Fuzzy dynamic programming problem for single additive constraint with multiplicatively separable return in terms of trapezoidal membership functions

摘要

Dynamic programming problems (DP) are multivariable optimization problems that can be decomposed into a series ofstages, and optimization is done at each stage with respect to one variable only. DP allows a suitable quantitative study procedurethat can be used to assess various optimization problems. The technique offers an efficient procedure for finding optimaldecisions. Here, we address a Fuzzy Dynamic Programming Problem with a single additive constraint and multiplicativelyseparable return, with the support of trapezoidal membership functions and related arithmetic operations. The procedure has beenadapted from Fuzzy Dynamic Programming Problem (FDPP). The fuzzified version of the problem is stated and illustrated with anumerical example, and it is shown that the proposed procedure is more efficient in handling the dynamic programming problemthan alternative classical procedures. As a final point, the optimal solution is provided in the form of fuzzy numbers withtrapezoidal fuzzy membership functions, and also the solution is compared with existing methodology in a numerical example.