Some Problem Of Gray Decision Theory Discussed

Society, economy, environment and other dynamic phenomenon is protean and intricate.In the system, with the existence of internal and external disturbances and the lower level,incomplete information is usual confronted in research practice.Therefore, in science,technology, social, economic, philosophy, thought and so many areas,uncertainty has beenbothering people’s work. But with the development of science and technology and theprogress of human society, the understanding of the uncertainty of all kinds of system havebeen gradually deepened, the research of uncertainty system is also increasingly deeper.Based on the more highly differentiated modern science and technology formed highlyintegrated big trend, which led to interdiscipline subject between the natural science andsocial science. Cross-sectional interdisciplinary reveals inner link between things more deeplyand more essential, which greatly contributed to the science and technology integrationprocess. Many fields of science is difficult to solve complex problems for a long time which iseasily solved with the cross-sectional interdisciplinary appear. The understanding of thenature and the evolution law of objective things has been gradually deepened with thecross-sectional interdisciplinary appear. In1982,the appearance of this new cross-sectionalinterdisciplinary—gray system theory made outstanding contribution to the study of themethod decisions. According to the present research situation of grey system theory, thisarticle proposes several kinds of grey forecast and decision methods:1Method of a Type ofMulti-objective Grey Situation Decision-making;2The Multi-attribute Decision Methodunder the Information of Three-parameter Interval Grey Number;3The Multi-attribute GreyTarget Decision Method for Attribute Value within Three-parameter Interval Grey Number;4Grey Multiple Attribute Decision Making Based on Entropy;5Grey Multiple Attribute GroupDecision Making Based on Relative Entropy.For multi-objective decision problems, the rationality of the target weight directly effectthe result of the decision accuracy. Because complexity and uncertainty of practical problems,in view of treat each target equally, the traditional grey situation decision making method can’t correctly reflect the different effect of each target in the decision-making process,usingentropy theory calculation of weight of the target, and discusses Method of a Type ofMulti-objective Grey Situation Decision-making. In current existing decision methods, thepeople only study the problems that the decision information is the real number, the intervalnumbers, the interval grey numbers. But when the decision information is three-parameterinterval numbers, the existed decision method can’t solve this kind of problem. Therefore,when the decision information is three-parameter interval grey numbers，disjoint degree anddominance relation of the three parameters interval number is defined and this theory isproved; then we figure out the equivalence relations which exist between the value ofadvantage relationship for decision making object and the sum three parameters intervalnumber values. Considering the uncertainty of goal weight, the multi-objective optimizationmodel is established based on disjoint degree and then goal weight is solved; the grey multi-attribute decision method under the information of three-parameter interval grey numbers isconstructed. Still, when the decision information is three-parameter interval numbers, themethod of interval grey numbers grey target decision is expanded. Then, the paper unites theexisted determining weigh method to explore the multi-attribute grey target decision methodunder the information of three-parameter interval grey number. Secondly, when the decisioninformation is three-parameter interval grey numbers，this paper put forward a kind of greymulti-attribute decision method, establishing multi-objective optimization model to determinethe goal weight based on entropy.Finally, in the process of group decision making, this paperput forward a kind of method to determine the expert weight based on relative entropy,establishing multi-objective optimization model, in which the attribute values are greynumbers；an example is also presented to illustrate the usefulness and effectiveness of themethods obtained in this paper.Above all, decision methods are simple and effective, can be operated easily withcomputers. They have provided the very good theory reference value for the beginners and theresearchers, provided advantageous theory support for the grey system theory development,expanded the space of developed of the grey theory.