Fundamentals of Fuzzy Optimization and Decision-Making Problems

The fundamental issues of classical optimization and fuzzy optimization are discussed. There is clarity about the feasible and optimal solutions for classical optimization problems, but the conventional concepts are not valid for fuzzy optimization, and hence new definitions are proposed. The single-objective and multi-objective optimization problems for classical and fuzzy environments are discussed. Some modern optimization techniques, viz., genetic algorithms, particle swarm optimization, neural network, etc., are applied to solve such problems. Many parameters are associated with optimization problems and may contain multiple-objective functions; some are conflicting. For such problems, Pareto’s optimal solution is determined. Sometimes, it is necessary to find the combined effect of the parameters in the solution. To combine the parameters, there is a need for an aggregation process. Recently, many excellent aggregation methods have been available in the literature. Apart from the aggregation process, the t-norms and t-conorms-based operators are used to solve decision-making problems. Some of these operators are studied.