Monotonic natural language is widely used to express experts' subjective appraisal opinions, such as "not less than," "at least," "not more than," and "at most," which covey the information of expert hidden psychological preference. A novel quantitative computational method based on the grey exponential cloud model is proposed, transforming the expert's uncertainty appraisal information into decision data by systematically mining the experts' hesitant fuzzy preference on specific linguistic options. The comprehensive meaning of monotonic hesitant fuzzy linguistic terms is introduced, and the interval grey number is used to represent the expert's grey preference and indicator weight. Additionally, a programming model is constructed by the exponential cloud model and ABC classification analysis method, which can obtain the order of alternatives related to the optimal solution. Finally, a numerical study is conducted to show the advantages and effectiveness of the new method against other comparable methods is demonstrated.