RT - Journal Article T1 - Posynomial geometric programming problem subject to max–product fuzzy relation equations JF - khu-mmr YR - 2022 JO - khu-mmr VO - 8 IS - 4 UR - http://mmr.khu.ac.ir/article-1-2917-en.html SP - 120 EP - 136 K1 - Fuzzy relation inequality K1 - Separable programming K1 - Least square technique K1 - Minimal solution K1 - Max-Product composition K1 - Fuzzy optimization. AB - In this article, we study a class of posynomial geometric programming problem (PGPF), with the purpose of minimizing a posynomial subject to fuzzy relational equations with max–product composition. With the help of auxiliary variables, it is converted convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. Some preliminary definitions are introduced. Since the feasible solutions are not convex the basic programming techniques are not applicable. It is shown that an optimal solution consists of a maximum feasible solution and finite number of minimal feasible solutions by an equivalent programming problem. In fact, there are a lot minimal solutions and to obtain all them is tedious steps, boring and time consuming. Furthermore, we propose some rules for full simplifying the problem. Then by using a branch and bound approach and fuzzy relational equations (FRE) path, it is presented an algorithm to achieve an optimal solution to the PGPF. Finally, a numerical experiment is given to illustrate the steps of the algorithm. LA eng UL http://mmr.khu.ac.ir/article-1-2917-en.html M3 ER -