The objective of this book is to present an uncertainty modeling approach using a new type of fuzzy system model via "Fuzzy Functions". Since most researchers on fuzzy systems are more familiar with the stan...
ISBN:
(数字)9783540899242
ISBN:
(纸本)3540899235
The objective of this book is to present an uncertainty modeling approach using a new type of fuzzy system model via "Fuzzy Functions". Since most researchers on fuzzy systems are more familiar with the standard fuzzy rule bases and their inference system structures, many standard tools of fuzzy system modeling approaches are reviewed to demonstrate the novelty of the structurally different fuzzy functions, before we introduced the new methodologies. To make the discussions more accessible, no special fuzzy logic and system modeling knowledge is assumed. Therefore, the book itself may be a reference for some related methodologies to most researchers on fuzzy systems analyses. For those readers, who have knowledge of essential fuzzy theories, Chapter 1, 2 should be treated as a review material. Advanced readers ought to be able to read chapters 3, 4 and 5 directly, where proposed methods are presented. Chapter 6 demonstrates experiments conducted on various datasets.
In this monograph, the authors introduce a novel fuzzy rule-base, referred to as the Fuzzy All-permutations Rule-Base (FARB). They show that inferring the FARB, using standard tools from fuzzy logic theory, yields an ...
ISBN:
(数字)9783540880776
ISBN:
(纸本)9783540880769
In this monograph, the authors introduce a novel fuzzy rule-base, referred to as the Fuzzy All-permutations Rule-Base (FARB). They show that inferring the FARB, using standard tools from fuzzy logic theory, yields an input-output map that is mathematically equivalent to that of an artificial neural network. Conversely, every standard artificial neural network has an equivalent FARB. The FARB-ANN equivalence integrates the merits of symbolic fuzzy rule-bases and sub-symbolic artificial neural networks, and yields a new approach for knowledge-based neurocomputing in artificial neural networks.
In conventional mathematical programming, coefficients of problems are usually determined by the experts as crisp values in terms of classical mathematical reasoning. But in reality, in an imprecise and uncertain envi...
ISBN:
(数字)9783540899150
ISBN:
(纸本)9783540899143
In conventional mathematical programming, coefficients of problems are usually determined by the experts as crisp values in terms of classical mathematical reasoning. But in reality, in an imprecise and uncertain environment, it will be utmost unrealistic to assume that the knowledge and representation of an expert can come in a precise way. The wider objective of the book is to study different real decision situations where problems are defined in inexact environment. Inexactness are mainly generated in two ways (1) due to imprecise perception and knowledge of the human expert followed by vague representation of knowledge as a DM; (2) due to huge-ness and complexity of relations and data structure in the definition of the problem situation. We use interval numbers to specify inexact or imprecise or uncertain data. Consequently, the study of a decision problem requires answering the following initial questions: How should we compare and define preference ordering between two intervals?, interpret and deal inequality relations involving interval coefficients?, interpret and make way towards the goal of the decision problem? The present research work consists of two closely related fields: approaches towards defining a generalized preference ordering scheme for interval attributes and approaches to deal with some issues having application potential in many areas of decision making.
Fuzzy Logic in Action: Applications in Epidemiology and Beyond, co-authored by Eduardo Massad, Neli Ortega, Lacio Barros, and Cludio Struchiner is a remarkable achievement. The book brings a major paradigm shift to me...
ISBN:
(纸本)3540690808;9783540690801;9783540690924
Fuzzy Logic in Action: Applications in Epidemiology and Beyond, co-authored by Eduardo Massad, Neli Ortega, Lacio Barros, and Cludio 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 So 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.
This book is focused on mathematical analysis and rigorous design methods for fuzzy control systems based on Takagi-Sugeno fuzzy models, sometimes called Takagi-Sugeno-Kang models. The author presents a rather general...
ISBN:
(数字)9783540899273
ISBN:
(纸本)9783540899266
This book is focused on mathematical analysis and rigorous design methods for fuzzy control systems based on Takagi-Sugeno fuzzy models, sometimes called Takagi-Sugeno-Kang models. The author presents a rather general analytical theory of exact fuzzy modeling and control of continuous and discrete-time dynamical systems. The main attention is paid to usability of the results for the control and computer engineering community and therefore simple and easy for linguistic interpretation knowledge-bases have been used. The approach is based on the author s theorems concerning equivalence between widely used Takagi-Sugeno systems and some class of multivariate polynomials. It combines the advantages of fuzzy system theory and classical control theory. Classical control theory can be applied to modeling of dynamical plants and the controllers. They are all equivalent to the set of Takagi-Sugeno type fuzzy rules. The approach combines the best of fuzzy and conventional control theory. It enables linguistic interpretability (also called transparency) of both the plant model and the controller. In the case of linear systems and some class of nonlinear systems, the engineer can in many cases directly apply well-known classical tools from the control theory both for analysis, and the design of the closed-loop fuzzy control systems. Therefore the main objective of the book is to establish comprehensive and unified analytical foundations for fuzzy modeling using Takagi-Sugeno rule scheme and their applications for fuzzy control, identification of some class of nonlinear dynamical processes and classification problem solver design.
Real-life decisions are usually made in the state of uncertainty such as randomness and fuzziness. How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer thes...
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ISBN:
(数字)9783540894841
ISBN:
(纸本)9783540894834
Real-life decisions are usually made in the state of uncertainty such as randomness and fuzziness. How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem. Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.
"Mathematics of fuzziness: Basic Issues" introduces a basic notion of 'fuzziness' and provides a conceptual mathematical framework to characterize such fuzzy phenomena in "studies in fuzziness a...
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ISBN:
(数字)9783540783114
ISBN:
(纸本)9783540783107
"Mathematics of fuzziness: Basic Issues" introduces a basic notion of 'fuzziness' and provides a conceptual mathematical framework to characterize such fuzzy phenomena in "studies in fuzziness and soft computing". The book systematically presents a self-contained introduction to the essentials of mathematics of fuzziness ranging from fuzzy sets, fuzzy relations, fuzzy numbers, fuzzy algebra, fuzzy measures, fuzzy integrals, and fuzzy topology to fuzzy control in a strictly mathematical manner. It contains most of the authors' research results in the field of fuzzy set theory and has evolved from the authors' lecture notes to both undergraduate and graduate students over the last three decades. A lot of exercises in each chapter of the book are particularly suitable as a textbook for any undergraduate and graduate student in mathematics, computer science and engineering. The reading of the book will surely lay a solid foundation for further research on fuzzy set theory and its applications.
This monograph is special in its orientation and contribution to current state of our understanding of decision-choice process and knowledge production. Its special orientation is to bring to the scientific community ...
ISBN:
(数字)9783540880875
ISBN:
(纸本)9783540880868
This monograph is special in its orientation and contribution to current state of our understanding of decision-choice process and knowledge production. Its special orientation is to bring to the scientific community the discussions on the epistemic structure of the relationships among uncertainty, expectations, risk, possibility, probability and how the rules of fuzzy paradigm and the methods of fuzzy rationality bring new and different understanding to the relationships. At the level of theory of knowledge, it presents the structure and epistemic analysis of uncertainty, expectations and risk in decision-choice actions through the characteristics of substitution-transformation and input-output processes in categorial dynamics of actual-potential duality. The interactive effects of rationality and expectation are examined around belief, prospect, time and conditions of belief justification where the relationship between possibility and probability as a sequential link between potential and actual is analyzed to provide some understanding of the role of relative costs and benefits in defining risk in both nature and society. The concepts of possibilistic and probabilistic beliefs are explicated in relation to rationality and the decision-choice process where the analytical relationship between uncertainty and expectation formation is presented leading to the introduction of two types of uncertainty composed of fuzzy uncertainty and stochastic uncertainty.
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