Study On Uncertain Group Decision-making Based On Factor Space

Group decision-making is a key issue in decision analysis,and it is also a difficult problem,which is widely existed in various fields of social activities.With the development of society,the progress of modern science and technology,especially information science and technology is changing with each passing day,and the decision-making environment is becoming more and more complicated.The main performance is that the uncertainty of the decision system is stronger.This uncertainty mainly comes from the following three aspects: First,due to the limitations of human cognition,it is difficult to obtain accurate data on some complex decision problems;Second,for some decision-making problems,decision-making information needs decision makers to rely on subjective judgment information to qualitatively describe,such as linguistic values,interval numbers,fuzzy numbers,etc.,because of the subjectivity,one-sidedness and hesitation of such judgment information,it will inevitably lead to the uncertainty in the decision-making system.Third,the uncertainty of decision-making caused by the inconsistency of opinions among experts.For uncertain decision information,traditional decision models and empirical judgment functions with strict conditional assumptions can no longer meet the decision requirements of complex data.Decision makers hope to process decision data through more effective techniques to obtain effective decision information and provide decision support for complex decision problems.Factor space is the transformation of certainty and uncertainty by establishing a universal coordinate frame for information description.It is a natural paradigm that simulates human cognitive processes.Based on the factor space theory,this paper introduces related theories such as uncertain information processing and decision analysis,and focuses on how to complete the decision-making elements and decision information integration in the factor space under the group decision-making environment.The main work of this paper is as follows:(1)First,we analyze and study how to determine the experts' weight in group decision making from a new perspective.We conduct cluster analysis on experts based on experts 'judgment information,and obtain appropriate classification of experts according to Akaike Information Criterion.Furthermore,the concept and formula of the compatible consistency measure are proposed,and the algorithm is designed to obtain the reduction of background factors that are the most consistent with the classification of experts.Then,the state attribute under the background factor is transformed into the decision utility.The experts' weight vector is obtained according to the maximum eigenvalue method.Then,based on the expert weightinformation,a variable weight method based on data reliability is proposed,and the state variable weight vector based on data reliability is constructed,which solves the problem of subjectively determining the equalization force in the traditional variable weight.Finally,a variable weight integrated group decision making method based on data reliability is presented.(2)From the perspective of "concept" in the factor space,the intuitionistic fuzzy decision information and the interval number decision information generation process are analyzed.Although the two are equivalent in mathematical structure,from the decision analysis process,the two have essential differences.Based on this,this chapter proposes two kinds of uncertain expressions of concept-intuitionistic fuzzy set expression and interval set expression under the factor space,and gives the construction method of feedback extension.Inspired by the information extension process of feedback extension,two kinds of group decision making methods are constructed based on the decision information provided by experts: DFE group decision making method based on double envelope of feedback extension and interval set decision making method based on feedback extension.Finally,the effectiveness and rationality of the method are illustrated by examples.(3)In order to make full use of data information,hesitant fuzzy sets are used as concept feedback extension.Furthermore,a two-layer envelope of concept extension is defined.The study finds that the double-layer envelope of concept extension is a new type of expansion of hesitant fuzzy sets-hesitant interval fuzzy sets.In this chapter,we define its algorithm and study its computational properties and ordering problems.At the same time,we point out the two key issues and their respective shortcomings in the study of hesitant fuzzy group decision making,and make corresponding improvements to the inadequacies: i)The concept of hesitant fuzzy entropy measure function and hesitant fuzzy information feature vector is proposed,and then the various measures of hesitant fuzzy information are studied in depth.ii)Based on the ordinal decision information provided by experts,the group consistency measure is studied.iii)A method for filling missing values of hesitant fuzzy information was proposed.Finally,according to whether the decision factor weight information is known,two specific group decision methods are proposed and the effectiveness and feasibility of the proposed method are illustrated by an application example.(4)Aiming at the complexity of the multiple factor sorting and the inconsistency of the classification results in group decision-making environment,a sorting method in group decision text based on background bases was proposed.The preference entropy of case information was defined first,then the integer programming model was established in order to select the case setwith the smallest average preference entropy and meet the consistency as the best case set from the case information provided by the decision makers.The best case set was used as a training sample and extract the background bases of each category.And then determine the category attribute by calculating the relationship between the scheme to be classified and the convex closure of various background bases.Finally,the feasibility and rationality of the method are illustrated by an example of MBA project classification.The paper has 7 pictures,24 tables,and 236 references.