Nonlinear Programming Model Integrating Different Preference Structures

In this correspondence paper, we consider a large group decision-making problem in which the decision makers provide their preferences over a number of alternatives using distinct preference structures, including the following: 1) utility values; 2) preference orderings; 3) multiplicative preference relations; 4) incomplete multiplicative preference relations; 5) fuzzy preference relations; and 6) incomplete fuzzy preference relations. We establish a nonlinear programming model to integrate all of these preference structures and then employ a genetic algorithm to find the solution to the problem. This model can be reduced to a variety of special models suitable for group decision-making situations in which the preferences are represented in one (or several) of the aforementioned preference structures. Finally, detailed numerical analysis is provided to verify the feasibility and effectiveness of the model.