Research On Data Filling And Decision-Making Algorithms Based On Interval-Valued Fuzzy Soft Sets

The interval-valued fuzzy soft set is extended by the soft set and interval-valued fuzzy set,which is an important mathematical tool for processing fuzzy information.The research on decision-making and parameter reduction algorithms based on complete interval-valued fuzzy soft sets has become very active.However,in practical applications,we have to deal with incomplete interval-valued fuzzy soft set data,and how to make efficient decisions on these filled fuzzy data is also crucial.Therefore,this thesis proposes a new data filling method and the related decision-making algorithm based on interval-valued fuzzy soft sets,and the effectiveness and feasibility of the proposed algorithms are demonstrated through experiments.The research in this thesis can be summarized into the following three aspects:(1)A KNN data filling(KNNDF)method based on incomplete interval-valued fuzzy soft sets is proposed.To address the problems of subjectivity in threshold setting,low accuracy of data filling results and high error rate in existing data filling methods,this thesis proposes a KNN data filling method based on incomplete interval-valued fuzzy soft sets.This method avoids the subjectivity of the threshold setting process by setting the attribute-based combination rules.The missing data is filled with the average of K complete nearest neighbors.Through comparative experiments,it is verified that the average accuracy and error rate of the KNN data filling methods is superior to existing methods.(2)A multi-attribute three-way decisions based on ideal solutions under interval-valued fuzzy soft set environment is proposed.The existing multi-attribute decision-making methods can only rank alternatives and cannot directly accept or reject an alternative,which is detrimental to the efficient decision-making process.This thesis proposes a multi-attribute three-way decisions based on ideal solutions for interval-valued fuzzy soft set.By introducing the idea of ideal solution,multi-attribute three-way decision is extended to interval-valued fuzzy soft set.It is clear that our method provides a more flexible and general model for dealing with uncertain multi-attribute decision-making problems.This method can not only get the sorting results of the alternatives,but also divide the alternatives into positive region,boundary region,negative region,which makes the decision results more reasonable and effective.(3)Application of the proposed data filling and decision-making algorithms based on interval-valued fuzzy soft sets.In this thesis,the proposed data filling and decision-making algorithms are applied to practical cases,respectively.The proposed scheme provides efficient and powerful theoretical support for decision makers.The effectiveness and feasibility of the proposed algorithms are validated through experiments.