Research On Uncertain Multi-attribute Three-way Group Decision Making Methods Based On Three-way Decision Theory

With the refinement of the social division of labor and the increase of complexity of the actual economic environment,some complex decision-making problems are usually studied from multiple perspectives by multiple experts in different fields.Therefore,multi-attribute group decision making(MAGDM),which combines group decision making with multi-attribute decision making,is widely used in many fields,such as economics,management,military,culture,engineering,etc.Additionally,due to the uncertainty and complexity of practical problems,as well as the ambiguity of human thinking and cognition,it is sometimes difficult for decision-makers to adopt precise numerical values to describe the evaluation information,and they often use uncertain information to express their opinions,such as interval numbers,intuitionistic fuzzy numbers,hesitant fuzzy numbers,linguistic variables,etc.As a result,it is very important and necessary to study the theory and methods of MAGDM for real-world uncertainty problems.In recent years,theories and methods of uncertain MAGDM have made great progress,but most of these methods are based on two-way decision theory,which not only requires high integrity of information,but also can only give two results of acceptance and rejection.Unlike the two-way decision theory,three-way decision(3WD)theory divides a universal set into three pairwise disjoint parts,namely,positive region,negative region and boundary region,by adding a delayed decision,and gives each region a corresponding decision action,which can effectively reduce the decision risk in the case of incomplete information.To this end,on the basis of 3WD theory,this thesis investigates and explores uncertain multi-attribute three-way group decision making methods to solve uncertain MAGDM problems and obtain 3WD mechanisms of objects.The specific research work and results are described as follows:(1)An interval-valued multi-attribute three-way group decision making method is constructed based on 3WD theory for interval-valued MAGDM problems.Firstly,under the individual interval-valued decision information,the conditional probability of the objects is determined by improving the interval-valued TOPSIS method.Then,the relative loss functions are calculated by using the intrinsic connection between the attribute values and the loss functions.Furthermore,the 3WD mechanism of each object is determined based on the Bayesian minimum risk principle,and two solution strategies of thresholds are further given according to the θ ranking method and the geometric mean ranking method of interval numbers,respectively.On this basis,the conditional probabilities and thresholds determined by different decision-makers are aggregated according to the weighted average operator and the weighted geometric operator,respectively,to obtain the group 3WD mechanism and result of objects.Finally,the proposed method is applied to a car parts supplier selection example,and the rationality and advantages of the proposed method are illustrated by a parameter sensitivity analysis and a comparison analysis.(2)An intuitionistic fuzzy multi-attribute three-way group decision making method is developed based on 3WD theory to solve the uncertain MAGDM problems where the attribute values are intuitionistic fuzzy numbers.Considering that it is difficult to objectively judge the accuracy and reliability of the aggregation result when the aggregation operators are used to aggregate the evaluation information provided by different decision-makers,this thesis establishes an aggregation evaluation matrix from an optimization perspective by utilizing the mathematical planning method with the two objectives of minimum difference and high similarity between group evaluation values and individual evaluation values.Then,in the group evaluation matrix,the conditional probability of the objects is estimated by using the ideal solutions and intuitionistic fuzzy similarity,and the relative utility functions of the objects are calculated based on the attribute evaluation values.Based on this,the maximum-utility-value 3WD mechanisms are derived by calculating the expected utility functions of the objects under different actions,and then the 3WD result of objects are obtained.Finally,a coalfield mining investment case study,along with a parametric sensitivity analysis and a comparative analysis is presented to discuss the practicality and superiority of the proposed method.(3)A hesitant fuzzy multi-attribute three-way group decision making method is presented based on 3WD theory to deal with the uncertain MAGDM problems in which the attribute values are hesitant fuzzy numbers.Firstly,in the individual hesitant fuzzy decision matrix,we utilize the similarity of hesitant fuzzy numbers and m-dimensional overlap functions to calculate the similarity class of the objects,and then the fuzzy state set is estimated by using the grey relational analysis method.Besides,the relative loss functions of the objects are calculated based on the hesitant fuzzy attribute values,and further a decision-theoretic rough fuzzy set model is constructed based on the Bayesian decision theory and a minimum-risk3 WD method is derived.On this basis,a three-way group decision making method is established based on the intersection calculation of classical sets.Finally,the proposed method is applied to an Internet company recruitment example,and the performance of the proposed method is illustrated by a parameter sensitivity analysis and a comparison analysis with the three-way group decision making method based on multi-granulation hesitant fuzzy decision-theoretic rough sets.(4)A sequential multi-attribute three-way group decision making method is proposed based on sequential 3WD theory to handle the complex MAGDM problems with hybrid information(interval numbers,linguistic variable,intuitionistic fuzzy numbers,hesitant fuzzy numbers).At first,a nested sequence of the set of attributes is constructed according to the attribute values provided by decision-makers have different consensus degrees for different attributes.Then,using mathematical programming methods,the evaluation information provided by different decision-makers is aggregated from an optimization perspective to obtain the aggregated decision matrix.On this basis,a multilevel granular structure for the MAGDM problems with hybrid information is constructed,and then the calculation of conditional probability and loss functions is explored in a single level granular structure,and the thresholds and3 WD mechanisms of the objects are further determined according to the principle of risk minimization.In addition,by using a sequential strategy,we establish a sequential multi-attribute three-way group decision making method under a multilevel granular structure.Finally,the practicality and advantages of the proposed method are demonstrated by a blockchain service provider selection case study,a parameter sensitivity analysis as well as a comparison analysis and discussions.In conclusion,this thesis systematically study uncertain multi-attribute threeway group decision making methods by combining the theories of 3WD and uncertain MAGDM together,and we further verify the performance and advantages of these methods by numerical case analysis.This study not only provides new ideas and strategies for uncertain MAGDM problems,but also broadens the application of 3WD theory.