Research On Decision-making Methods Based On Interval Intuitionistic Fuzzy Sets And Type-two Intuitionistic Fuzzy Sets

With the development of society,decision-making problem is becoming more and more complex and changeable in real life.In many practical decision-making problems,due to the limitation of the level of knowledge of decision makers,the lack of work experience,and the ambiguity of cognitive thinking,decision makers show certain uncertainty and hesitation in dealing with decision-making problems.The founding of fuzzy set theory provides a powerful mathematical tool for processing fuzzy information and uncertain information.Interval-valued intuitionistic fuzzy sets use interval numbers to describe membership,non-membership and hesitation,which makes interval-valued intuitionistic fuzzy sets more comprehensively and delicately describe the hesitation and uncertainty of decision information.Therefore,it has been widely utilized in decision-making fields such as the evaluation of project risk,the selection of talents,the choice of suppliers and emergency management.In addition,the type-2 intuitionistic fuzzy set has the dual nature of representing the high degree of uncertainty of the system and the hesitation of the decision makers to consider the problem,which can more effectively describe the strong ambiguity of the decision problem.Therefore,it is of high theoretical significance and application value to study the decision-making problem under interval-valued intuitionistic fuzzy environment and type-2 intuitionistic fuzzy environment.Based on the existing research,this thesis investigates decision making methods under interval-valued intuitionistic fuzzy environment and type-2 intuitionistic fuzzy environment.The results obtained are as follows:(1)Multi-attribute group decision-making method based on interval-valued intuitionistic fuzzy sets.Firstly,this thesis proposes a new distance measure formula between interval-valued intuitionistic fuzzy sets,this distance measure formula satisfies the non-negative,symmetry and triangular inequality of classical distance measure.When interval-valued intuitionistic fuzzy sets degenerate into intuitionistic fuzzy sets,this distance measure formula degenerates into the distance measure formula between intuitionistic fuzzy sets.Secondly,the weights of decision makers and attributes are determined objectively by using interval-valued intuitionistic fuzzy entropy.Moreover,based on the new distance measure formula between interval-valued intuitionistic fuzzy sets,an extended VIKOR multi-attribute group decision method under interval-valued intuitionistic fuzzy environment is proposed.Finally,the feasibility and validity of this method are verified by two examples,and the advantages of the proposed method are illustrated by comparison with the existing methods.(2)Multi-attribute group decision-making method based on type-2 intuitionistic fuzzy sets.Firstly,a new distance measure formula between type-2 intuitionistic fuzzy sets is proposed.This distance measure formula satisfies the non-negative,symmetry and triangular inequality of classical distance measure.When the type-2 intuitionistic fuzzy sets degenerate into the type-2 fuzzy sets,this distance measure formula degenerates into the distance measure formula between the type-2 fuzzy sets,which shows that this distance measure formula applies to a wider environment.Then,based on the new type-2 intuitionistic fuzzy distance measure formula,a multi-attribute group decision method under type-2 intuitionistic fuzzy environment is proposed in this thesis.Finally,the feasibility and effectiveness of this method are proved by case analysis.