A method to fuzzy multi-objective problems under random environment

Randomness and fuzziness are two common uncertainties in decision process, and they always coexist in many real multi-objective problems such as resources allocation, complex system optimization. So it is a widespread research content on the process problem of the two uncertainties in academic and application fields. In this paper, aimed at the multi-objective programming with fuzzy goals and random coefficients, we first propose the level effect function and construct the effect probability of fuzzy events by regarding the fuzzy goals as the fuzzy events. Then we discuss the probability of fuzzy number and the probability formulas of several special fuzzy events are further given. Besides, we establish the multi-objective programming maximum effect probability model (abbreviated as MOP-MEP model). Finally, we illustrate the validity of MOP-MEP model in combination with a case.