Group Decision Making Problem With Uncertainty Information Based On Compatibility

There are a variety of uncertain problems in real world.While probability theory,fuzzy sets,interval mathematics,rough set,and other mathematical tools are well-konwn and often useful approaches to describing uncertainty,each of these theories has its inherent difficulties.In recent years,experts proposed the fuzzy soft set has its specific advantages in dealing with uncertain information.In this paper,we mainly research the application of fuzzy soft set in uncertain decision theory.We convert the similarity based on fuzzy soft set problems to the discussion of the differences between fuzzy soft matrix,and analyze whatever differences can be acceptable,then we propose and study the concept and properties of similarity and compatibility of fuzzy soft matrix,and analyze its application in multiple attribute group decision making problems.Firstly,we review the problem and background of group decision problem,fuzzy soft set problem,compatibility problem and image recognition,and we give their significance,conclude their definition and operation rules.We summarize the development process of the research on compatibility from the two aspects of judgment matrix and preference relation.Secondly,we use the approach of image recognition to construct the similarity of fuzzy soft matrix,moreover,with the help of COWA operator,we handle the compatibility of fuzzy soft matrix and contrast with similarity.Then we propose two decision models,one is the expert decision model based on similarity and the other is the decision model based on similarity and compatibility.A numerical example is given to illustrate the rationality of the decision model with give the algorithm steps.In addition,we study the method of solving the inverse problem by using interval number information,we convert the interval number evaluation information given by the experts into reciprocal judgment matrix,and judge the difference of expert level by constructing statistics.Finally,we conclude the article and summarize the advantages and disadvantages of current research work and determine the goal of future research.