Researches On Uncertain Multi-Attribute Decision Making Based On Evidential Reasoning

Most decision problems in the real-word are multi-attribute decision making (MADM) which is an important branch of artificial intelligence. The complexity and uncertainty of real-life and vagueness of human judgement have arisen great interest in the development of scientific and objective methods for uncertain MADM (UMADM). Currently, although much effort has been made in the field, the results are far fewer than those on UMADM. So it is necessary and significant to further researches on theories and applications for UMADM. In this dissertation, by using the advanced evidential resoning (ER) approach which has perfect performance in solving the uncertainty, rule theory, fuzzy sets, intuitionistic fuzzy sets and muti-attribute utility theory, we study the problems of UMADM, in which we solve the expression and aggregation of evidences with incompele and imprecise information taking forms of mumbers, interval numbers linguistic variable, intuitionistic fuzzy and interval-valued intuitionistic fuzzy numbers and finish the ranking and decision of schemes. The main contributions are as follows:1. The D-S evidence method would involved invalid results in dealing with high conflict information. Considering this problem and combination efficiently the evidences with different importance and credibility, a new weighted average method based on overall weight discounted of evidences is proposed. First, according to the importance or credibility and the associated characteristic between evidences, the overall weight is acquired by aggregating linearly the static weight and dynamic weight of each evidence.Then, an evidential reasoning model with discounting trust is built, where the overall weight plays the role as a discounting factor. Finally, the modified evidences are combined together by the weighted average method proposed. Two kinds of pignistic transformation schemes are given to get approximate probability function in the decision making approach based on belief measure. A numerical example shows the effectiveness of the new combination method in the integration of those evidences which are in sharp conflict with each other.2. A hierarchical evaluation framework and ER approach for hybrid UMADM problem involving multiple schemes of both quatitative and qualitative attributes with imprecise and incomplete information is presented.Based on equivalent rule techniques and muti-attribute utility theory (MAUT), the quatitative datas with precise numbers or interval numbers and qualitative attirbutes can be transformed to construct the basic probabity assignments (bpa) in order that various types of information can be assessed in a unified manner using belief distribution assessment matrixes. The synthetic assessment is realized using the evidential reasoning(ER),or the weighted sum method and the new weighted averaging method based on overall weight discounting of evidence. Based on the expected utility value intervals and an approximate single-valued expected utility function via the pignistic transformation, the ranking order is determined. An investment assessment and a supplier evaluation and selection problem show the effectiveness of the proposed synthetical assessment and decision making.3. Group linguistic MADM in uncertain environment using ER approach is studied, while the pure and mix linguistic MADM are also concerned. Particularly, the group pure or mix linguistic MADM based the weighted sum method approach by two transforming methods in the forms of triangular fuzzy number and the direct grade assesement is presented, in which the former is that transforms linguistic variable to triangular fuzzy numbers under the different scales of language, then transforms it to a precise number by COWA operations, and constructs the original belief degrees. At last, the alternatives are ranged using the the weighted sum method, MAUT and a priority ordered approach. The latter is that the linguistic values are directly assessed to one or two continuous overall linguistic assessment grades or not be given by the decision makers, the original belief degrees can be constructed and evaluated by the weighted sum method approach. Finally, ranging is ended by MAUT. Numerical example is provided to illustrate that the proposed method is rational and efficient for group linguistic MADM.4. The methods for dealing with GMADM problems, the decision attribute values with intuitionistic fuzzy and interval intuitionistic fuzzy multiple attributes group decision making based on the the weighted sum method are studied. In the former, the decision attribute values with intuitionistic fuzzy information evaluated to the two or more than two evaluation grades for GMADM problems are synthesized based the weighted sum method and made a decision.Then, the decision making method using the the weighted sum method involving the interval intuitionistic fuzzy information for GMADM problems is presented. These methods provide a new idea in using the intuitionistic fuzzy set or interval intuitionistic fuzzy set in solving the problems of GMADM based on the evidence theory, and broaden the using scope of the fuzzy MADM. The examples show that the feasibility and availability of these methods.