Study On Theories And Methods Of The Group Preference Aggregation Based On The Judgment Matrices

Group preference aggregation plays an important role in the process of group decision making and is more and more attached the great importance in terms of theories, methods and applications of group decision making. Group decision making is a comprehensive interdisciplinary involved in multiple disciplines, such as social psychology, operational research, management science, decision science and computer communication theory, etc. In recent years, research works in the field of group decision making are mainly concentrated in two aspects: multi-criteria methods for group decision making and aggregation of the preference informations provided by decision making experts. Judgment matrix is the major form expressing preference informations provided by the experts for the decision making problem and the important basis of aggregating the preference informations. Therefore, this paper mainly studies the decision theories and methods about the group preference aggregation based on the individual judgment matrices.With the development of society and the progress of science and technology, there are more and more complicated decision making problems. Most complicated decision problems involve these factors such as the fuzziness of decision expert knowledge, incomplete decision informations, multiple decision objectives, dynamic decision making time, uncertain decision making environment and nonexperimental decision programs etc. Thus it is often difficult to decision experts reach an agreement. It appears that decision expert evaluation conclusions are opposite. As a result, the process and efficiency of group decision making are badly affected, suffer from failure or mistakes for decision making. Group preference aggregation based on the individual judgment matrices still exists the following problems: the individual judgment matrix usually do not have the perfect consistency or satisfactory consistency, the existing standards and methods of consistency test for judgment matrix have some defects and controversies; If an individual judgment matrix has no satisfactory consistency, then it must be improved until it has satisfactory consistency, existing methods for improving the consistency of the judgment matrix focus on the mathematical consistency and lose sight of the validity of the improved judgment matrix; If an individual judgment matrix has no the perfect consistency, different priority vector methods result in different decision outcomes, at the same time there is no relatively optimal priority vector method, it is controversial and confused to choose which priority vector method; Existing group preference aggregation methods based on the individual judgment matrices still have some defects and controversies, such as group consensus, pareto optimality, bounded rationality, etc. This paper has further researched these problems, the main research contents are as follows:(1) Researching on the judgment matrix consistency testing problems. First, this paper briefly overviews the related concepts, the natures and the theorems on the judgement matrix and consistency, introduces a variety of commonly used definitions and expressions of the consistency indices, and analysises the problems existing in the Saaty test standard(CR ?0.1). Then, on the base of the Saaty test standard(CR ?0.1) as the research basis, based on the statistical theories and methods, such as hypothesis testing, maximum likelihood estimation and mathematical expectation etc, this paper proposes two kinds of statistics methods for testing the consistency of the judgment matrix and revises the fixed threshold(0.1) of the consistency ratio of judgment matrix, which improves the flexibility and practicability of the judgment matrix consistency test.(2) Researching on the judgment matrix consistency improving problems. First, this paper briefly reviews theories and methods for improving the judgment matrix consistency, points out the problems in the existing methods for improving the judgment matrix consistency, puts forward the research direction on the judgment matrix consistency improvement. Then, regarding all elements in the judgment matrix as random variables with logarithmic normal distribution, this paper proposes a Bayesian revision method for improving the judgment matrix consistency based on bayesian statistical theories and methods, and puts forward the algorithms and steps for solving the Bayesian resivion matrix, which improves the simplicity and operability of Bayesian revision method for improving the judgment matrix consistency.(3) Researching on the methods for solving the prority vector based on the judgment matrix. First, this paper briefly overviews the theoretical basis of the prority vector methods and definitions, models and expressions of the existing prority vector methods and introduces the theoretical basis of eigenvector method(EM). By the compare, analysis and summary on several prority vector methods in the existing literature, this paper points out advantages and disadvantages of the existing prority vector methods. Then, through mathematical derivation and proof, this paper puts forward three kinds of prority vector methods: nearest consistency matrix method(NCMM), maximum similarity matrix method(MSMM) and Bayesian revision matrix method(BRMM), and provides the implementation procedures of three kinds of prority vector methods. In addition, based on the cosine similarity theory, the cosine consistency index(CCI) of the judgement matrix is derived.(4) Researching on the methods for the group preference aggregation based on the individual judgment matrices. First, this paper briefly introduces the theory foundation of the group preference aggregation and basic aggregation methods, analyzes on the advantages and existing problems of the basic aggregation methods: AIJ and AIP, and puts forward the improvement direction and following principles on AIJ and AIJ. Then, based on the aggregation methods: AIJ and AIP, through the mathematical derivation and proof, this paper puts forward three kinds of methods for the group preference aggregation: aggregation of the individual consistency matrices(AINCM), aggregation of the individual maximum similarity matrices(AIMSM) and aggregation of the individual Bayesian revision matrix(AIBRM), and provides the implementation procedures of three kinds of methods for group preference aggregation.Group preference aggregation is important research content and decision method in the field of group decision making. Judgment matrix is on the basis of the group preference aggregation. Therefore, theories and methods for group preference aggregation based on the individual judgment matrices are worth further researching, which not only to provide the technical support for the group decision support system, but also enrich the group decision theory and method. In addition to the above research contents and results, this paper also points out some frontier problems and research direction in the field of the group preference aggregation.