Geometric Programming Problems with Triangular and Trapezoidal Twofold Uncertainty Distributions

Geometric programming is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a geometric programming problem are deterministic and accurate. However, in the real-world geometric programming problem, the parameters are frequently inaccurate and ambiguous. To tackle the ambiguity, this paper investigates the geometric programming problem in an uncertain environment, with the coefficients as triangular and trapezoidal twofold uncertain variables. In this paper, we introduce uncertain measures in a generalized version and focus on more complicated twofold uncertainties to propose triangular and trapezoidal twofold uncertain variables within the context of uncertainty theory. We develop three reduction methods to convert triangular and trapezoidal twofold uncertain variables into singlefold uncertain variables using optimistic, pessimistic, and expected value criteria. Reduction methods are used to convert the geometric programming problem with twofold uncertainty into the geometric programming problem with singlefold uncertainty. Furthermore, the chance-constrained uncertain-based framework is used to solve the reduced singlefold uncertain geometric programming problem. Finally, a numerical example is provided to demonstrate the effectiveness of the procedures.