Study on fuzzy optimization methods based on quasi-linear fuzzy number and genetic algorithm

Fuzzy optimization is a well-known optimization problem in artificial intelligence, system control, manufacturing and management, establishing general and operable fuzzy optimization methods are important in both theory and application. In this paper, starting from the structure of fuzzy information and the mechanism of fuzzy optimization, we propose the concept of quasi-linear fuzzy number, and discuss its approximation properties and the features on arithmetic operations. Further, by distinguishing principal indices and secondary indices, we establish the fuzzy optimization model based on synthesizing effect by combining the compound quantification strategy of fuzzy information, and give a fuzzy optimization method based on principal operations and genetic algorithm (FOM-BPO⊞GA). Finally, we consider the convergence of our algorithm using the theory of Markov chains and analyze its performance through two concrete examples. All these indicate that FOM-BPO⊞GA can effectively merge decision preferences into the optimization process and it also possess better global convergence, so it can be applied to many fuzzy optimization problems.