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Obviously, {a1} is not a true reduction.
This time, the attribute reduction set E is NULL
So E={a2,a3} is a reduction and it is a true reduction.
“An Attribute and Value Reduction and Rule Extraction Algorithm”, Computer Engineering & Science,Vol. 30, pp. 61-63.(2008) [3] L.J.Huang, Z.M.Zhang,C.Y.Zhou,M.H.Huang, “Method of Data Reduction Based on Boolean Matrix”.
“A New Method of Complete Data Reduction Based on the Boolean Matrix”.

Data showed that three work stations namely, peeled trim station, arrangement before cooked station, and arrangement in tray station, needed to be improved.
Data in figure 1 was showed that 80 percent of cost was indicated at peeled trim station and arrangement before cooked station.
Then researchers selected those problems to solve and compare data between before and after improvement.
The improvement of process applying industrial technique is one of the best techniques to cost reduction [4].
Finally, the evaluation of proposed technique was recorded to compare between before and after improvement at each station using statistic data.

Energy consumption data, in the recent five years, are collected from more than 20 hotels in Shanghai and other eastern China regions.
These data exclude the development of non-star chain hotels.
All analytical data is shown in Table 1.
Data collection and assessment have been conducted in three-star hotels having been run for 15 to 20 years or so.
This data is a good hint for the relevant departments and enterprises on a good energy saving revelation, the reduction of power consumption and primary energy saving in hotels.

(2) Data preprocessing, feature extraction and data fusion.
The available sensor data and status monitoring data include the available online data and historical data off-line.
Appropriate data preprocessing methods include noise reduction, smoothing, imputing missing values and so on
(2) The data reduction method is applied to the research of PHM, and the method of extending the existing data to drive PHM.
PCA [2] is typical data reduction method

Reduction of NO by iron.
Fig. 3 presents the NO reduction efficiency by iron.
According to the thermodynamic calculation using the basic data from JANAF tables (1985), metallic iron could be completely oxidized to Fe2O3 at 700-900 °C and when the concentration of NO is lower than 500 ppm.
In the NO reduction experiments, the final temperature was 1100°C.
The NO reduction efficiencies increased when CO was added.

Especially, the energy consumption of the reduction furnace in the thermal reduction process is more than 70% of the total energy consumption.
The reduction jar is the core equipment of the reduction furnace, where the reduction reaction to produce Mg occurs at high temperature and under perfect vacuum.
The Mg-reduction jar is a consumable equipment rather than an energy-consuming one in the thermal reduction process of silicothermic method.
Cross Section Design of Reduction Jar The cross section of the traditional reduction jar is regular ring, as shown in Fig. 1(a).
Based on the data fitting of Table 1, the dependence of the elastic modulus E on the temperature T is E=-0.0843T+234

This paper takes 7 indexes, using AHP, obtained weights of the five power plants by integrated evaluation which can evaluate the effect of energy-saving and emissions reduction. 1 Evaluation indexes of energy-saving and emission reduction Many factors affect energy-saving and emission reduction of the coal-fired power generation.
We want to choose the power plant of the best effect by using the 7 indexes’ data of 5 power plants.
According the data in 依据表2中五个电厂的7个指标的数据，利用同样的方法构造第三层对第二层每个准则的判断矩阵。
Integrated Evaluation of Energy-saving and Emission Reduction.
Study on Evaluation System of coal-fired power generation energy-saving emission reduction.

Finally, the correctness and superiority of this algorithm are proved from the reduction experimental results of related data sets.
Due to factors such as a large amount of data and multi-sample properties, the attribute reduction in rough set theory, often fail to find the smallest reduction in the limited time period.
Faults features are selected based on the attribute reduction algorithm of rough set of particle swarm and the diagram of particle encoding is shown in Fig. 2: In terms of the selection of training set and the test set in evaluation of particle adaptability, 200 sets are respectively chosen randomly from normal data and three kinds of fault data as the training set from the primary simulating original data while 300 sets are respectively chosen randomly as the test set.
The obtained data shall be first preprocessed then dimensioned and normalized before corresponding fault feature extraction and selection.
Table 1 Results of Attribute Reduction in Each Data Set Name of the data set Number of the attributes record Number of the records Number of the reduction attributes Number of the minimum reduction attributes The excellent rate The running time Vote 17 435 9 8 90 6453.751 Wine 14 178 6 5 80 1082.538 Soybean_ large 36 307 9 9 100 4031.657 Zoo 17 101 6 5 80 463.136 Lymphography 19 148 6 6 100 737.375 Sponge 45 76 8 8 100 417.636 The following indicators will be used to compare and measure the influence of this algorithm on the reduction performance: (1) the number of reduction attributes, (2) the excellent rate, (3) the running time From the effect of the reduction, the algorithm can acquire a reduction on the relatively small number of attributes in all data sets, which is attributed to the larger search space of particle based on the optimization capability of the PSO algorithm.

Results show that characteristic of this method contained all the information of the original data, and dimension is less than GIS insulation defect category numbers, and it can realize data dimension reduction without information loss, which improve the pattern recognition rate.
Feature Extraction Based on the Class Mean Kernel Principal Component Dimension Reduction and Compression of PD Data.
According to the experiment in section 2.2, every set of data was extracted 24 characteristic parameters. 50 groups of sample data were got from every discharge model.
The N kinds sample data was set as .
Matrix-based Kernel Method for Large-scale Data Set.

Every original variable is conveyed by k factors (f1, f2, f3,……,fk) of the linear combination: (1) xi means the index data what measured in practice.
The method of data processing such as the influencing factor of energy-saving and emission-reduction can be referenced by literature [7], the energy efficiency x1 can be calculated by formula 3, as is shown below: (3) The rest data of this paper obtained from Jiangxi Statistical Yearbook 2008-2011, the unit of energy consumption was transformed to standard million tons of coal both in 2007 and 2008.
We need not to deal with positive indexes which are used in data analysis.
Data standardization is used to comparing variables and eliminating the influence which caused by difference of observation dimension and the order of magnitude.
Eigenvalue, contribution rate of eigenvalue and cumulative contribution rate can be obtained through data statistics from 2007 to 2010 by using SPSS software analysis, as is shown below: Table 1.