Research On Some Problems In The Multiple Attribute Decision Making Based On Evidential Reasoning Approach

The evidential reasoning (ER) approach is an effective approach in dealing with Multiple Attribute Decsion Making (MADM) problem. It is especially suitable and valid to tackle with MADM problems in situation that the decision environment is subjective uncertain and quantitative & qualitative attributes coexist. The ER approach for solving MADM problems has been extended in situation of uncertainties, but most of the extentions are on interval frame of dircernment, interval belief degrees and interval weights. The type of attributes are also limited to profit attributes and cost attributes. The ER approach in dealing with MADM problems under fuzzy environment and attributes of other types have not been studied yet. Fuzzy information may be involved in real assessment problems, and interval number could not reflect these decision circumstances effectively. Moreover, attributes of other types except profit and cost attributes are always involved in the decision making process.In this paper, the ER approach under uncertainties to deal with MADM problems are firstly reviewed, based on which some problems to be solved are pointed out and studied. Some innovative results are also obtained. The ER based MADM problems under fuzzy information are studied, and triangular fuzzy weights are introduced to the ER based MADM problems, the combination of fuzzy judgment information of experts under group decision circumstances are analysed. The utility expressions of frame of discernment are extended from accurate value to interval value, and the ER baased MADM approach under interval utility expressions is studied. Deviating attribute, deviating interval attribute, fixation attribute and interval attribute are introduced to the ER baased MADM approach, the presentation and transformation rules of these 4 types of attributes are analysed. The main contents of the paper are shown as follows:(1) The weights in the ER approach is extended to triangular fuzzy numbers, thus the group decision making problem which is more general in real world could be solved by the ER approach. At first, the triangular fuzzy judgment matrix can be contructed based on the comparison of every two attributes by each expert; The fuzzy analytic hierarchy process (FAHP) is then used to compute the triangular fuzzy weights of attributes given by each expert; The weighted arithemetic mean method (WAMM) is used to combine the weights of attributes assigned by all experts, and the combined triangular fuzzy weights can be obtained. It reflects the perspective on the weights of attributes by all experts and avoids the decision error by only one single expert that may be resulted by his/her uncertain or incorrect judgment. We called our weight assignment approach in the circumstance of group decision making as group fuzzy analytic hierarchy process (GFAHP) .(2) a cut is used to transform the combined triangular fuzzy weights generated by group of experts to interval weights, it combines fuzzy information and evidence effectively. Nonlinear programming models of ER approach are constructed, where the overall belief degrees of each evaluation grade and uncertainty on assessed alternative is considered to be objective functions, interval weights calculated by a cut on the combined triangular fuzzy weights is assumed to be constraints. The overall belief degrees interval of the assessed alternative on each evaluation grade could then be computed by calculating the model. Sensitivity analysis is also done to discuss the impact of different a cut to the weight intervals, thereby the impact to the assessment of alternatives is analyzed.(3) The utilities of evaluation grades in the frame of discernment are extended from accurate values to interval values, thus the group decision making problem in real complex environment can be tackled more effectively and reasonably. We construct nonlinear programming models to calculate the overall utility of the assessed alternative, where the utility of assessed alternative is considered to be the objective function, the interval utility of each evaluation grade and the interval weights cut by a value on the combined triangular fuzzy weights are assumed to be constraits. Sensitivity analysis is conducted to analyze the impact of different a value to the interval weights, thereby the impact to the overall utility of alternative is done; The impact on the overall utility of alternative is also conducted on utility intervals of evaluation grades.(4) Deviating attribute, deviating interval attribute, fixation attribute and interval attribute are introduced to the ER approach, thus the applications of the ER approach are expended, and the effectiveness of dealing with real problems is also inhanced. The evidence representation is analyzed based on these four kinds of attributes, and the transformation rules from the values of these four kinds of attributes to belief degrees on the general frame of discernment is discussed. We also get the evidence combination rules based upon these four kinds of attributes together with profit attributes and cost attributes to tackle the complex MADM problem.(5) The ER approach under uncertain decision making circumstance is applied to R&D production assessment in a large enterprise, and the effectiveness and reliability of the proposed approaches are checked. The assessment attribute system which is comprised of both quantitative and qualitative attributes is constructed, and the frame of dircernemnt associated with each attribute is also constructed. The overall belief degrees and utilities of the assessed R&D productions are computed by both the accurate weights calculated under GAHP and combined triangular fuzzy weights calculated under GFAHP. Sensitivity analysis is also conducted to interval utilities of evaluation grades and interval weights under a cut.