Multi-attribute Decision-making Methods Based On Interval-valued Intuitionistic Fuzzy Sets

This thesis deals with the multi-attribute decision-making methods based on interval-valued intuitionistic fuzzy Sets.It consists of four chapters.In the first chapter,we mainly introduce the origin and current research situations of decision making problems based on interval-valued intuitionistic fuzzy sets.Furthermore,we list the main contribution of this paper.In the second chapter,the multi-criteria decision-making methods based on interval-valued intuitionistic fuzzy sets are studied.First,two interval-valued intuitionistic fuzzy point operators are introduced and discussed.By using the interval-valued intuitionistic fuzzy point operators,a series of new score functions for interval-valued intuitionistic fuzzy sets are defined.Furthermore,two new methods are presented for solving multi-criteria decision-making problems based on interval-valued intuitionistic fuzzy sets,which generalize the related methods for sovling multi-criteria decision-making problems based on intuitionistic fuzzy sets.Finally,several illustrative examples are given to demonstrate the feasibility and practicability of the proposed methods.In the third chapter,a method for solving multi-attribute decision-making problem is presented,in which the importance degree of each attribute and the value of each alternative with respect to every attribute are represented by interval-valued intuitionistic fuzzy numbers,respectively.According to the interval-valued intuitionistic fuzzy weighted arithmetic averaging operator and the interval-valued intuitionistic fuzzy weighted geometric averaging operator, several nonlinear programming models are constructed to generate the optimal weights and get the priorities of alternatives.The proposed method can also be applied to solve the multi-attribute decision-making problem based on intuitionis- tic fuzzy numbers.Finally,several illustrative examples are given to demonstrate the practicability and effectiveness of the proposed method.In the forth chapter,a method is presented to deal with the fuzzy multiattribute decision making problem with preference values on alternatives,in which the information about attribute weights is incomplete,the attribute values and the preference information on alternatives are given in the form of interval-valued intuitionistic fuzzy numbers.According to the preference information on alternatives given by decision makers,multi-objective programming model is constructed to obtain the attribute weights.Then,intuitionistic fuzzy weighted arithmetic averaging operator is used to aggregate the intuitionistic fuzzy information corresponding to each alternative,and the alternatives are ranked by the score function. Finally,an illustrative example is given to demonstrate the practicability and effectiveness of the proposed method and the proposed method can also be applied to solve the multi-attribute decision-making problem based on intuitionistic fuzzy numbers.