Research On Optimal Aggregation Model And Algorithms For Group Decision Making With Multi-attribute Fuzzy Preference Information

A single decision maker or decision algorithm cannot provide accurate decision results for decision-making problems in real society or intelligent systems.Thus,multi-attribute group decision making(MAGDM)has always been a research hotspot in system engineering.Due to time pressure,complex decision-making environment,and incomplete matching of decision makers' research fields,decision makers' preference information is usually described by fuzzy information,which greatly increases the difficulty of decision-makers' preference information aggregation.In recent years,researchers have begun to focus on multi-attribute group decision making with fuzzy preference information.The process of solving the multi-attribute group decision making problem with fuzzy information can be roughly divided into three steps: the numerical expression of the decision-maker's preference information(preference description),the aggregation of the decision-maker's preference(preference aggregation)and the determination of alternative decision-making alternatives(alternative ranking).For preference description,the intuitionistic fuzzy sets,triangular intuitionistic fuzzy sets,neutrosophic sets and fuzzy number intuitionistic fuzzy sets proposed by researchers can accurately describe the decision makers' fuzzy preference information.For preference aggregation,novel aggregation operators are constructed by extending classical operators such as weighted average operator(WA)and weighted geometric operator(WG)recently.For alternative ranking,construct accuracy function or TOPSIS and its extension method are employed by researchers to evaluate alternatives.This study focuses on preference aggregation and alternative ranking.An optimal aggregation model and method based on Steiner-Weber problem are proposed.A number of typical examples are presented to illustrate the feasibility and effectiveness of the proposed approach.The contributions are as follows:Multi-attribute group decision making with fuzzy information is an important research topic in the field of system engineering in recent years.The process of solving multi-attribute group decision making problem with fuzzy information can be roughly divided into three steps: describing decision makers' preference information,aggregating decision makers' comprehensive preference and evaluating alternatives.For the first stage,researchers present intuitionistic fuzzy sets,interval intuitionistic fuzzy sets,triangular intuitionistic fuzzy sets,trapezoidal intuitionistic fuzzy sets,neutrosophic sets and fuzzy number intuitionistic fuzzy sets to describe decision makers' fuzzy preference information.It has successfully solved the problem of increasing ambiguity of preference information in decision making problems due to time pressure,complex decision-making environment and poor matching of decision-makers' professional knowledge.This study focuses on the aggregation of decision makers' comprehensive preference and the evaluation of alternatives,and proposes new aggregation models and aggregation methods.Also,a number of examples are employed to prove the effectiveness and superiority of the proposed methods.(1)The construction of fuzzy mapping modelexisting aggregation operators use different pretreatment methods to process or transform different types of fuzzy data before aggregating information which usually leads to "distortion" of fuzzy information.In order to solve this problem,eight kinds of fuzzy mapping models are constructed by this study for six kinds of fuzzy data sets,including intuitionistic fuzzy sets,interval-valued intuitionistic fuzzy sets,single-valued neutrosophic,interval-valued neutrosophic,fuzzy number intuitionistic fuzzy sets and interval-valued intuitionistic triangular hesitant fuzzy sets.Fuzzy data are mapped as points,areas,support points or areas cluster in plane or space,so that the complex relationship between fuzzy data can be transformed into simple Euclidean distance relationship between points.The two important advantages of these fuzzy mapping models are: first,the construction of model is simple,understandable and visualized,and it can quickly straighten out the relationship between fuzzy information.Second,this method substantially is not redundant operations to the fuzzy data,and fuzzy information will not be "distorted".(2)Design of Fuzzy Information aggregation algorithmthe quality of fuzzy data aggregation matrix directly affects the accuracy of alternative ranking.Most of the existing aggregation operators are extended or mixed by classical operators such as weighted averaging operator,weighted geometric operator,ordered weighted averaging operator and ordered weighted geometric operator.There are a number of multiply continuously in the process of aggregation,the aggregation results will have large errors when there are special values such as "0" or "1" in the fuzzy data.To solve this problem,a number of fuzzy information aggregation algorithms aim at different fuzzy mapping models are proposed by this thesis.These algorithms aggregate fuzzy information by finding the optimal aggregation point in plane or space.Because the fuzzy data are mapped to the plane or space rectangular coordinate system,the fuzzy data with special values become ordinary points or areas.Therefore,the process of finding the optimal aggregation point or the optimal aggregation area with the minimum sum of Euclidean distances from these points or regions is not affected by the special value.The fuzzy data aggregation matrix established by this method has high accuracy,and can aggregate the decision maker's fuzzy preference information more reasonably in practical problems.(3)Design of alternative scheme evaluation methodRanking alternatives according to the relationship between alternatives and ideal alternatives is the main method to select the optimal alternatives for multi-attribute group decision making problems.In this paper,the TOPSIS method is used to select the positive and negative ideal solutions from the decision makers' aggregation preference matrix,and the scoring algorithm is constructed by calculating the projection values of the comprehensive alternatives on the positive and negative ideal solutions,thus completing the alternative ranking.This method has two advantages: First,the algorithm process is simple,understandable and general.Secondly,by synthesizing the similarity between the alternatives and the positive/negative ideal solutions,the method can provide double insurance,thus improving the accuracy of the alternative scoring.(4)Design of evaluation criteria of aggregation methoddifferent aggregation methods may get different alternative ranking when solving the same multi-attribute group decision-making problem.At present,there is few researches on evaluation criteria of the performance of aggregation methods.Aiming at this problem,this paper proposes a method to evaluate the performance of the aggregation methods based on the similarity measure,distance measure,correlation coefficient and entropy measure between the aggregation fuzzy data set and the given fuzzy data sets.Several examples are used to prove the reliability of the evaluation criterion in this thesis.