Mathematical Preliminaries

This chapter is devoted to mathematical preliminaries, which will be used in the remainder of this book. Starting with several basic definitions involving fuzzy sets, operations on fuzzy sets, especially fuzzy numbers, are outlined. Bellman and Zadeh’s approach to decision making in a fuzzy environment, called fuzzy decision, is then examined. Fundamental notions and methods of multiobjective, interactive multiobjective, and interactive fuzzy multiobjective linear programming are briefly reviewed. A brief discussion of genetic algorithms is also given.