Three-way Decision-making Based On Decision Rough Sets In A Single-valued Neutrosophic Environment

The three-way decision mainly divide a neighborhood into three pair-wise disjoint regions and select appropriate behavioral strategies on some or all of these regions.Decision-theoretic rough set model is a typical three-way decision model,which divides the neighborhood into three disjoint regions by loss function.Few previous studies on decision-theoretic rough sets have considered the case where the loss function is the single-valued neutrosophic number,and the existing models cannot process the single-valued neurosophic information.Therefore,three three-way decision models based on decision rough set with single-valued neutrosophic information are proposed in this paper.The main difference between these models lies in the application of different ranking methods:the first is a ranking method based on cosine similarity measure,the second is a ranking method based on Euclidean distance,and the third is a ranking method based on scoring function and accuracy function that fully considers the relationship between the membership functions of the single-valued neutrosophic numbers.After the modeling,an algorithm is presented to show the key steps in the modeling process.Then,an example of breakfast shop location problem is selected to prove the rationality and practicability of each proposed model.Finally,this paper makes a comparative analysis among the three proposed models and between the aforementioned models and other relevant models previously studied.The thesis is divided into four chapters,the main contents are as follows:Chapter 1 Introduces the basic knowledge and concepts,those are essential in the process of modeling.For example,single-valued neutrosophic set,decisiontheoretic rough set,three-way decision and so on.Chapter 2 Introduces the cosine similarity measure,Euclidean distance and score function and accuracy function and corresponding ranking methods.And puts forward three new three-way decision model based on decision-theoretic rough set in single-value neutrosophic sets.At the same time,the key steps are clearly demonstrated through an algorithm in the application of those model.Chapter 3 By an example of the location of a breakfast shop,based on the algorithm given in the previous chapter,three models are established.In this way,the feasibility and rationality of the model establishment can be proved.At the same time,the characteristics of each model can be more intuitively felt,which provides reference for the subsequent application Suggestions.Chapter 4 Compares the three proposed models in this paper based on the decision-making process and results in chapter 3,pointed out the respective advantages,disadvantages and the applicable situation.The superiority between those model and other related models are also described in this chapter.Chapter 5 This chapter has made a general summary to the full text.