Mathematical Modeling Using Fuzzy Logic

Mathematical Modeling using Fuzzy Logic has been a dream project for the author. Fuzzy logic provides a unique method of approximate reasoning in an imperfect world. This text is a bridge to the principles of fuzzy logic through an application-focused approach to selected topics in engineering and management. The many examples point to the richer solutions obtained through fuzzy logic and to the possibilities of much wider applications. There are relatively very few texts available at present in fuzzy logic applications. The style and content of this text is complementary to those already available. New areas of application, like application of fuzzy logic in modeling of sustainability, are presented in a graded approach in which the underlying concepts are first described. The text is broadly divided into two parts: the first treats processes, materials, and system applications related to fuzzy logic, and the second delves into the modeling of sustainability with the help of fuzzy logic. This book offers comprehensive coverage of the most essential topics, including: Treating processes, materials, system applications related to fuzzy logic Highlighting new areas of application of fuzzy logic Identifying possibilities of much wider applications of fuzzy logic Modeling of sustainability with the help of fuzzy logic The level enables a selection of the text to be made for the substance of undergraduate-, graduate-, and postgraduate-level courses. There is also sufficient volume and quality for the basis of a postgraduate course. A more restricted and judicious selection can provide the material for a professional short course and various university-level courses.

The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.

Fuzzy Logic in Action: Applications in Epidemiology and Beyond, co-authored by Eduardo Massad, Neli Ortega, Laécio Barros, and Cláudio Struchiner is a remarkable achievement. The book brings a major paradigm shift to medical sciences exploring the use of fuzzy sets in epidemiology and medical diagnosis arena. The volume addresses the most significant topics in the broad areas of epidemiology, mathematical modeling and uncertainty, embodying them within the framework of fuzzy set and dynamic systems theory. Written by leading contributors to the area of epidemiology, medical informatics and mathematics, the book combines a very lucid and authoritative exposition of the fundamentals of fuzzy sets with an insightful use of the fundamentals in the area of epidemiology and diagnosis. The content is clearly illustrated by numerous illustrative examples and several real world applications. Based on their profound knowledge of epidemiology and mathematical modeling, and on their keen understanding of the role played by uncertainty and fuzzy sets, the authors provide insights into the connections between biological phenomena and dynamic systems as a mean to predict, diagnose, and prescribe actions. An example is the use of Bellman-Zadeh fuzzy decision making approach to develop a vaccination strategy to manage measles epidemics in São Paulo. The book offers a comprehensive, systematic, fully updated and self- contained treatise of fuzzy sets in epidemiology and diagnosis. Its content covers material of vital interest to students, researchers and practitioners and is suitable both as a textbook and as a reference. The authors present new results of their own in most of the chapters. In doing so, they reflect the trend to view fuzzy sets, probability theory and statistics as an association of complementary and synergetic modeling methodologies.

Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.

The world we live in is pervaded with uncertainty and imprecision. Is it likely to rain this afternoon? Should I take an umbrella with me? Will I be able to find parking near the campus? Should I go by bus? Such simple questions are a c- mon occurrence in our daily lives. Less simple examples: What is the probability that the price of oil will rise sharply in the near future? Should I buy Chevron stock? What are the chances that a bailout of GM, Ford and Chrysler will not s- ceed? What will be the consequences? Note that the examples in question involve both uncertainty and imprecision. In the real world, this is the norm rather than exception. There is a deep-seated tradition in science of employing probability theory, and only probability theory, to deal with uncertainty and imprecision. The mon- oly of probability theory came to an end when fuzzy logic made its debut. H- ever, this is by no means a widely accepted view. The belief persists, especially within the probability community, that probability theory is all that is needed to deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley, “The only satisfactory description of uncertainty is probability.

This work is by two of the leading researchers in the field of fuzzy set theory and fuzzy logic. It deals with the notions of fuzzy numbers with levels of perception and levels of presumption. Many new results, examples and novel applications in engineering and management science are presented. This approach makes the book interesting and easy to understand, and provides mathematical tools which readers may find useful in the study of their own problems. Of particular interest are the discussions of applications in areas employing zero-based budgeting, the Delphi method, critical path optimization, reliability modelling, filtering and transportation. The first section is devoted to the theoretical basis for these mathematical models. The second part deals with a variety of applications in engineering and management science. There are also seven appendices which contain some special mathematical operations (Minkowaski's operations) on fuzzy quantities and detailed biographical material.

Rule-based fuzzy modeling has been recognised as a powerful technique for the modeling of partly-known nonlinear systems. Fuzzy models can effectively integrate information from different sources, such as physical laws, empirical models, measurements and heuristics. Application areas of fuzzy models include prediction, decision support, system analysis, control design, etc. Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering points of view. It focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements (fuzzy identification), and on the design of nonlinear controllers based on fuzzy models. To automatically generate fuzzy models from measurements, a comprehensive methodology is developed which employs fuzzy clustering techniques to partition the available data into subsets characterized by locally linear behaviour. The relationships between the presented identification method and linear regression are exploited, allowing for the combination of fuzzy logic techniques with standard system identification tools. Attention is paid to the trade-off between the accuracy and transparency of the obtained fuzzy models. Control design based on a fuzzy model of a nonlinear dynamic process is addressed, using the concepts of model-based predictive control and internal model control with an inverted fuzzy model. To this end, methods to exactly invert specific types of fuzzy models are presented. In the context of predictive control, branch-and-bound optimization is applied. The main features of the presented techniques are illustrated by means of simple examples. In addition, three real-world applications are described. Finally, software tools for building fuzzy models from measurements are available from the author.

Provides a unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various types of applications. The book is divided into two parts. The first part contains an extensive presentation of the theory of fuzzy modeling. The second part presents selected applications in three important areas: control and decision-making, image processing, and time series analysis and forecasting. The authors address the consistent and appropriate treatment of the notions of fuzzy sets and fuzzy logic and their applications. They provide two complementary views of the methodology, which is based on fuzzy IF-THEN rules. The first, more traditional method involves fuzzy approximation and the theory of fuzzy relations. The second method is based on a combination of formal fuzzy logic and linguistics. A very important topic covered for the first time in book form is the fuzzy transform (F-transform). Applications of this theory are described in separate chapters and include image processing and time series analysis and forecasting. All of the mentioned components make this book of interest to students and researchers of fuzzy modeling as well as to practitioners in industry. Features: Provides a foundation of fuzzy modeling and proposes a thorough description of fuzzy modeling methodology Emphasizes fuzzy modeling based on results in linguistics and formal logic Includes chapters on natural language and approximate reasoning, fuzzy control and fuzzy decision-making, and image processing using the F-transform Discusses fuzzy IF-THEN rules for approximating functions, fuzzy cluster analysis, and time series forecasting Insight into Fuzzy Modeling is a reference for researchers in the fields of soft computing and fuzzy logic as well as undergraduate, master and Ph.D. students. Vilém Novák, D.Sc. is Full Professor and Director of the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Irina Perfilieva, Ph.D. is Full Professor, Senior Scientist, and Head of the Department of Theoretical Research at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Antonín Dvorák, Ph.D. is Associate Professor, and Senior Scientist at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic.

A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world a