Research On The Theory And Application Of Decision-analysis Models Based On Grey System And Rough Set

With the ever-changing science and technology,human understanding of the objective world is experiencing a process of diversification.Decision-making environment has become increasingly complex,and the achieved decision-making information often presents grey uncertainty characteristics that are small sample and poor information with partial information known and the other unknown.Grey number is the basic unit of grey system theory which characterizes grey uncertainty.Therefore,the research on decision analysis methods under grey number information environment has important theoretical significance and application value.In this paper,the decision problems under grey information environment based on grey system and rough set were analyzed.The main research results are as follows:(1)The decision-making methods that consider the value distribution of grey numbers were studied.First,for a type of multi-attribute decision-making problems with interval grey numbers whose value distribution information is asymmetric,the whitening weight function was adopted to shown the value distribution information of interval grey number.The novel extended definitions,including kernel,degree of greyness,relative kernel,whitenization standard deviation,novel measure function and the gravity distance,of interval grey number were given based on the whitening weight function,Then,we introduced the thought of Markowitz's portfolio mean-variance methodology into the classical grey target decision method and proposed a multiscale grey target decision method that considers the value distribution of grey number.In addition,an entended hybrid grey TODIM method was put forward with considering the irrational psychological factors of decision-makers.(2)The knowledge acquisition method of incomplete information system under the grey dominance relation was studied.This paper analyzed the advantages and disadvantages of the existing interval dominance relations,and constructed a parameterized grey dominance relation according to the characteristics of information system with three-parameter interval grey number.On the basis of this,for information system with three-parameter interval grey number,an object sorting method based on comprehensive dominance degree and an attribute reduction method based on improved discernibility matrix were proposed respectively.And then,for the incomplete and inconsistent decision table,a heuristic algorithm of attribution reduction was taken into account based the significance of attributes.At last,the method of extracting simplest decision rules from incomplete decision table was discussed.(3)In order to evaluate the probability of ice disaster loss caused by the adverse events,and reveal the development between ice regime data and ice disaster risk under grey information environment,the combined model of grey system and rough set was constructed to assesse and analyze the ice disaster risk in Ning-Meng reach of yellow river.The research results not only enrich the risk identification,risk assessment and risk development analysis of ice disaster,but provide scientifically decision basis for ice prevention preparedness in Ning-Meng reach of Yellow River.