Research On Methods Of Multiple Attribute Group Decision Making Based On Interval-valued Intuitionistic Fuzzy Sets

Multiple attribute decision making method is considered to be an important content of operations research, and it is widely used in engineering cases, technical analysis, project evaluation and path planning, and other fields. It often leads to uncertainty of decision making information in a complex real circumstance, due to the changing internal parameters of the research object and external interference by human beings. With further study on fuzzy theory, it shows that interval-valued intuitionistic fuzzy sets(IVIFS) could be used to effectively describe such problems. Therefore, this paper focuses on the following two aspects for the multiple attribute group decision making problems of interval-valued intuitionistic fuzzy sets.In order to solve completely unknown group decision weights and attribute weights, the interval score function and interval accuracy function of interval-valued intuitionistic fuzzy sets are firstly proposed, and the formula of possibility degree is applied to compare the interval score function and interval accuracy function respectively. Furthermore, the complementary judgement matrix of interval score function and interval accuracy function are employed in ranking the attribute value. Secondly, the interval-valued intuitionistic fuzzy entropy is used to obtain the weights of group decision making and attributes, and then all the group decision making matrices are aggregated into a weighted collective decision making matrix with group decision weights by the interval-valued intuitionistic fuzzy hybrid averaging(IVIFHA) operator. Finally, based on grey relational analysis(GRA), the distance between every alternative and the ideal-positive alternative is calculated by the distance formula of interval-valued intuitionistic fuzzy sets, then the interval grey relational coefficient and the interval grey correlation degree with attribute weights of every alternative from the ideal-positive alternative are derived. Hence, the ranking order of all the alternatives is determined. Through theoretical analysis and simulation examples, it verifies that the grey correlation analysis method is more flexible than TOPSIS method on ranking results.In the case of attribute weights with constraints, set pair analysis theory is introduced into the solution of the multiple attribute group decision making problems. Firstly, according to the relationship between interval number and binary connection number, interval Intuitionistic fuzzy number is converted to intuitionistic fuzzy number in the form of binary connection number. Secondly, some aggregation operators in the form of binary connection number are defined based on the operational rules of binary connection number and intuitionistic fuzzy sets, and a collective decision making matrix is aggregated by binary connection number intuitionistic fuzzy hybrid aggregation(BCNIFHA) operator. To calculate attribute weights, the optimization model for the score of alternatives is built based on the score function of binary connection number, then the alternatives are ranked by their scores of attribute weights. Finally, the analysis of uncertainty demonstrates that the ranking of alternatives will be slightly different when the argument i in binary connection number values differently.