Fuzzy geometric programming.
The book introduces a relatively new branch of fuzzy optimization -- fuzzy geometric programming -- to a wider community of readers. The branch was originated by the author's contribution at the second IFSA conference in 1987. The book summarizes the main results of this scientific discipline achieved since 1987. The material of the book can be divided into three main parts. The first part provides the reader with necessary mathematical preliminaries as for instance the introduction to the theory of fuzzy sets, the concept of fuzzy matrices, vectors and functions, and their properties as well as the introduction to the classical non-fuzzy geometric programming. The second part represents the main aim of the book. It consists of five chapters, in which various approaches to the fuzzification of the classical geometric programming problem and solution methods of the resulting fuzzy optimization problems are presented. The author introduces the fuzzy posynomial geometric programming problem, develops an appropriate duality theory and describes primal and dual algorithms for its solution. Geometric programming problems with various types of fuzzy coefficients (e.g. \((.,c)\)-type, (\(L\)-\(R\))-type, flat fuzzy coefficients), as well as various types of fuzzy variables (e.g. \(T\)-fuzzy or trapezoidal fuzzy variables) are investigated and appropriate solution methods for these problems are suggested. A special chapter is devoted to fuzzy multiobjective geometric programming problems with fuzzy coefficients and fuzzy variables. The third part consists of the last two chapters of the book. In the first of the two chapters, fuzzy geometric programming is applied to some power plant engineering problems and fuzzy multiobjective geometric programming is applied to a problem from postal services. In the last chapter of the book, the concept of antinomy which is known from linear programming is extended to fuzzy geometric programming. Besides, directions of future research and applications of fuzzy geometric programming are discussed.
fuzzy multiobjective geometric programming
scientific article; zbMATH DE number 1940289