in a broad variety of fields. The papers are divided in four parts on mathematical issues, methodological issues, application areas, and cross-disciplinary issues.

Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.

A comprehensive introduction to mathematical structures essential for Rough Set Theory. The book enables the reader to systematically study all topics of rough set theory. After a detailed introduction in Part 1 along with an extensive bibliography of current research papers. Part 2 presents a self-contained study that brings together all the relevant information from respective areas of mathematics and logics. Part 3 provides an overall picture of theoretical developments in rough set theory, covering logical, algebraic, and topological methods. Topics covered include: algebraic theory of approximation spaces, logical and set-theoretical approaches to indiscernibility and functional dependence, topological spaces of rough sets. The final part gives a unique view on mutual relations between fuzzy and rough set theories (rough fuzzy and fuzzy rough sets). Over 300 excercises allow the reader to master the topics considered. The book can be used as a textbook and as a reference work.

This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering. It covers the basics leading to: fuzzy clustering, fuzzy pattern recognition, fuzzy database, fuzzy image processing, soft computing, fuzzy applications in operations research, fuzzy decision making, fuzzy rule based systems, fuzzy systems modeling, fuzzy mathematics. It is not a book designed for researchers - it is where you really learn the "basics" needed for any of the above-mentioned applications. It includes many figures and problem sets at the end of sections.

This book contains thirty timely contributions in the emerging field of Computational Intelligence (CI) with reference to system control design and applications. The three basic constituents ofCI are neural networks (NNs). fuzzy logic (FL) I fuzzy reasoning (FR). and genetic algorithms (GAs). NNs mimic the distributed functioning of the human brain and consist of many. rather simple. building elements (called artificial neurons) which are controlled by adaptive parameters and are able to incorporate via learning the knowledge provided by the environment, and thus respond intelligently to new stimuli. Fuzzy logic (FL) provides the means to build systems that can reason linguistically under uncertainty like the human experts (common sense reasoning). Both NNs and FL I FR are among the most widely used tools for modeling unknown systems with nonlinear behavior. FL suits better when there is some kind of knowledge about the system. such as, for example, the linguistic information of a human expert. On the other hand. NNs possess unique learning and generalization capabilities that allow the user to construct very accurate models of nonlinear systems simply using input-output data. GAs offer an interesting set of generic tools for systematic random search optimization following the mechanisms of natural genetics. In hybrid Computational Intelligence - based systems these three tools (NNs, FL, GAs) are combined in several synergetic ways producing integrated tools with enhanced learning, generalization. universal approximation. reasoning and optimization abilities.

The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies."

Analog to digital and digital to analog converters are essential interfaces between computers and the outside world. They interface most signal processing devices and are embedded in an ever larger number of integrated circuits used currently in telecom, remote control devices, medical electronic instruments, and so on. This book surveys recent progress and gives an account of the working principles, describing the architectures of integrated converters and their accuracy and speed. The accompanying web site provides a MATLAB toolbox which allows the reader to experiment with some of the concepts explained in the book.

This volume contains the papers selected for presentation at the Seventh Int- national Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing (RSFDGrC 99) held in the Yamaguchi Resort Center, Ube, Y- aguchi, Japan, November 9-11, 1999. The workshop was organized by Inter- tional Rough Set Society, BISC Special Interest Group on Granular Comp- ing (GrC), Polish-JapaneseInstitute of Information Technology, and Yamaguchi University. RSFDGrC 99providedaninternationalforumforsharingoriginalresearch results and practical development experiences among experts in these emerging ?elds.An importantfeatureoftheworkshopwasto stresstheroleofthe integ- tion of intelligent information techniques. That is, to promote a deep fusion of these approaches to AI, Soft Computing, and Database communities in order to solve real world, large, complex problems concerned with uncertainty and fuz- ness. In particular, rough and fuzzy set methods in data mining and granular computing were on display. The total of 89 papers coming from 21 countries and touching a wide spectrum of topics related to both theory and applications were submitted to RSFDGrC 99. Out of them 45 papers were selected for regular presentations and 15 for short presentations. Seven technical sessions were organized, namely: Rough Set Theory and Its Applications; Fuzzy Set Theory and Its Applications; Non-Classical Logic and Approximate Reasoning; Information Granulation and Granular Computing; Data Mining and Knowledge Discovery; Machine Lea- ing; Intelligent Agents and Systems. TheRSFDGrC 99programwasenrichedbyfourinvitedspeakers: Zdzis law Pawlak, Lot? A. Zadeh, Philip Yu, and Setsuo Arikawa, from Soft Computing, Database, and AI communities. A special session on Rough Computing: Fo- dations and Applications was organized by James F. Peters."

Fuzzy sets were introduced by Zadeh (1965) as a means of representing and manipulating data that was not precise, but rather fuzzy. Fuzzy logic pro vides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associ ated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for rep resentating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic and classical probablity theory do not provide an appropriate conceptual framework for dealing with the representation of com monsense knowledge, since such knowledge is by its nature both lexically imprecise and noncategorical. The developement of fuzzy logic was motivated in large measure by the need for a conceptual framework which can address the issue of uncertainty and lexical imprecision. Some of the essential characteristics of fuzzy logic relate to the following [242]. * In fuzzy logic, exact reasoning is viewed as a limiting case of ap proximate reasoning. * In fuzzy logic, everything is a matter of degree. * In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables. * Inference is viewed as a process of propagation of elastic con straints. * Any logical system can be fuzzified. There are two main characteristics of fuzzy systems that give them better performance fur specific applications.

This volume constitutes the thoroughly refereed post-workshop proceedings of an international workshop on fuzzy logic in Artificial Intelligence held in Negoya, Japan during IJCAI '97.
The 17 revised full papers presented have gone through two rounds of reviewing and revision. Three papers by leading authorities in the area are devoted to the general relevance of fuzzy logic and fuzzy sets to AI. The remaining papers address various relevant issues ranging from theory to application in areas like knowledge representation, induction, logic programming, robotics, pattern recognition, etc.

During the past few years two principally different approaches to the design of fuzzy controllers have emerged: heuristics-based design and model-based design. The main motivation for the heuristics-based design is given by the fact that many industrial processes are still controlled in one of the following two ways: - The process is controlled manually by an experienced operator. - The process is controlled by an automatic control system which needs manual, on-line 'trimming' of its parameters by an experienced operator. In both cases it is enough to translate in terms of a set of fuzzy if-then rules the operator's manual control algorithm or manual on-line 'trimming' strategy in order to obtain an equally good, or even better, wholly automatic fuzzy control system. This implies that the design of a fuzzy controller can only be done after a manual control algorithm or trimming strategy exists. It is admitted in the literature on fuzzy control that the heuristics-based approach to the design of fuzzy controllers is very difficult to apply to multiple-inputjmultiple-output control problems which represent the largest part of challenging industrial process control applications. Furthermore, the heuristics-based design lacks systematic and formally verifiable tuning tech niques. Also, studies of the stability, performance, and robustness of a closed loop system incorporating a heuristics-based fuzzy controller can only be done via extensive simulations."

Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start.

Contents:
HVAC Control Systems. Basic concepts. HVAC control strategies. Distributed control. System configuration. References. Device Technology. Sensors. Control elements. PID controllers. References. System modelling. Simple room modelling for control analysis. Accounting for fabric in room modelling. Heat emitter and non-linear modelling. A coupled room and emitter model. Component modelling. References. System Stability. Feedback control. Stability test. Feedforward control. Model reduction. References. Discrete-time Systems. The z-transformation. Representing discrete-time systems. Stability tests in discrete-time. The sampling interval. Digital control algorithms. References. Multivariable Systems. State-space representation of systems. The transfer function matrix. The multivariable control problem. Design of multivariable compensators. References. System Identification and Controller Tuning. System identification. Assessing the quality of response. Fixed parameter controller tuning method. References. Adaptive Control. Adaptive controllers. Direct and indirect adaptive control algorithms. Model reference adaptive control. Gain scheduling. Progress in HVAC adaptive control. References. Advanced Methods. Robust Control. Expert systems. Fuzzy logic control. Artificial neural networks. References.