Traditionally, the DM process under uncertainty was explored using the DM paradigm to choose one from two or more alternatives, and human’s irrational DM was modeled using a variety of cognitive biases such as certainty effect or common ratio effect. However, until now, no attempt has been made to generalize such a DM process. Moreover, there are many cases where it is difficult to choose one of the two alternatives. When the preference of each alternative is nearly equal, it is difficult to make decision on which alternative to take. This forces us to loose important information that is necessary for investigating more detailed characteristics of DM process. In such a case, it is recommended that the preference for each alternative should be expressed numerically. Such an evaluation of alternatives has not been tried until now. This study attempted to propose a new approach to decision making process to get more into the insight of the DM process.