Probabilistic Hesitant Fuzzy Information Integration And Its Application In Multiple-attribute Group Decision-making

With the rapid development of society,the decision-making environment is increasingly complex.On the one hand,the problem is becoming more and more comprehensive,which makes more and more attributes and decision makers need to be considered in the decision-making processes.In this case,the demand for the theory and method of multi-attribute decision-making(MADM)is higher and higher.On the other hand,most of the decision-making problems are no longer limited to a single field,but need to be coordinated by decision makers from multiple department and agency.In recent years,group decision-making(GDM)has become the mainstream.Therefore,the research of multi-attribute group decision-making(MAGDM)method is very urgent and meaningful.For most MAGDM problems,information from different dimensions(attributes,experts,etc.)needs to be integrated.Obviously,information integration methods play an important role in it.It is not a simple information stacking,but a dynamic process of integrating and optimizing multi-dimensional information resources according to the needs of specific fields and users.However,with the increasing complexity of the actual decision-making problems,the information integration methods based on real numbers has been unable to carry such a large amount of data.Therefore,starting from fuzzy sets(FSs),people gradually began to seek new ways of information expression to solve such a problem.Probabilistic hesitant fuzzy set(P-HFS)is one of the latest research results of related work.P-HFS,which can show the weight behind each membership,contains two dimensions of information--membership and probability.It fundamentally makes up for the natural defects of hesitant fuzzy set(HFS),and is one of the most informative information units in current decision-making theory.The decision-making method based on probabilistic hesitant fuzzy information is a combination of qualitative and quantitative methods.It not only overcomes the shortcomings of simple mathematical modeling method,but also has more profound mathematical principles.The research on it is beneficial to the development of information integration and the innovation of MAGDM methods.However,the existing probabilistic hesitant fuzzy information integration methods still have some defects.This seriously restricts the development of probabilistic hesitant fuzzy MAGDM.Based on the above background,this paper refines the following four types of research problems based on probabilistic hesitant fuzzy information,and carries out the corresponding innovative research work:(1)Operation laws(especially the "addition")is the basis of probabilistic hesitant fuzzy information integration.There are three important problems in the existing operation laws of probabilistic hesitant fuzzy elements(P-HFEs):a.The loss of probability information in the calculation process.To solve this problem,two solutions are proposed in this paper:one is to assign an unknown membership degree to the missing probability information in the element with incomplete probability information,and then interact with the decision makers at any time in the calculation process to gradually improve the information of the unknown membership degree,so as to obtain accurate information integration results under the premise of ensuring efficiency;the other is to use a special way to deal with the probability information in the calculation process so as to make it attenuate as little as possible.b.The loss of evaluation information in the calculation process.In this paper,the idea of weighted average and geometric average is adopted,so that the evaluation information can be completely preserved on the premise that the calculation process is closed.c.A large number of membership degrees will be generated in the calculation process,which makes the integration process complex and difficult to apply.In this paper,combined with the idea of union,the number of membership degree in the calculation process is greatly reduced.(2)The continuity of probabilistic hesitant fuzzy information.Previous studies on continuous P-HFEs are only limited to the definition,and there is no follow-up.In fact,the continuous processing of discrete information can effectively simplify the process of probabilistic hesitant fuzzy information integration,which is very important for the practical application of the P-HFS with complex structure.Based on the knowledge of probability and statistics,two kinds of integration methods of continuous probabilistic hesitant fuzzy information by using mathematical derivation and computer fitting are presented in this paper.And they are applied to the evaluation of water resources emergency management schemes,which also verifies their effectiveness and reliability.This research result provides a possible direction for the continuity of fuzzy information.(3)Probabilistic hesitant fuzzy distance measure.Distance measure is an important tool of MAGDM.However,there are two problems in the current research of probabilistic hesitant fuzzy distance measure,that is,the poor mathematical properties and complex calculation process,which makes it less reliable and less applicable.Based on this,a probabilistic hesitant fuzzy distance measure based on the idea of splitting is proposed,which is also a follow-up research result of the information integration method proposed in this paper.It effectively solves the above two problems,makes the decision-making results more accurate and reliable,and widens the application range of probabilistic hesitant fuzzy distance measures.(4)Based on the above research results,combined with the classic TOPSIS method and other emerging decision-making theories,such as evidence-based reasoning,a new MAGDM method based on probabilistic hesitant fuzzy information is proposed.And it is applied to the subject evaluation problem.