Fuzzy interactive decision making for multiobjective 2-level nonlinear programming problems

Focuses on large-scale multiobjective two-level nonlinear programming problems (LSMO2-NLPs) with block angular structures, where the leader and the follower work together to seek their interests. In order to cope with such problems with the leader and the follower, instead of the well-known concept of the Pareto-optimal solution for the usual multiobjective programming problems, a new solution concept called a two-level type M-Pareto optimal (2-MPO) solution is introduced. An interactive algorithm to obtain a satisfying solution from the 2-MPO solution set is proposed, where the leader updates the minimal acceptable levels for his/her membership functions and the follower updates the reference membership values for his/her membership functions. In the proposed algorithm, 2-MPO solutions are obtained efficiently by applying the dual decomposition method to deal with LSMO2-NLPs with block angular structure.