On Solving Linguistic Bi-Level Programming Problem Using Dynamic Programming - Singh, Vishnu Pratap (International journal of fuzzy system applications, 2021)
In this work, a linguistic bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of the leader and the follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation most of the time, it is inconvenient to find the veracious relationship between the objective functions of leader, follower, and the decision variables. It is expected that the source of information which gives some command about the objective functions of leader and follower is composed by a block of fuzzy if-then rules. In order to analyze the model, a dynamic programming approach with a suitable fuzzy reasoning scheme is applied to calculate the deterministic functional relationship linking the decision variables and the objective functions of the leader as well as the follower. Thus, a bi-level programming problem is constructed from the actual fuzzy rule-based to the conventional bi-level programming problem. A numerical example has been solved to signify the computational procedure.