| With the popularity of Web2.0 and the rapid development of social media,social networks are very common.The information communication among persons is convenient,and social contact is more and more frequent.Decision-making is regarded as the cognitive process resulting in the selection of a belief or a course of action among several alternative possibilities,and it widely exists in the social,economic,management and other fields.With the arrival of big data,the gross information content is expanding rapidly and social division of labor becomes more professional.Group decision making where multiple decision makers act collectively,analyze problems,evaluate alternatives,and select a solution from a collection of alternatives receives more and more attention.Moreover,with the natural and economic environment changing,the group decision-making problem presents a trend from small-scale group decision-making to complex large-scale one.At present,researches on complex group decision-making under the social network environment,especially the large-scale group decision-making,are relatively few.Therefore,studying the complex group decision-making problem in the social network environment is not only conducive to addressing realistic decision making,but also can further extend the group decision-making theory.Based on the systematic analysis of the traditional group decision-making methods,the complex group decision-making problem with fuzzy judgment matrices under the social network environment is studied.The results are applied to the business recommendation.Specific research contents and innovations in this paper are shown as follows:1.Based on the theory of trust relationship,group decision making method with fuzzy decision matrix is proposed considering the trust relations among decision makers.(1)According to the transfer and aggregation of trust/untrusted relationship,a repairing method of incomplete fuzzy judgment matrix is proposed.(2)Study the properties of acceptable consistency and complementarity of the fuzzy judgment matrix.(3)Define the group judgment matrix based on the trust relation.On this basis,the consensus of the group decision maker is studied,and a feasible group consensus adjustment algorithm is proposed.The innovation of the above researches are shown as follows.On the one hand,the trust/non-trust relationship between decision-makers is added to the repairing method of incomplete fuzzy judgment matrix.That provides a new perspective which is different from the constructing mathematical models.That is in line with the actual decision-making situation.On the other hand,the proposed consensus adjustment algorithm that considers the trust relationship can avoid the loss of the original judgment information to some extent.2.Based on the theory of social network analysis,group decision making method with fuzzy decision matrix is proposed considering the adjacency relation among decision makers is studied.(1)According to the incomplete fuzzy judgment matrix of decision-making individuals,the degree of similarity between decision-making individuals is defined.According to the adjacency relation between decision-making individuals,the "familiarity" between decision-making individuals is defined.According to degrees of similarity degree and familiarity,the repairing method of incomplete fuzzy judgment matrix is proposed,and the consistency judgment and adjustment of the fuzzy judgment matrix are presented.(2)Define the "influence"of the decision-making individual according to the degree of familiarity among the decision-making individuals;define the group judgment matrix based on the influence of the decision-making individuals using the IOWA operator.(3)Propose a visual interaction of group consensus adjustment algorithm,and prove the convergence properties of the adjustment algorithm.The innovation of the above researches are shown as follows.On the one hand,it provides a method to meet the actual decision-making situation of the fuzzy and incomplete judgment matrix.On the other hand,it puts forward the consensus adjustment algorithm based on decision-making individual’s influence,which does not only consider the important social characteristics,but also show the consensus adjustment process intuitively.3.Based on the theory of community analysis,the complex large-scale group decision-making problem with incomplete fuzzy judgment matrices in the social network environment is studied.(1)According to the degree of similarity between decision-making individuals and the degree of proximity in the social network,the cluster degree between decision-making individuals is defined.On this basis,the community discovery method based on fuzzy equivalence matrix clustering is proposed.The importance weight of the community is determined by their corresponding closeness centralities.(2)According to the results of community division,a repairing method of incomplete fuzzy judgment matrix based on the cluster degree between decision makers is proposed,and the consistency judgment and adjustment of the fuzzy judgment matrix are presented.(3)Weighting of the decision-making individuals after the community division is obtained to get the aggregation judgment matrix.Define the group consensus index.On this basis,the two-stage interaction group consensus algorithm is proved and its convergence is proved.The innovation of the above researches are shown as follows.On the one hand,it provides an effective and realistic method for the repairing of the large-scale fuzzy judgment matrix under the social network environment.On the other hand,the complex large-scale decision-making is discussed at the community level of the divisions,and a two-stage interactive consensus model is proposed to improve the efficiency of group decision-making.4.The decision-making process and practical application of the group decision making with fuzzy judgment matrices considering the social network relation are studied.(1)The process of group fuzzy decision matrix decision-making method considering the trust relationship among decision-making individuals are put forward,and the validity of the method is illustrated by an example.(2)The decision-making process of the group fuzzy decision matrix decision-making method considering the adjacency relation among the decision-making individuals is put forward and applied to the location problem.(3)The process of large-scale group decision making with fuzzy judgment matrix based on community analysis under social network is proposed and applied to the decision-making of selecting a flexible manufacturing system.(4)In particular,the large-scale group decision making with fuzzy matrices based on community analysis is applied in the intelligent service recommendation of take-away 020 platform.According to the difference between the social characteristics of the decision makers and the size of the decision-making scale,the corresponding decision-making process to meet the needs of different decision-making environments are proposed.The methods proposed in this paper have been applied in group decision-making.Related research results can further extend and enrich the group decision-making method based on the fuzzy judgment matrices at the theoretical level,and provide the new tools and methods for the service recommendation of the online business at the application level. |
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