Adaptive fuzzy dynamic programming (AFDP) technique for linear programming problems lps with fuzzy constraints

An adaptive fuzzy dynamic programming technique is proposed to solve linear programming problems having fuzzy constraints. Both the left hand sides and the right hand sides of the constraints are fuzzy. Dynamic programming technique ensures the existence of the solution for the Fuzzy Linear Programming FLP problems. Initially, a solution technique is proposed for linear programming problems with both left and right hand sides fuzzy. The dynamic programming technique for the LP's is then revised to address linear programming problems in which the constraints are fuzzy. The proposed adaptive fuzzy dynamic approach is then implemented on a numerical example. The results obtained showed that the proposed method better optimized the fuzzy linear programming problem. It is shown that the objective function of our fuzzy linear programming improves from 19.5 to 38 by a value of 18.5. Thus a 94.8% improvement is recorded. Thus the proposed technique better optimize the FLP. The proposed approach incorporates fuzzy type uncertainty in modeling the LP problem. It is more practicable, robust and flexible.

Automated summary

An adaptive fuzzy dynamic programming technique is proposed to solve linear programming problems with fuzzy constraints. The technique can handle the case where both the left and right hand sides of the constraints are fuzzy. It ensures the existence of a feasible solution for fuzzy linear programming problems.