Research And Application Of Evidence Theory In Group Decision-Making

Evidence theory, also called DS Theory, was presented by Dempster and developed by Shafer. DS theory can describe many uncertainties properly. New explanations and definitions of probability are given in evidence theory, and the combination rule of different evidences is also given in it. So it can be used as a group-decision method.All that mentioned above make the DS Theory be studied as a group decision-making method, and many useful conclusions have been presented, but studies should be continued, and this dissertation mainly studies the following aspects:(1)Study on the computational complexity of DS combination formula. In DS theory, mass function is used to describe the preference of single decision-maker, and the DS combination formula is used to combine different decision-maker's single decision. One of the major points of criticism the DS combination rule has to face is the computational complexity. The computational complexity of DS formula is NP-Complete. In this dissertation, approximation algorithms will be presented and the efficiency will be proved. This dissertation presents two new approximation algorithms and a new combination formula. One approximation algorithm is called projection approximation algorithm, the other one is called approximation algorithm based on the transferable degree of focal elements. Efficiency of projection algorithm is proved and the similarity and dissimilarity among the Bayesian approximation algorithm, projection approximation algorithm and approximation algorithm based on the transferable degree of focal elements are analyzed.(2)Study on the consistency analysis of single decision-maker's decision. In most group decision-making methods, consistency analysis should be carried out before the final result is made in order to make the final decision more reasonable and more acceptable. If the decisions given by all decision-makers are satisfied to the condition of the consistency, final decision can be gotten according to the combination rule. The combination rule of evidence theory is DS formula, and this formula can combine any evidences as long as the confliction coefficient is not equal to 1.How to carry out the consistency analysis is studied in this dissertation. This dissertation presents three restriction conditions of a proper definition of similarity between evidence bodies and present a new method to measure the similarity of different evidences. Then a new method to define the consistence of evidences and three methods to adjust the evidences when the consistence is not satisfied are presented.(3) Study on the methods to dispel the absurdities of DS combination rule. The result of each decision-maker is influenced by the decision-maker's knowledge, preference, and judgment ability. Each decision made by the single decision-maker may conflict to others. When the evidences contradict to others, some absurdities might be generated if the DS formula is used to combine the evidences. In order to settle this problem, this dissertation presents several methods to dispel the absurdities. These methods are universal methods to dispel the absurdities. And the presuppositions of all these methods are not to change the DS formula in combining the evidences.(4)Study on the steps of using the group-decision method based on the DS theory in actual decision problems. Detailed steps of using the group-decision method based on the DS theory and the systematical construction are presented. The systematical construction includes all have been studied above. Samples of using the group-decision method based on DS theory in uncertainty decision problems are used to illustrate the steps and the systematical construction in the end.