Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction.
This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.
Fuzzy Logic and Intelligent Systems reflects the most recent developments in neural networks and fuzzy logic, and their application in intelligent systems. In addition, the balance between theoretical work and applications makes the book suitable for both researchers and engineers, as well as for graduate students.
Paul Williams, a leading authority on modeling in integer programming, has written a concise, readable introduction to the science and art of using modeling in logic for integer programming. Written for graduate and postgraduate students, as well as academics and practitioners, the book is divided into four chapters that all avoid the typical format of definitions, theorems and proofs and instead introduce concepts and results within the text through examples. References are given at the end of each chapter to the more mathematical papers and texts on the subject, and exercises are included to reinforce and expand on the material in the chapter.
Chapter 1 gives a basic introduction to logic and its aims, and goes on to explain the Propositional and Predicate Calculus. Chapter 2 explains Linear Programming (LP) and Integer Programming (IP) using the machinery of logic; explains the fundamental structural and mathematical properties of these types of models, along with the main methods of solving IP models; covers main areas of practical application; and attempts to distinguish between computationally ‘difficult’ and ‘easy’ classes of problem. Chapter 3 applies logic to the formulation of IP models using the methods explained in chapter 1 and looks at the deeper mathematical concepts involved. Chapter 4 then covers the fundamental problem of computational logic: the satisfiability problem, which lies at the heart of the entire book. Methods of solving with both logic and IP are given and their connections are described. Applications in diverse fields are discussed, and Williams shows how IP models can be expressed as satisfiability problems and solved as such.
The authors explore how MADM methods can be used for descriptive purposes to model: the existing decision-making process; noncompensatory and scoring methods; accommodation of soft data; construction of a multiple-decision support systems; and the validity of methods. The advanced procedures of TOPSIS and ELECTRE are also presented.