It has been found that hesitant fuzzy information and probabilistic hesitant fuzzy information have some problems with calculating, such as cumbersome calculations and incompatibility with quantitative calculation rules. In this work, we propose a set of solutions, based on the reconciled hesitant fuzzy elements(RHFEs), to solve these problems. By defining the RHFEs as a set of probabilistic hesitant fuzzy elements (PHFEs) with the same probability distribution, this work bridges the gap between hesitant fuzzy information and probabilistic hesitant fuzzy information, and incorporates them into a unified processing framework. Based on this, we build a reconciled hesitant fuzzy multi-attribute decision-making(MADM) method, by developing the operation rules, the information aggregation operators, the distance measures and the hybrid entropy measure for RHFEs, and further apply it to evaluate the command and control(C2) capability of the army's combined brigades. Numerical experiments show that the theory of reconciled hesitant fuzzy decision-making overcomes the shortcomings of existing theories, and has some advantages of controllable calculations, easy to program and compatible with quantitative calculation rules.