Study on fuzzy optimization methods based on principal operation and inequity degree

Fuzzy optimization is a well-known optimization problem in artificial intelligence, manufacturing and management, so establishing general and operable fuzzy optimization methods are important in both theory and application. In this paper, by distinguishing principal indices and secondary indices, we give a method for comparing fuzzy information based on synthesizing effect and an operation for achieving fuzzy optimization based on a principal indices transformation. Further, we propose an axiomatic system for fuzzy inequity degree based on the essence of constraint, and give an instructive metric method for fuzzy inequity degree. Then, by combining with genetic algorithm, we give some fuzzy optimization methods based on principal operation and inequity degree (denoted by BPO&ID-FGA, for short). 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 BPO&ID-FGA can effectively merge decision preferences into the optimization process and that it also possesses better global convergence, so it can be applied to many fuzzy optimization problems.