Fuzzy Genetic Algorithms with Fuzzy Solutions

Many decisions need to be made based on imprecise or incomplete initial information. In such cases, decision makers are generally more interested in some sets of the most promising solutions rather than the best single solution. Therefore, in contrast to conventional optimisation approaches that aim to find exact optimal points, we aim to find optimal ranges with variable satisfaction degrees. This paper presents a fuzzy-set-based approach for representation and optimisation of practical problems with imprecise properties where evolutionary computation is used to obtain fuzzy solutions through guided searching. The representation of fuzzy sets, their initialisation, crossover, mutation, and validation, the ranking approach for fuzzy objective values, and the propagation method of fuzzy information are discussed. Several examples for illustrating the fuzzy evolutionary optimisation approach are provided.