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

In this paper, 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, traditional mathematical programming techniques may have difficulty in yielding efficient solutions for such problems. In this paper, we apply the two‐phase approach, utilizing the min operator and the average operator to aggregate those objectives, to yield an efficient solution. A numerical example is provided to illustrate the procedure.