Deviation Square Priority Method for Distinct Preference Structures Based on Generalized Multiplicative Consistency

Preference structures, such as fuzzy preference relations, incomplete fuzzy preference relations, utility values, and preference orderings, are very useful in depicting the decision makers' preferences over the considered objects in group decision making. They have been attracting great interest from both researchers and practitioners in recent decades. An important issue on these preference structures is to investigate the techniques of deriving priority weights of the objects from them. In this paper, based on generalized multiplicative consistency, we establish a general nonlinear optimization model with fuzzy preference relations, incomplete fuzzy preference relations, utility values, and preference orderings. By solving the model, we get a system of nonlinear equations and prove the uniqueness of its solution. Then, a convergent iterative algorithm is devised to derive the priority weights from this system of equations. The model and the algorithm include a variety of special cases suitable for group decision making with one or several of the aforementioned preference structures. A practical case illustration concerning a manufacturing company that is searching for the best compression ignition engine design is provided, and the numerical results of the developed models and the algorithm and the existing ones are also compared and analyzed in order to demonstrate the advantages and practicality of our models and algorithm.