The classical rough set theory is established based on the equivalent relation,but for the information systems containing numerical attribute value must be discredited first,resulting in loss of information.The weights based on the concept of algebra(the influence of the attribute to definite classification subset) and the concept of granularity(the influence of the attribute to indefinite classification subset) are carried on the organic integration based on dominance relationship.To computer a new attribute importance in rough set,providing an optimal determining weights method.The method is applied to agricultural PPI,which shows that the method is feasible,and makes the evaluation results consistent with objective evaluation information and meet the requirements of decision maker.

Aiming at the difference and antinomy of the weighting in the rough set,the relative entropy of two probability distributions is extended to the relative entropy of two one-dimension vectors.The relative entropy is viewed as a distance measurement.The values range of optimal weights are determined by determinations of attribute importance in algebra view and knowledge granularity view respectively,and a single objective optimization model is established on the grounds that attribute values of alternatives are far away from negative ideal values and as close as to ideal values.On the other hand,since the limitation of equivalence relations,dominance relations are introduced to the method of determining the attribute weights.The weights in algebra view and knowledge granularity view are carried on the organic integration by the relative entropy optimization model based on dominance relations,in order to obtain optimal solution of the attributes in Multiple Attribute Decision Making(MADM).The analysis result indicates the validity and efficiency of the model.

Based on membership function of attribute in rough set,two methods of using loading matrix of common factors and fuzzy entropy of rough set are put forward to determine the weighted standard decision matrix,and then an ideal solution and a negative-ideal solution are chosen to calculate the distance between the alternatives in the reality and them.The measurement is regarded as a comprehensive evaluation criteria to determine which is optimal in all alternatives.TOPSIS method is improved from the two aspects of statistics and informatics,the former has determined the common factors which have an effect to all original variables in the process of the original variables transforming into principal components,using eigenvalues of principal components and loading matrix of common factors to definite weight,it reflects the relative importance of each variable to common factors,and overcomes the influence of subjective factors,the reality relations between the samples are reflected objectively.The latter has measured the information size of attribute truthfully,different attribute has dif- ferent information capacity for different decision scheme.

In the comprehensive evaluation,the allocation of weights affects directly the accuracy and scientificity of evaluation results.Based on gray rough sets,a new method of determining weight in comprehensive evaluation is put forward in this paper,making the weight coefficient is easy to explain,and more objective and accurate.Energy consumption of East China is analyzed,obtaining comprehensive place for energy consumption of six provinces and one city in East China,and providing some suggestions for energy distribution.

In the comprehensive evaluation,the allocation of weights affects directly the accuracy and scientificity of evaluation results.Based on fuzzy entropy of the rough sets,a new method of determining weight in comprehensive evaluation is put forward in this paper,expressed effectively the different indicators to the different appraisal schemes have different information capacity,therefore each indicator to the different appraisal schemes should be given different weights,making the weight coefficient is easy to explain,and more objective and accurate.City facility level of North China,Northeast,and East China is analyzed by TOPSIS method,obtaining comprehensive place for city facility level of the three regions,the advantages and disadvantages of the three regions for city facility construction are discovered,and providing some suggestions for city facility construction of the three regions.

The application of RS&SVR method,which is support vector machine regression(SVR) based on attribute reduction algorithm of rough sets,on forecast of China's power supply is dealt with in this paper.According to historical data of power output and its influencing factors,a decision table is built up,and discretization of continuous attributes in the table is done by means of dynamic layer cluster.Using the attribute reduction algorithm to eliminate some redundant attributes from the table,the kernel factors are determined.Taking these kernel factors as the attributes of both training and testing samples,the power supply forecasting is conducted.Five-year forecasting results show that,compared with SVR which chooses attributes of input vectors in light of experience,the method of RS&SVR could make use of less but cardinal predictors' information,and the forecasting accuracy is improved.