Theoretical Research And Decision-making Application Of The Matrix Of Dominant Support Parameters Of Soft Sets

Soft set is a mathematical tool for dealing with uncertain problems and has been widely used in many fields.Decision-making is inevitable in the human in the production and living problems,real data in the complex and changeable,while at the same time the ambiguity and uncertainty,how to gain the best decisions from huge amounts of data,how to make scientific decisions,and how to apply it in real life has been a decision in the field of scholars focus on the research subject.When information is uncertain and incomplete,it is difficult to make two-way decision,the three-way decision-making theories provide effective decision-making tools.Soft set theory is different from probability theory,rough set theory,fuzzy set theory and other mathematical models,and it has natural advantages when dealing with decision problems.The combination of soft set and other mathematical theories enriches the theory of soft set and enhances the ability of soft set to deal with practical problems.The matrix of dominant support parameters of soft set expresses the advantages and disadvantages between objects,analyzes and processes the soft set from the point of view of advantage relation,and has been successfully applied to the parameter reduction of soft set.In this paper,the properties and characteristics of thematrix of dominant support parameters of soft set are analyzed in detail,and the operation of the proposed soft set is studied by virtue of the matrix of dominant support parameters,as well as the application of the matrix of dominant support parameters of soft set to the three-way decision-making problem of the soft set.The specific work content of this paper is as follows:(1)Extending the logical operation of the soft set,proposes the fusion operation of the internal information of the soft set,and derives the change rule of the matrix of dominant support parameters of the soft set in the fusion process.First,discuss the binary operation on the Boolean set,introduce 0-1 vector Boolean operation,there are a total of 16 operations;secondly,use the 0-1 vector Boolean operation to fuse the internal information of the soft set to calculate the internal information of the soft set Fusion mathematical formula;then,describe and analyze the change rule of the0 matrix of dominant support parameters in the operation process,and prove its correctness;finally,give the automatic update algorithm of the advantage matrix.(2)Based on the research on the three-way decision-making concept of the soft set,the characteristics of different decision-making area objects in the qualitative model of the soft set three-way decision-making,and their performance characteristics in the matrix of dominant support parameters of soft set are analyzed.In the process of the model,the threshold pair ??),(is solved for complex situations,considering the object's pros and cons as the evaluation value of decision-making,the maximum advantage value of the soft set is used as the principle of dividing the threshold,and the object is divided into three different subsets,that is,positive,negative and boundary regions.The rationality of the algorithm is verified and analyzed through examples,which makes the three-way decision-making process of the soft set more efficient.