Intuitionistic Fuzzy Bilevel Programming by Particle Swarm Optimization

Bilevel programming problem (BLPP) is widely used in the control and management area. While solving the BLPP, global optimization and fast solving speed are very critical. As intuitionistic fuzzy is the most important extension of basic fuzzy theory. This paper firstly converts the basic BLPP problem into its intuitionistic fuzzy form, which is intuitionistic fuzzy bilevel programming (IFBLP). The membership and non-membership function could drive the IFBLP to the global optimum result. An interactive computational method is proposed for obtaining the global optimal solution of IFBLP. The method adopts the improved PSO algorithm, by imposing a mechanism to improve the diversity and expand the search space of the particle, makes the PSO algorithm more easily to get to the global solution of the problem. The proposed method can solve both the linear and non-linear and integer BLPP. The solving procedure of the proposed problem is given. To demonstrate the efficiency of the proposed computational method, benchmark computational experiments are carried out.