| The purpose of group evaluation is to comprehensively evaluate economic practice activities based on relevant information integration technology by multiple evaluation subjects,and to solve the multiple evaluation and decision-making problems faced in socio-economic management.Group evaluation expands the evaluation subject of a single object in the traditional multi-attribute comprehensive evaluation to the coexistence of multiple evaluation subjects,and the multiple evaluation subjects greatly improve the evaluation quality in the complex environment in which the socio-economic development is advanced in depth.Group evaluation gathers collective wisdom,absorbs different opinions more widely,and breaks through the logical limitations in the practical activities of a single evaluation subject.In essence,group evaluation is a comprehensive evaluation of multiple indicators.There is no big difference in the determination of the target of the evaluation object,the integration of the evaluation information and the analysis of the evaluation results in the evaluation activities.Can we continue to use the classic comprehensive evaluation technology of multiple indicators in the implementation of economic management decisions? After a little consideration,it is found that group evaluation is aimed at increasingly complex decision-making problems.When the characteristics of the evaluation object are unclear,the single evaluation subject often faces an adverse situation in the acquisition of evaluation information and the integration of evaluation information.The internal connection of multiple stakeholders and the uncertainty of evaluation make the economic practice tend to be complicated.It is necessary to focus on the two key technical issues of the integration of evaluation information and how to integrate it scientifically.The quantitative evaluation of the evaluation object from multi-dimensional perspective based on uncertain data has greatly expanded the application field of group evaluation and broken the shackles of traditional comprehensive evaluation based on accurate value that is difficult to make decisions.Fermatean fuzzy set,as a new form of uncertain data expression,expands the membership degree and non-membership degree constraints of intuitionistic fuzzy set and Pythagorean fuzzy set,and can contain more uncertain information in a larger range,making the application prospect of group evaluation in Fermatean fuzzy environment broader.In view of the new situation of incomplete information and fuzzy information,Fermatean fuzzy information form from point estimation to interval estimation and probability estimation to confidence level is developed.At the same time,problems such as the extensive correlation between evaluation indicators in group evaluation,the diversified development of risk preference of multiple evaluation subjects,the conflict of opinions of multiple evaluation subjects,and the single structure of comprehensive evaluation methods need to be further studied and improved,and the theory,method and application of group evaluation based on Fermatean fuzzy cluster information should be enabled to develop highquality social economy.In view of this,this paper will carry out systematic research from the following perspectives:(1)Research on hesitant Fermatean fuzzy MULTIMOORA group evaluation integration mechanism.The evaluation object is described by multidimensional evaluation index information,and the evaluation subject often hesitates when giving the evaluation information.First of all,based on Fermatean fuzzy set,the form of hesitant Fermatean fuzzy set is developed to express the evaluation information.Then,the consensus weight among group members is obtained by measuring the consensus distance between the evaluation subject and each evaluation index under the evaluation object.Secondly,in order to give consideration to the integrity and unity of the subjective weight and objective weight of the evaluation index,the grade difference maximization method is used to integrate the subjective weight of the average value and the objective weight of Shannon entropy.Then,input the above evaluation information,group member weight and evaluation index weight into the multi-objective optimization on the basis of a ratio analysis plus the full(MULTIMOORA)method,and construct the hesitant Fermatean fuzzy MULTIMOORA group evaluation integration technical framework.Finally,on the basis of the evaluation index system of green development level in the innovative development region,taking the evaluation of green development level of five provinces and cities along the Yangtze River Economic Belt as an example,the robustness test and comparative analysis intuitively demonstrated the good characteristics of the decisionmaking model to adapt to the complex environment.(2)Research on probabilistic hesitant Fermatean fuzzy extension MULTIMOORA group evaluation integration mechanism.Based on the proposed hesitant Fermatean fuzzy set,the evaluation subject usually gives multiple evaluation information values that do not meet the same importance,and multiple possible evaluation values should be given different probabilities.Therefore,a probabilistic hesitant Fermatean fuzzy data form is proposed to express the evaluation information.Although it covers more uncertain information,the redundant relationship between evaluation indicators has not been resolved.Based on the previous research,using Dombi operations to fuse Choquet integral measures,geometric operator ensemble evaluation information in probabilistic hesitant Fermatean fuzzy environments is developed.In addition,the Choquet score measures the relative importance of group members and indicators.Considering the limitations of integrating evaluation utility values using ordinal dominance theory,the reference point method in the traditional MULTIMOORA method is extended to a negative ideal solution.At the same time,the evaluation results of the three subsystems in the MULTIMOORA method are integrated using the Borda rule to obtain a comprehensive evaluation utility value,and a probabilistic hesitant Fermatean fuzzy extended MULTIMOORA group evaluation integration technical framework is established.Finally,taking the evaluation of the level of green restoration in five provinces and cities along the Yangtze River Economic Belt as an example,the scientific nature of the decision-making framework was effectively verified through robustness testing and comparative analysis.(3)Research on interval-valued Fermatean fuzzy prospect theory group evaluation integration mechanism.In the face of complex economic practice,it is often difficult for the evaluation subject to give the accurate membership degree and non-membership degree of Fermatean fuzzy set.The interval-valued number is more flexible than the accurate value,so the interval-valued Fermatean fuzzy data form is proposed to express the evaluation information.In addition to the above information integration operator measures the correlation of indicators,correlation coefficients in statistics can effectively depict the correlation between evaluation indicators,and interval-valued Fermatean fuzzy number correlation coefficients are proposed to measure the relative importance of indicators.At the same time,multiple evaluation subjects represent the interests of all parties,and it is unrealistic to implement economic practice activities with rational psychology,while it is unrealistic to use prospect theory to evaluate the risk preference of evaluation subjects,and calculate the prospect weight information of the next indicator in the evaluation object.Then,in order to obtain the stable and non-singular evaluation values,the generalized interval-valued Fermatean fuzzy weighted power Heronian average operator is proposed to integrate the evaluation information,and the interval-valued Fermatean fuzzy prospect theory group evaluation integration technical framework is built.Finally,taking the evaluation of the effectiveness of the regional rural revitalization,empowerment and poverty alleviation as an example,the robustness test and comparative analysis strongly demonstrate the practicability of the decision-making framework.(4)Research on probabilistic interval-valued Fermatean hesitant fuzzy DNCo Co So group evaluation integration mechanism.Based on the above research on probabilistic hesitant Fermatean fuzzy set and interval-valued Fermatean fuzzy set,the form of uncertain data has been expanded.In order to cope with the more complex decision-making environment,the evaluation information is expressed in the form of probabilistic interval-valued Fermatean hesitant fuzzy set.In view of the current problem of normalization and simplification of evaluation information,a dual normalization strategy is adopted,which combines the target linear normalization method based on Euclidean distance and the target vector normalization method based on score value.At the same time,the method of determining the importance of indicators based on the criteria importance through intercriteria correlation(CRITIC)is used to solve the redundancy problem of indicators mentioned above,and the comprehensive weight of indicators is determined in combination with subjective weight.Then,we use the prospect theory based on the index value function to determine the prospect weight information of the evaluation subject,which overcomes the limitation that the classical value function cannot better cover the risk aversion selection of the evaluation subject.Through the above related strategies,the evaluation information can be integrated.Then,through the combined compromise solution(Co Co So)method,the probabilistic interval-valued Fermatean hesitant fuzzy DNCo Co So group evaluation integrated technical framework is constructed.Finally,taking the selection and evaluation of national parks in China as an example,the robustness test of the relevant parameters and the comparative analysis with the existing comprehensive evaluation methods prove the effectiveness and feasibility of the model framework.(5)Research on self-confidence Fermatean fuzzy social network consensus MABAC group evaluation integration mechanism.The previous article has made a beneficial attempt to the shortcomings of the group comprehensive evaluation and the improvement research,but it still ignores the social network trust relationship of multiple evaluation subjects in the process of information interaction,which is of great significance to the scientific nature of the group evaluation results.At the same time,the evaluation subject is not completely confident when giving the evaluation opinions.Therefore,the self-confidence Fermatean fuzzy data form is proposed to express the evaluation information.Then,a new trust propagation efficiency function is defined to solve the incomplete trust network among group members.Then,the reliable weight sources of three evaluation subjects are fully considered to comprehensively measure the weight information of group members,which are social network trust,opinion selfconfidence level and relative deviation between evaluation subjects.In addition,the correlation coefficient of the evaluation index determines its relative importance and has eliminated the influence of correlation.At the same time,a consensus feedback strategy based on selfconfidence level and trust network is established to eliminate the opinion conflict of multiple evaluation subjects.Then,through the multi-attributive border approximation area comparison(MABAC)method to integrate the evaluation information,the self-confidence consensus MABAC group evaluation integrated technical framework of Fermatean fuzzy social network is constructed.Finally,taking the selection of new energy vehicle power battery recovery service network as an example,the scientific nature of the model framework is verified through multi-dimensional robustness analysis and quantitative and qualitative comparative analysis with similar decision-making methods.The above research not only enriches the expression form of Fermatean fuzzy numbers,but also makes interesting exploration and supplement for the shortcomings of existing group evaluation methods.Specifically,in terms of the correlation of evaluation indicators,the irrational evaluation psychology of evaluation subjects,the social trust and opinion consensus of multiple evaluation subjects,and the comprehensive evaluation integration method,Fermatean fuzzy cluster group evaluation integration theory,method and application are expanded.Each chapter closely revolves around Fermatean fuzzy evaluation information,solving the group comprehensive evaluation problem of different uncertain data layer by layer,both matching and complementing each other and forming a logical system.It is expected to provide a scientific and normative evaluation decision-making system for the socio-economic related evaluation practice with significantly increased uncertainty factors,and improve the scientific of the evaluation results. |
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