Research On Multi-Attribute Group Decision-Making Model Based On Neutrosophic And Plithogenic Information

The concept of multi-attribute group decision-making is to use reasonable logical methods to analyze and process various linguistic information collected by decision-makers.With the continuous development of objective things and the limitations of human cognitive thinking,more and more uncertain information has emerged in the process of decision-making,making it difficult for decision-makers to deeply and truly quantify uncertainty and express cognitive preferences through traditional fuzzy and intuitionistic fuzzy information.Therefore,Smarandache successively put forward the concepts of neutrosophic set and plithogenic set,and many expression forms of decision-making information have been extended on this basis and merged with uncertain information processing methods such as rough set and probabilistic linguistic term set,which fully described the fuzziness,hesitation and probability characteristics contained in the membership degree,indeterminacy membership degree and non-membership degree of the evaluation object.Although there have been rich achievements in the research of multi-attribute group decision-making theory and methods based on the neutrosophic and plithogenic information,the constructed decision-making model still has the following problems:(1)Many studies in the environment of plithogenic rough and plithogenic probabilistic linguistic are carried out on the premise that the weight information is partially or completely known,with less consideration of attributes and decision-makers’ weights given to the combination of subjective and objective factors,multiple perspectives,and other comprehensive aspects.(2)Many decision-making models based on neutrosophic and plithogenic information compare the initial evaluation value of attributes or relation of information measure with reference points to realize the alternative ranking process,which is difficult to reflect the real information characteristics of the uncertain environment and the discrimination of decision-making results,and the consideration of the decision-maker’s psychological behavior preferences under bounded rationality is insufficient.In order to solve the above problems and further enrich the multi-attribute group decisionmaking theory,this paper conducts research on multi-attribute group decision-making problems with neutrosophic and plithogenic information to express the uncertainty,fuzziness or hesitation of evaluation information.According to the decision-making logic of considering the decision-maker’s preference factors under the uncertainty weight information from partially known to completely unknown,from complete rationality to bounded rationality,this paper establishes several multi-attribute group decision-making models under the environment of neutrosophic,plithogenic,plithogenic rough and plithogenic probabilistic.(1)Research on multi-attribute group decision-making model of interval neutrosophic and triangular neutrosophic by quantifying uncertain evaluation information and considering bounded rationality of decision-makers.Firstly,the information measure contained in attributes is measured by the interval neutrosophic CRITIC method and the objective weights are obtained,the initial evaluation matrix and the attribute weights are aggregated based on the INWAA operator.Considering the risk preference of bounded rationality decision-makers,based on the improved score function,and according to the extended TODIM method to obtain the overall dominance ranking of alternatives,the problem of risk assessment of green supply chain financial considering the risk attitude of decision-makers in the interval neutrosophic environment is solved.Secondly,the different trust relationships and social influence of bounded rationality decision-makers in the triangular neutrosophic environment are considered.Based on the distance measure and comparison relationship,the prospect value matrix is obtained according to the value function and probability weight function.Combining the weight characteristics of attributes with the boundary approximation area obtained by the MABAC method,a reasonable ranking result of alternatives is obtained.Finally,the prospect theory is extended through the operation of cumulative probability,and the compromise solution of the alternative is obtained on the basis of the comprehensive cumulative prospect value matrix combined with the VIKOR method.The proposed model defines the maximizing deviation measure and uniformity of attributes with independence and superiority and inferiority relationship represented by triangular neutrosophic numbers.The importance weights of decision-makers are measured by the distance relationship between the decision matrix and the ideal one,and the optimal ranking of alternatives is carried out according to the compromise sort index value.Sensitivity analysis and comparative analysis also demonstrate the effectiveness and superiority of the proposed decision-making model.(2)Research on the aggregation of plithogenic and plithogenic rough information and multi-attribute group decision-making model with completely unknown weight information.The former first applies the plithogenic aggregation operator to gather the attribute information quantified by the neutrosophic number,and obtains the subjective weight of attribute through the distance measure of the aggregated matrix.A nonlinear programming model is established that considers both the maximizing deviation and the difference in uniformity to determine the objective weight of attribute and achieve comprehensive weighting.Defining the similarity characteristics of the distance measurement between the decision matrix and the average decision matrix to measure the importance weight of decision-makers.Based on the obtained weight information,the TODIM method is improved by expanding the score function and the comparison relationship of distance,which highlights the decision preferences of decisionmakers when facing risks under plithogenic information.A case study based on the multidimensional evaluation index system of supply chain financial credit risk verifies the effectiveness and scientificity of the proposed model.The latter is based on the advantages of plithogenic rough sets in dealing with uncertainty and fuzziness,as well as reducing the impact of imprecision when evaluating information boundaries.By maximizing the deviation of attributes,similarity of decision matrices,and conflict characteristics,the objective weight information of attributes and decision-makers are comprehensively considered,thus avoiding the adverse effects of completely subjective decision-making.The COPRAS method is used to measure the proportional relationship between the importance weights and utility functions of different categories of attributes in the alternative,thereby determining the ranking of alternatives.Case analysis,comparative analysis,and correlation comparative analysis demonstrate the feasibility of the decision-making results.(3)Research on multi-attribute group decision-making model considering the risk preference of decision-makers with aggregate information of plithogenic probabilistic linguistic terms and completely unknown weight information.The expression of plithogenic probabilistic linguistic term set is defined,and the initial evaluation information is assembled by using the transformation function,score function and plithogenic aggregation operator of the probabilistic linguistic,and the trust relationship between decision-makers is further considered.A subjective and objective attribute weighting model is constructed by means of the subjective preferences of decision-makers and objective information measurement of consistency adjusted coefficient,and a comprehensive weight determination method based on entropy theory is proposed considering the proportional relationship between the subjective and objective weights.In order to overcome the ranking inversion and effectively deal with the phenomenon of random dominance,based on the cumulative probability measure and fluctuation similarity,an improved VIKOR group decision-making model with cumulative prospect theory is established,and the ranking result with high discrimination is obtained by calculating the cumulative prospect value matrix and the compromise sort index.Finally,taking the financial risk assessment of a sustainable supply chain as a case study,the effectiveness and feasibility of the proposed model are illustrated.