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

Abstract

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

Keywords

• trapezoidal fuzzy numbers
• fuzzy dynamic programming problem
• fuzzy additive constraint
• fuzzy multiplicatively separable return