Uncertain chance-constrained programming based on optimistic and pessimistic values: models and solutions

Abstract

To solve the uncertainty in real decisions and overcome the limitations of random programming and fuzzy programming in application, we proposed two novel uncertain chance-constrained programming models based on optimistic and pessimistic value of uncertain variables in this paper. Firstly, the optimistic value and pessimistic value of uncertain variables were introduced as the objective functions and the chance constraints of uncertain programming were defined as constraint functions, then the optimistic value model and pessimistic value model were established. Secondly, two lemmas were proposed and proved to transform the uncertain chance-constrained programming model into an equivalent deterministic programming model. Finally, the feasibility and effectiveness of the proposed models and solutions were verified by a numerical example.