On a Simple and Efficient Approach to Probability Distribution Function Aggregation

In group decision making, it is inevitable that the individual decision maker's subjectivity is involved, which causes difficulty in reaching a group decision. One of the difficulties is to aggregate a small set of expert opinions with the individual subjectivity or uncertainty modeled with probability theory. This difficult problem is called probability distribution function aggregation (DFA). This paper presents a simple and efficient approach to the DFA problem. The main idea of the proposed approach is that the DFA problem is modeled as a nonlinear function of a set of probability distribution functions, and then a linear feedback iteration scheme is proposed to solve the nonlinear function, leading to a group judgment or decision. Illustration of this new approach is given by a well-known DFA example which was solved with the Delphi method. The DFA problem is a part of the group decision problem. Therefore, the proposed algorithm is also useful to the decision making problem in general. Another contribution of the this paper is the proposed notation of systematically representing the imprecise group decision problem with the classification of imprecise information into three classes, namely incomplete information, vague information, and uncertain information. The particular DFA problem dealt with in this paper is then characterized with this general notation.