A Two-Stage Multi-objective Programming Model to Improve the Reliability of Solution

Randomness is a common uncertainty encountered in practical multi-objectives decision-making. But it is always a challenge for decision-makers to process randomness in multi-objective programming problems. This paper takes the decision-making objectives as fuzzy events and aims to solve numerical multi-objective programming problems under random environment. We first analyze the effects of randomness on multi-objective decision-making results. With the expectation value and the probability of fuzzy events as quantitative index of randomness, we then establish a two-stage random multi-objective programming model based on reliability (i.e., TS-MOPM). Specifically, we give several probability calculation methods of fuzzy events with common distributions, and further present the corresponding calculation procedures for solving TS-MOPM. Finally, a case study is implemented to test the proposed model TS-MOPM. Theoretical analysis and case study indicate that our model has better interpretability and operability. The research results enrich the existing random multi-objective programming methods to some extent.