Optimal solution of multi-objective linear programming with inf-→→ fuzzy relation equations constraint

This paper aims to solve the problem of multiple-objective linear optimization model subject to a system of inf-→→ composition fuzzy relation equations, where →→ is R-, S- or QL-implications generated by continuous Archimedean t-norm (s  -norm). Since the feasible domain of inf-→→ relation equations constraint is nonconvex, these traditional mathematical programming techniques may have difficulty in computing efficient solutions for this problem. Therefore, we firstly investigate the solution sets of a system of inf-→→ composition fuzzy relation equations in order to characterize the feasible domain of this problem. And then employing the smallest solution of constraint equation, we yield the optimal values of linear objective functions subject to a system of inf-→→ composition fuzzy relation equations. Secondly, the two-phase approach is applied to generate an efficient solution for the problem of multiple-objective linear optimization model subject to a system of inf-→→ composition fuzzy relation equations. Finally, a procedure is represented to compute the optimal solution of multiple-objective linear programming with inf-→→ composition fuzzy relation equations constraint. In addition, three numerical examples are provided to illustrate the proposed procedure.