This is a comprehensive and self-contained monograph on the applications of fuzzy sets to economics and engineering. The authors seamlessly combined advanced theoretical material with carefully selected and practically relevant examples of applications that altogether lead to the sound methodology of coping with uncertainty and granular information.
The material is thoroughly organized in a way in which everybody can fully appreciate the role of fuzzy sets in a broad spectrum of technical problems. The material is self-contained and the reader who is not fully versatile with fuzzy sets definitely benefits from an introductory chapter being a concise and systematic introduction to the area. The main topics concern fuzzy sets and their \(\alpha\)-cuts representation, fuzzy arithmetic and fuzzy numbers as well as fuzzy functions and possibility theory. Chapter 3 introduces the reader to the basic equations with fuzzy numbers of the form \(AX +B = C\) that are solved with respect to an unknown fuzzy set \(X\) for \(A\), \(B\), and \(C\) given. The balance that was established between the fundamentals and practice is directly reflected in the organization of the chapters. We have an in-depth coverage of fuzzy nonlinear regression, fuzzy differential and difference equations, fuzzy partial differential equations, and fuzzy eigenvalues as well as fuzzy integral equations. The algorithmic facet of the material is augmented by the study on evolutionary algorithms – an important optimization environment when dealing with fuzzy numbers. The authors guide the reader through numerous application areas in finance (e.g., annuities, portfolio analysis) and operations research (linear programming, PERT, inventory control, queueing theory, network analysis).
Overall, the book is an authoritative, thorough, and balanced coverage of the important and practically relevant core of fuzzy sets that comes with an evident benefit to those interested in exploiting this technology to deal with complex decision-making problems in economics and engineering.