Research on Fuzzy Multi-objective Programming based on Effect Probability

Crisp multi-objective programming has been applied successfully in many fields. But in real applications, the decision environment often exists randomness and the objectives are fuzzy. So it is significant and valuable to establish a fuzzy multi-objective programming model under random environment. In this paper, we use fuzzy number to represent the fuzzy events and fuzzy objectives. Firstly, the general formula of effect probability based on continuous distributions is given combined with effect theory, and a special one based on normal distribution is further given. Secondly, an effect probability-based fuzzy multi-objective programming (abbreviated as FMO-EP) model is proposed by regarding fuzzy objectives as fuzzy events. Finally, the effectiveness and interpretability of FMO-EP is proved through a case.