Solving linear optimization problem with fuzzy relational equations as constraints

Implementation of fuzzy relation equations (FREs) as constraints in a linear optimization model for decision making problems is the central concept of the present paper. Due to non-convex nature of the solution set of FREs, it (the solution set) is characterized as lattice and a feasible domain of the optimization model has been obtained. The objective function of linear model has been characterized over the feasible domain. An algorithm to compute all the minimal solutions is obtained. A basic algorithm is also presented to find optimal solution of the problem and has been illustrated through a constructed example.