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A series of methods for the formation of higher-type information granules represented by Interval Type-2 Fuzzy Sets are also shown, via multiple approaches, such as Coefficient of Variation, principle of justifiable granularity, uncertainty-based information concept, and numerical evidence based. And a fuzzy granular application comparison is given as to demonstrate the differences in how uncertainty affects the performance of fuzzy information granules.

It provides readers with all the necessary tools for making statistical inference in the case of incomplete information or insufficient data, where classical statistics cannot be applied. The respective chapters, written by prominent researchers, explain a wealth of both basic and advanced concepts including: fuzzy probability distributions, fuzzy frequency distributions, fuzzy Bayesian inference, fuzzy mean, mode and median, fuzzy dispersion, fuzzy p-value, and many others.

To foster a better understanding, all the chapters include relevant numerical examples or case studies. Taken together, they form an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on fuzzy statistics. Moreover, by extending all the main aspects of classical statistical decision-making to its fuzzy counterpart, the book presents a dynamic snapshot of the field that is expected to stimulate new directions, ideas and developments. 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.

An Introduction to Fuzzy Control Hardcover, 2nd rev. Hellendoorn, M.


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They can be found either as stand-alone control elements or as integral parts of distributed control systems including conventional controllers in a wide range of industrial process control systems and consumer products. Applications of fuzzy controllers have become a well established practice for Japanese manufacturers of control equipment and systems, and are becoming more and more common in Europe and America. The main aim of this book is to show that fuzzy control is not totally ad hoc, that there exist formal techniques for the analysis of a fuzzy controller, and that fuzzy control can be implemented even when no expert knowledge is available.

Thus the book is mainly oriented toward control engineers and theorists, although parts can be read without any knowledge of control theory and may be of interest to Al people. This 2nd, revised edition incorporates suggestions from numerous reviewers and updates and reorganizes some of the material.

Fundamenta Informaticae - Volume 27, issue 2,3

Mordeson, Davender S. Malik, Terry D. 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.

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The final chapter discusses Georgescu's degree of similarity of two fuzzy choice functions. Contains a discussion of cutting-edge technology supplemented by the analysis of several successful applications in the areas of approximate reasoning, fuzzy control and fuzzy analysis. Includes scores of exercises, problems, worked examples, step-by-step solutions and comprehensive references.

Classical Descriptive Set Theory Hardcover, ed. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises over , and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar.

Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc. It covers fuzzy structures, systems, rules, operations as well as important applications, e. It is dedicated to Enric Trillas as an acknowledgement for his pioneering research in the field.

The book include a foreword by Lotfi A. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification.

These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present. Tzafestas, A. 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 s. 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.

Fuzzy Engineering and Operations Research Paperback, ed. The 5th ICFIE, built on the success of previous conferences, and the GDORC, first held, are major Symposiums, respectively, for scientists, engineers practitioners and Operation Research OR researchers presenting their updated results, developments and applications in all areas of fuzzy information and engineering and OR. It aims to strengthen relations between industry research laboratories and universities, and to create a primary symposium for world scientists in Fuzziology and OR fields.

Written by an international team of researchers this edited volume covers the modeling, analysis and synthesis of fuzzy control systems.

Features include:? Comprehensive coverage of fuzzy dynamical systems, robustness, stability and sensitivity -- giving the reader a good grasp of the fundamentals of fuzzy control? Applications of fuzzy control to aircraft systems, rocket engines and automotive engines? Problems and examples illustrating how fuzzy approaches may be applied to the modeling, analysis and synthesis of closed-loop systems Design and control engineers will value the advanced control techniques and new design and analysis tools presented.

Postgraduates studying fuzzy control will find this book a useful reference on synthesis, systems analysis and advanced nonlinear control methods. Patyra, D.


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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.

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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. 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.

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. Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand- book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand- book.

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At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem- inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria.

Much of the material of this volume is related to the Twenti- eth Seminar held in February , material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas. Fuzzy Model Identification for Control Hardcover, ed.

Set Theory - Introduction

Simulated examples and real-world applications from chemical and process engineering illustrate the main methods and techniques. Welcome to Loot. Checkout Your Cart Price. Status Available to order On special 11 New releases 2 Recent releases 2.