Multi-objective optimization with a max-t-norm fuzzy relational equation constraint

In this project, we consider minimizing multiple linear objective functions under a max-t-norm fuzzy relational equation constraint. Since the feasible domain of a max-Archimedean t-norm relational equation constraint is generally nonconvex, traditionally mathematical programming techiniques may have difficulty in yielding efficient solutions for such problems. In this paper, we apply the two-phase approach, which utilizing the min operator and the average operator to aggregate those objectives, to yield an efficent solution. A numerical example is provided to illustrate the procedure.