Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment,and their comparison or ranking is very important for application purposes. Despite many methods suggested in theliterature, there is no single measure that is universally applicable to a wide variety of situations. This paper sug-gested a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimiz-ing possibility using an index of optimism in [0,1] reflecting the decision makers’ risk taking attitude. The methodis simple, but has many comparative advantages.