Fuzzy chance-constrained geometric programming: the possibility, necessity and credibility approaches

Geometric programming (GP) is a powerful tool for solving a variety of optimization problems. Most GP problems involve precise parameters. However, the observed values of the parameters in real-life GP problems are often imprecise or vague and, consequently, the optimization process and the related decisions take place in the face of uncertainty. The uncertainty associated with the coefficients of GP problems can be formalized using fuzzy variables. In this paper, we propose chance-constrained GP to deal with the impreciseness and the ambiguity inherent to real-life GP problems. Given a fuzzy GP model, we formulate three variants of chance-constrained GP based on the possibility, necessity and credibility approaches and show how they can be transformed into equivalent deterministic GP problems to be solved via the duality algorithm. We demonstrate the applicability of the proposed models and the efficacy of the introduced procedures with two numerical examples.