Linear fractional programming problem with max-Hamacher FRI - Aliannezhadi, Samaneh; Molai, Ali Abbasi (Iranian journal of science (Online), 2018)
In this paper, the linear fractional programming problem subject to a system of fuzzy relation inequalities (FRI) with the max-Hamacher composition operator is studied. First, the structure of its feasible domain is investigated, and its feasible solution set determined. Then, some sufficient conditions are given that under them, some of the optimal components of the problem are directly determined. The optimal solution of the linear fractional programming problem might not be any of the minimal solutions. However, in the process of obtaining the optimal solution, we need to compute the minimal solutions. Therefore, some reductions are presented that under them, we can compute the minimal solutions fast. The original problem can be transformed into some traditional linear fractional programming subproblems and eventually optimized in a small search space. Finally, an algorithm is designed to solve the problem based on the above reductions. An application and some numerical examples are provided to illustrate the procedure.