Minimizing a linear objective function under a max-t-norm fuzzy relational equation constraint

This paper aims to solve the problem of minimizing a linear objective function subject to a max-T fuzzy relational equation constraint, with T a continuous t-norm. This study makes two contributions. First, two extensions are given based on the results in Fang et al., where the max–min or max–product fuzzy relational equation constraint is considered. Second, a procedure for solving optimization problems with the max–Archimedean t-norm fuzzy relational equation constraint is provided. A numerical example is provided to illustrate the procedure.