Uncertainty Measures Of Several Information Granules And Its Application In Multi-attribute Decision-making

With the development of social economy,the problem of multi-attribute decision-making is becoming more and more complex.Traditional decision-making methods are often difficult to effectively evaluate the uncertainty in multi-attribute decision-making.In particular,when there are differences among multiple decision makers,most decision-making models lack flexible and efficient means to deal with them.For these reasons,this paper proposes some uncertainty measures based on information granules of different information systems by combining fuzzy theory,rough set theory,soft set theory and information entropy theory,and applies it to multi-attribute decision-making problem.This paper combines a variety of mathematical tools to deal with uncertainty and closely relates to practical applications,so that mathematical theory research has more practical value.The main research contents are as follows:(1)Based on the granular structure of soft neighborhood and information entropy theory,five soft neighborhood entropy and its variants are defined,and the relationship between them and some important properties are explored.On this basis,two multi-attribute decision-making methods with soft neighborhood entropy are proposed.By comparison,it is found that the decision results of soft neighborhood entropy of type 1 and type 2 are more distinct,and the effectiveness of the method is illustrated by relevant examples.(2)In view of the problem that the traditional dominance relationship is not fine enough,the dominance degree parameter is introduced into fuzzy information systems,and a new superior-inferior relation is proposed.By means of this relation,we construct the information granular structure of superior-inferior relation class and propose a new uncertainty measure,namely superior-inferior relation entropy and its variants,which can characterize the superior-inferior degree between the two samples from different granularity levels.We then study the important properties of the entropy.Furthermore,a new multi-attribute decisionmaking method is established based on decision theory.Finally,through comparative analysis,Spearman’s rank correlation coefficient and sensitivity analysis,the validity and feasibility of this decision-making method are illustrated.(3)Three-way decision is a new decision making tool which can effectively reduce decision risk.But it still has some limitations in practical application.On the one hand,most of existing three-way decision models are not suitable for heterogeneous environments with incomplete decision information.On the other hand,it is difficult to obtain effective decision information for multi-attribute decisionmaking problems with multiple decision makers.Therefore,this paper proposes a new three-way multi-attribute decision model.Firstly,the weighted conditional probability is constructed by tolerance granule.Secondly,a new uncertainty measure,tolerance entropy,is proposed based on tolerance information granule.It considers both upper and lower approximation information,and can effectively characterize the uncertainty in heterogeneous incomplete environments.Finally,a three-way multiattribute decision-making model based on tolerance entropy is constructed.Experimental analysis show the advantages of the proposed model.