Linear programming problem with the bipolar max- Einsteinfuzzy relation equation constraints

The linear programming problem subject to a system ofBipolar Fuzzy Relation Equations (BFREs) using themax-Einstein operator is studied in this paper. Its feasiblesolution set structure is specified using lower and upperbound vector of its feasible domain. It is proved that there isan optimal solution for the problem which its componentsare the corresponding components of either the lower orupper bound vector. Its objective function is equivalentlyrewritten in a specific form. The properties help us todesign a value matrix based on the characteristic matrix. Amatrix-based algorithm is proposed to find the optimalsolution of the problem

کلیدواژه ها:

Fuzzy relation equation ، linear programming ، Max-Einstein ، Branch-and-bound algorithm