Fuzzy data envelopment analysis approach based on sample decision making units

The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.

Design of a spatial sampling scheme considering the spatial autocorrelation of crop acreage included in the sampling units

Information on crop acreage is important for formulating national food polices and economic planning. Spatial sampling, a combination of traditional sampling methods and remote sensing and geographic information system （GIS） technology, provides an efficient way to estimate crop acreage at the regional scale. Traditional sampling methods require that the sampling units should be independent of each other, but in practice there is often spatial autocorrelation among crop acreage contained in the sampling units. In this study, using Dehui County in Jilin Province, China, as the study area, we used a thematic crop map derived from Systeme Probatoire d＇Observation de la Terre （SPOT-5） imagery, cultivated land plots and digital elevation model data to explore the spatial autocorrelation characteristics among maize and rice acreage included in sampling units of different sizes, and analyzed the effects of different stratification criteria on the level of spatial autocorrelation of the two crop acreages within the sampling units. Moran＇s/, a global spatial autocorrelation index, was used to evaluate the spatial autocorrelation among the two crop acreages in this study. The results showed that although the spatial autocorrelation level among maize and rice acreages within the sampling units generally decreased with increasing sampling unit size, there was still a significant spatial autocorrelation among the two crop acreages included in the sampling units （Moran＇s / varied from 0.49 to 0.89）, irrespective of the sampling unit size. When the sampling unit size was less than 3000 m, the stratification design that used crop planting intensity （CPI） as the stratification criterion, with a stratum number of 5 and a stratum interval of 20% decreased the spatial autocorrelation level to almost zero for the maize and rice area included in sampling units within each stratum. Therefore, the traditional sampling methods can be used to estimate the two crop acreages. Compared with CPI, there was still a strong spatial correlation among the two crop acreages included in the sampling units belonging to each stratum when cultivated land fragmentation and ground slope were used as stratification criterion. As far as the selection of stratification criteria and sampling unit size is concerned, this study provides a basis for formulating a reasonable spatial sampling scheme to estimate crop acreage.

Application of Monetary Unit Sampling Based on Extended Audit Game

On account of the lack of monetary unit sampling( MUS), an extended audit game model based on uncertainty information,which centers on audit risk and combines audit game with statistical sampling,is established to improve the effectiveness of audit risks analysis and sampling errors control. In this paper,an example concerning practical problems is given to demonstrate the process of extended audit game and confirm the truth of the effectiveness of the method. Not only does this method enhance the role of audit technology and the extension of audit procedures in deterring material irregularities,but also helps the auditors measure and control audit risk and sample sizes under uncertainty,conducive to improving the effect of cost control,risk evaluation,and decisionmaking optimization in audit sampling.

Evaluating the impact of sampling schemes on leaf area index measurements from digital hemispherical photography in Larix principis-rupprechtii forest plots

Background:Digital hemispherical photography(DHP)is widely used to estimate the leaf area index(LAI)of forest plots due to its advantages of high efficiency and low cost.A crucial step in the LAI estimation of forest plots via DHP is choosing a sampling scheme.However,various sampling schemes involving DHP have been used for the LAI estimation of forest plots.To date,the impact of sampling schemes on LAI estimation from DHP has not been comprehensively investigated.Methods:In this study,13 commonly used sampling schemes which belong to five sampling types(i.e.dispersed,square,cross,transect and circle)were adopted in the LAI estimation of five Larix principis-rupprechtii plots(25m×25 m).An additional sampling scheme(with a sample size of 89)was generated on the basis of all the sample points of the 13 sampling schemes.Three typical inversion models and four canopy element clumping index(Ωe)algorithms were involved in the LAI estimation.The impacts of the sampling schemes on four variables,including gap fraction,Ωe,effective plant area index(PAIe)and LAI estimation from DHP were analysed.The LAI estimates obtained with different sampling schemes were then compared with those obtained from litter collection measurements.Results:Large differences were observed for all four variable estimates(i.e.gap fraction,Ωe,PAIe and LAI)under different sampling schemes.The differences in impact of sampling schemes on LAI estimation were not obvious for the three inversion models,if the fourΩe algorithms,except for the traditional gap-size analysis algorithm were adopted in the estimation.The accuracy of LAI estimation was not always improved with an increase in sample size.Moreover,results indicated that with the appropriate inversion model,Ωe algorithm and sampling scheme,the maximum estimation error of DHP-estimated LAI at elementary sampling unit can be less than 20%,which is required by the global climate observing system,except in forest plots with extremely large LAI values(~>6.0).However,obtaining an LAI from DHP with an estimation error lower than 5%is impossible regardless of which combination of inversion model,Ωe algorithm and sampling scheme is used.Conclusion:The LAI estimation of L.principis-rupprechtii forests from DHP was largely affected by the sampling schemes adopted in the estimation.Thus,the sampling scheme should be seriously considered in the LAI estimation.One square and two transect sampling schemes(with sample sizes ranging from 3 to 9)were recommended to be used to estimate the LAI of L.principis-rupprechtii forests with the smallest mean relative error(MRE).By contrast,three cross and one dispersed sampling schemes were identified to provide LAI estimates with relatively large MREs.

The assessment of soil loss by water erosion in China

Soil erosion is a major environmental problem in China.Planning for soil erosion control requires accurate soil erosion rate and spatial distribution information.The aim of this article is to present the methods and results of the national soil erosion survey of China completed in 2011.A multi-stage,unequal probability,systematic area sampling method was employed.A total of 32,948 sample units,which were either 0.2-3 km2 small catchments or 1 km2 grids,were investigated on site.Soil erosion rates were calculated with the Chinese Soil Loss Equation in 10 m by 10 m grids for each sample unit,along with the area of soil loss exceeding the soil loss tolerance and the proportion of area in excess of soil loss tolerance relative to the total land area of the sample units.Maps were created by using a spatial interpolation method at national,river basin,and provincial scales.Results showed that the calculated average soil erosion rate was 5 t ha-1 yr-1 in China,and was 18.2 t ha-1 yr-1 for sloped,cultivated cropland.Intensive soil erosion occurred on cropland,overgrazing grassland,and sparsely forested land.The proportions of soil loss tolerance exceedance areas of sample units were interpolated through the country in 250 m grids.The national average ratio was 13.5%,which represents the area of land in China that requires the implementation of soil conservation practices.These survey results and the maps provide the basic information for national conservation planning and policymaking.