In recent years, wind power has played a significant role in energy generation of micro-grids (MGs). However, randomness nature of wind speed leading to uncertainty in wind power forecast, imposes some problems such as overestimating wind power on optimized scheduling of MG. In this paper, we propose an adaptive probabilistic concept of confidence interval (APCCI) to address these problems. The main purpose of the proposed APCCI is to modify the risk we endure to schedule wind power with other distributed energy resources (DERs) in order to degrade the unnecessary rigors and upgrade the other ones. The forecasting method which is used in this paper is artificial neural network (ANN). In order to increase the accuracy of forecasting, wavelet decomposition (WD) is applied to the wind power time series then the results are sent to ANN. After that, dependable levels for the predicted wind power based on APCCI are obtained. An energy storage system (ESS) is utilized not only to decrease the impact of forecasting errors on the MG but also to increase the flexibility of the planning. A comprehensive formulation with operational constraints is employed to model the optimization problem. An economic dispatch based non-dominated sorting genetic algorithm II (EDNSGA-II) is proposed and applied to solve the multi-objective optimization problem. The optimization algorithm produces some alternatives which consist of different combination of objectives (cost and emission). Techniques for order preference by similarity to an ideal solution (TOPSIS) method is utilized to make a compromised decision between the alternatives. Eventually, the proposed algorithm is applied to a typical MG which consists of micro turbine (MT), fuel cell (FC), photo voltaic (PV), wind turbine (WT) and energy storage system (ESS). Evaluation of the results show that the proposed APCCI works well and can adapt the level of confidence interval in various situations. Moreover, the results confirm the superiority of WNN over ANN. The results also show that the proposed EDNSGA-II is more efficient in comparison with the well-known NSGA-II. (C) 2017 Elsevier Ltd. All rights reserved.