To solve the Grey-Stochastic Multi-Criterion Decision-Making (GSMCDM) problems with the criterion weights evaluated interval numbers and the alternatives evaluated Trapezoidal Grey-Stochastic Numbers (TGSN) on the criterion, a new method based on the Trapezoidal Continuous-interval-argument Ordered Weighted Averaging (TC-OWA) operator was designed. In this method, the TGSN was firstly defined to describe the incomplete certain evaluations of the alternatives on the criterion. On the other hand, according to the characteristics of the Basic Unit-interval Monotonic (BUM) function, the C-OWA oper...