A Study On Multiperson Decision Making With Different Preference Representation Structures And Its Application

According to the number of decision-makers, decision making problems can be divided into individual decision making problems and Group decision making(GDM) problems. Because GDM(or call Multiperson Decision Making, MPDM) can make full use of the wisdom of various experts in different fields, more and more of these questions appear in the political, economic and daily life. The GDM problems attract an increasing number of scholars’ attention, and have become an important branch of modern decision analysis theory. In reality, because of the difference of educational backgrounds, education, and life experiences and other aspects of decision makers, many decision makers in the GDM problem express their opinion in different preference presentation structures. Most traditional researches on GDM problem with different preference presentation structures consider four kinds of preference presentation structures at most, and it is limited to preference presentation structures of numeric type, such as fuzzy preference relations and preference orderings. In reality, many decision makers will use linguistic preference relation to evaluate alternatives. In order to supplement the existing GDM theory, on the basis of previous studies, this paper study the GDM problems with five kinds of preference presentation structures(including preference orderings, utility functions, fuzzy preference relations, multiplicative preference relations and linguistic preference relations). To consider the group consensus and the bounded rationality of the decision makers, we use Minimum Cost Consensus Model(MCCM) and Cumulative Prospect Theory(CPT) to design direct consensus methods for GMD problems with different preference representation structures, and apply it to the asset allocation decision making problems. It further enriches and improves the existing method of GDM, and provides an entry of financial problem to GDM. It also provides investors with an objective and feasible decision-making method to select. This research contents are as follows:Firstly, a direct consensus method based on MCCM for GDM problems with different preference representation structures is built. The traditional MCCM only considers the GDM problem with one alternative, and did not apply to the direct consensus framework of GDM problem. Taking into account its utmost to preserve the original information, we extend it to the GDM problem with multiple alternatives, and apply the extended MCCM to assist the information feedback adjustment of GDM. First, determine the transformation function of different preference representation structures and a standardized method, and define consensus measure. Then according to the suggestion of extended MCCM, adjust the original preference information to improve the consensus level. Finally, a numerical example shows that this method can effectively solve the problem and the convergence is fast.Secondly, a direct consensus method based on CPT for GDM problems with different preference representation structures is built. Regard to that the Prospect Theory is more rational than expected utility theory to reflect decision maker’s opinion under the situation of uncertainty, we use CPT to solve GMD problem. First, we provide the method to determine reference points and gains and losses matrix, and introduce the cumulative prospect value function and the model to get weighted vector. Then define the consensus measure based on prospect value, and further propose the decision making method based on the guidance of CPT. Finally, a numerical example shows that the method works.Finally, the above decision making methods are applied to the asset allocation problems. First, analysis China’s current economic fundamentals based on Merrill Lynch Investment Clock and the performance of the four asset classes, which declares the complexity of current economic activity. As a result, different research team gives different asset allocation alternatives. So we apply the above decision making methods to asset allocation GDM problem. The result shows the final alternatives ranking is the same and accord with development state of current economic and asset classes.In general, based on MCCM and CPT, this paper builds direct consensus methods for GMD problems with different preference representation structures. It not only enriches the modern decision making theory, but also has practical significance for the GDM problem, and provide a empirical analysis for the interaction of GDM and financial investment decision.