A Study On Theory And Application Of Multiple Attributes Decision Making With Interaction

Multi-attribute decision making (MADM) has always been a hot spot in research areas due to its wide application in practice fields of engineering, economics and management, where many problems can be modeled by MADM. However, application achievements in MADM are not as abundant as theoretical achievements in this area. In order to strengthen the combination of theory and application of MADM, MADM with interaction has recently turned out to be a forward position technology in decision-making field.There are still many problems in the area of MADM with interaction needed to be studied and solved in the future, such as the definition of the correlation of alternatives, the MADM problems with variable weights when the criteria are interaction, and the hierarchical MADM problems under the poor-information situation when the attributes are interaction. Therefore, the purpose of this paper is to do a deep research on all of these three questions. The detailed arrangement of this paper stands out as follows:(1) Study on the interaction among alternatives in MADM. First of all, the interaction among alternatives is defined, and then correlation among the alternatives'interaction, independence of irrelevant alternatives and reversal ranking are analyzed. Second, through case study and theory deduction, alternatives'interaction in linear allocation method, weighted average method and TOPSIS method are studied, based on which two ranking preservation methods for WA (Weighted Average) are proposed. Finally we can draw the conclusion that alternatives'interaction can also be introduced into absolute TOPSIS while the decision-making results from the pairwise comparison of TOPSIS may not satisfy the rule of transitivity.(2) Study on the MADM theory with attributes'interaction. Considering the wide application ofλfuzzy measure in decision-making problem,λfuzzy measure and its two transforming forms-M?bius transformation and interaction coefficients-are deduced based on the existing references. Taking the shortcoming of the constant weights into consideration, the definitions and properties of the variable weights with interaction (R-variable weights) and local state variable weight vector with interaction (R-local state variable weight) are analyzed based on fuzzy measure theory and traditional variable-weight theory. The research results demonstrate the fact that the R-variable weight (or R-local state variable weight) is the general form of the variable weight (or local state variable weight). (3) Study on the MADM method with attributes'interaction. The new methods called linear allocation method with interaction, weighted average method with interaction, TOPSIS method with interaction, ELECTRE method with interaction and ordered Sugeno method are proposed in the light of fuzzy measures and integrals. Then the properties and application steps of these methods are also discussed, and their validity is tested with examples. After that, MADM method with variable weights when attributes are interaction is discussed based on the R-variable weights theory. Finally, corresponding model is established to compute the weights of attributes and their coalitions, and one example is used to illustrate the validity of the model as well as the method.(4) Study on the hierarchical MADM method with attributes'interaction. Firstly, a new method to divide hierarchical structures for complex systems is put forward based on the integration of DEMATEL and ISM, and then the hierarchical MADM model is analyzed. Since it is often difficult for decision makers and experts to provide enough preference information for reference attributes and alternatives, under the poor-information situation the method of solving the hierarchical MADM problem with constant weights and variable weights are analyzed respectively when attributes are interactive. The fact that the hierarchical MADM method with constant weights and variable weights when attributes are interaction are the general form of hierarchical MADM method with constant weights and variable weights when attributes are independent is concluded.(5) Study on application of the MADM theory with attributes'interaction to trans-regional investment of coal enterprise. Firstly, setting in the background of trans-regional investment of coal enterprise, it studies determinants of period choice, and with variable-weights MADM method with interaction, the period choice for the trans-regional investment of coal enterprise is discussed. Then the determinants of location choice are researched, based on which, the location choice for the trans-regional investment of coal enterprise is solved by hierarchical MADM theory with interaction.