Research On Group Decision-Making Methods Based On Probabilistic Dual Decision Information

As an important part of decision-making theory,group decision-making(GDM)is widely used in various fields such as engineering,management and economy.Probabilistic dual hesitant fuzzy sets(PDHFSs)and dual probabilistic linguistic term sets(DPLTSs)depict decision information from both membership degree and non-membership degree and express different preferences of decision-makers for different evaluation information,which can describe the fuzziness of human thinking and objective things reasonably and well solve the GDM problem.However,the existing GDM methods based on probabilistic dual hesitant fuzzy environment and dual probabilistic linguistic environment have some shortcomings.For example,the probabilistic dual hesitant fuzzy information correlation coefficient measure can only reflect the intensity of correlation without reflecting the polarity of correlation and the GDM methods based on dual probabilistic linguistic aggregation operators can only solve the decision-making problem without interaction among attributes or with interaction between two attributes.Therefore,in this thesis,different GDM methods are proposed in the following environments,namely PDHFSs,DPLTSs,probabilistic dual hesitant fuzzy preference relations(PDHFPRs)and dual probabilistic linguistic preference relations(DPLPRs),and the effectiveness of the proposed GDM methods is verified by selecting cases of different environmental protection measures.The specific research work and innovations are summarized as follows:(1)Based on the improved probabilistic dual hesitant fuzzy correlation coefficient measure,a probabilistic dual hesitant fuzzy GDM method with unknown attribute weight is proposed.Firstly,a new probabilistic dual hesitant fuzzy correlation coefficient measure and a weighted correlation coefficient measure are proposed to measure the correlation level between decision information,and the excellent properties of the proposed correlation coefficient measures are analyzed.Secondly,the objective attribute weight is calculated by the constructed probabilistic dual hesitant fuzzy information entropy,and combined with the subjective attribute weight given by decision-maker to obtain the comprehensive weight of attribute.Finally,a GDM method based on probabilistic dual hesitant fuzzy correlation coefficient measure is designed and applied to the selection of haze control strategies.Experimental results show that the proposed probabilistic dual hesitant fuzzy decision-making method has good robustness and effectiveness.(2)Based on the Archimedean power Muirhead mean operator for DPLTSs,a dual probabilistic linguistic GDM method with unknown attribute weight is proposed.Firstly,the Archimedean T-norm and S-norm are extended to DPLTSs,and the dual probabilistic linguistic operational laws based on Archimedean T-norm and S-norm are proposed.Combining the advantages of power average operator and Muirhead mean operator,the dual probabilistic linguistic Archimedean power Muirhead mean operator and its weighted form are proposed.Secondly,the objective attribute weight is calculated by the proposed dual probabilistic linguistic information entropy,and combined with the subjective attribute weight given by the decision-maker to obtain the comprehensive weight of attribute.Finally,a GDM method based on dual probabilistic linguistic weighted power Muirhead mean operator is proposed,and the effectiveness of the method is verified by the selection case of photovoltaic power generation projects.(3)Based on the group consensus for PDHFPRs,two probabilistic dual hesitant fuzzy GDM methods considering the group consensus are proposed.Firstly,several concepts,including individual similarity measure,group consensus measure,consensus measure between the row vectors for PDHFPRs,and group consensus measure for the alternatives are defined to measure the consensus level for PDHFPRs.Secondly,for the PDHFPR that does not reach the expected consensus threshold,the group decision-makers’ preferences can reach the expected consensus threshold by changing the decision-makers’ preferences and modifying the importance weights of decision-makers,respectively.Finally,based on different consensus reaching strategies,two probabilistic dual hesitant fuzzy GDM methods are proposed,and the effectiveness of the proposed methods is verified by the case of industrial solid waste treatment facility site selection.(4)Based on the consistency and group consensus for DPLPRs,a dual probabilistic linguistic GDM method considering the group consensus is proposed,which can ensure that all DPLPRs satisfy the acceptable consistency when reaching the consensus threshold.Firstly,the concepts of distance measure,multiplicative consistency and consistency index for DPLPRs are defined,and a local consistency improvement algorithm for DPLPRs with convergence is proposed.Secondly,based on the distance measure for DPLPRs,the similarity measure and the group consensus measure for DPLPRs are defined respectively,and the consensus reaching strategy for DPLPRs is proposed.Finally,combined with the local consistency improvement algorithm and the consensus reaching strategy,a GDM method based on DPLPRs is proposed,and the effectiveness of the proposed method is verified by a green battery supplier selection case.The GDM methods based on probabilistic dual decision information proposed in this thesis can better solve GDM problems under probabilistic dual hesitant fuzzy environment and dual probabilistic linguistic environment from theory and can provide new ideas for the selection of different environmental protection measures from application.