Variable fuzzy assessment of water use efficiency and benefits in irrigation district

Ming-hui Wang，Guang-heng Shao*，Jia-jia Meng，Chang-ren Chen，Dou-ou Huang

aSuqian Water Survey and Design Research Co.Ltd，Suqian 223800，PR China

bKey Laboratory of Efficient Irrigation-Drainage and Agricultural Soil-Water Environment in Southern China，Ministry of Education，College of Water Conservancy and Hydropower Engineering，Hohai University，Nanjing 210098，PR China

cHuai'an Water Resources Planning Office，Huai'an 223005，PR China

dWater Resources Department of Jiangsu Province，Nanjing 210029，PR China

Received 10 December 2013；accepted 20 June 2014

Available online 17 August 2015

Variable fuzzy assessment of water use efficiency and benefits in irrigation district

Ming-hui Wanga，b，Guang-cheng Shaob，*，Jia-jia Mengc，Chang-ren Chend，Dou-dou Huangb

aSuqian Water Survey and Design Research Co.Ltd，Suqian 223800，PR China

bKey Laboratory of Efficient Irrigation-Drainage and Agricultural Soil-Water Environment in Southern China，Ministry of Education，College of Water Conservancy and Hydropower Engineering，Hohai University，Nanjing 210098，PR China

cHuai'an Water Resources Planning Office，Huai'an 223005，PR China

dWater Resources Department of Jiangsu Province，Nanjing 210029，PR China

Received 10 December 2013；accepted 20 June 2014

Available online 17 August 2015

Abstract

In order to scientifically and reasonably evaluate water use efficiency and benefits in irrigation districts，a variable fuzzy assessment model was established.The model can reasonably determine the relative membership degree and relative membership function of the sample indices in each index's standard interval，and obtain the evaluation level of the sample through the change of model parameters.According to the actual situation of the Beitun Irrigation District，which is located in Fuhai County，in Altay City，Xinjiang Uyghur Autonomous Region，five indices were selected as evaluation factors，including the canal water utilization coefficient，field water utilization coefficient，crop water productivity，effective irrigation rate in farmland，and water-saving irrigation area ratio.The water use efficiency and benefits in the Beitun Irrigation District in different years were evaluated with the model.The results showed that the comprehensive evaluation indices from 2006 to 2008 were all at the third level（medium efficiency），while the index in 2009 increased slightly，falling between the second level（relatively high efficiency）and third level，indicating an improvement in the water use efficiency and benefits in the Beitun Irrigation District，which in turn showed that the model was reliable and easy to use.This model can be used to assess the water use efficiency and benefits in similar irrigation districts.

©2015 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license（http:// creativecommons.org/licenses/by-nc-nd/4.0/）.

Variable fuzzy assessment；Water use efficiency and benefits；Beitun Irrigation District

1.Introduction

In recent years，China has focused on the development，utilization，conservation，and protection of water resources，and formulated a series of policies and regulations to improve the water use efficiency and benefits in irrigation districts（Ye et al.，2011），resulting in an increase in irrigation water use efficiency.However，distribution of the available water resources will change significantly in the coming decades due to an increase in the water requirements of other sectors，such as the natural environment，and a foreseen reduction in rainfall due to climate change effects in China（Cruz-Blanco et al.，2014）.There is still a large gap between China and developed countries in the water use efficiency and benefits.Thus，in order to ease severe water shortage pressure in China，we should further improve the irrigation efficiency and fully explore the potential of agricultural water-saving measures（including strengthening and perfecting irrigation and water supply projects，and establishing efficient water-saving projects in the field）.

Irrigation water use represents the major fresh water use in the world（Braud et al.，2013）.According to the Food and Agriculture Organization，about 60%of total water resourcesall over the world are used for agricultural irrigation（Lin et al.，2012）.The role of water in agricultural production is very complex and affected by many factors（Kaneko et al.，2004）.Water resources utilization varies greatly across different irrigation districts in China，so it is necessary to evaluate the water use efficiency and benefits in each irrigation district with a scientific and reasonable method，which can provide a scientific basis for making decisions and organizing subsequent water conservation work.Agricultural water use efficiency is a key index in assessment of irrigation water use from the water source to the crop（Martin et al.，2004）. Traditionally，field experiments are conducted to quantify and evaluate water management practices in irrigation systems（Singh et al.，2006）.

There have been many studies offering methods of evaluating the water use efficiency and benefits in irrigation districts，including the fuzzy comprehensive evaluation method put forward by Wang（2011），Zhang and Fan（2001），and Ye et al.（2011）；the comprehensive evaluation method based on principal component analysis used by Chen et al.（2011）；the remote sensing-based method（Cruz-Blanco et al.，2014）；and distributed ecohydrological modeling（Singh et al.，2006）. However，these methods all have their own limitations.For the fuzzy comprehensive evaluation method，the algorithm used to process large and small values is unreasonable and some problems related to the maximum membership degree principle need to be solved（Wang et al.，2007）.For the comprehensive evaluation method based on principal component analysis，the selection of different eigenvalue vector combinations may cause a wide range of fluctuations in evaluation results（Sun and Qian，2009）.In general，specific recommendations obtained from field experiments cannot be generalized to the regional level with different ecohydrological conditions（Singh et al.，2006）.There is a general consensus about the importance of finding a more effective and universal way to assess the water use efficiency and benefits in irrigation districts.

Of the developed methods，the variable fuzzy evaluation method has proved to have the highest reliability and operability（Huang et al.，2013；Zhao and Chen，2008），and it can scientifically and reasonably determine the relative membership degree and relative membership function of sample indices in the standard interval of each index（Huang et al.，2013）.The variable fuzzy evaluation method has also been widely used in many fields，such as flood risk analysis and evaluation（Li et al.，2012）and reservoir water quality evaluation（Huang et al.，2013）.Compared to other methods，it can be used with less quantitative information and it can simplify the mathematical process so that we can analyze complex multi-criteria problems（Zhang，2009）.However，there has been little examination of the method when applied in the evaluation of the water use efficiency and benefits in an irrigation district.Therefore，the objective of this study，with the Beitun Irrigation District（in Xinjiang Uyghur Autonomous Region，in China）as an example，was to determine the reasonable water use efficiency and to evaluate the benefits of water use in the irrigation district using the variable fuzzy evaluation method.

2.Model of variable fuzzy assessment

We assume that U is a fuzzy concept，andandrepresent the attractability and repellency，respectively.For any element u（u∈U）is the relative membership degree of u tois the relative membership degree of u to，and.

We assume that X0=［a，b］is the attraction domain of Von the real axis，X=［c，d］is the range domain containing X0（X0⊂X），M is the point ofin the attraction domain［a，b］，and x is a random point.The positional relationships among points x and M and domains［a，b］and［c，d］are shown in Fig.1.

It is hypothesized that there is a sample index matrix X for identifying the water use efficiency and benefits in an irrigation district:

where xijis the ith index of the jth sample；i=1，2，…，m，where m is the total number of indices；and j=1，2，…，n，where n is the total number of samples.

Every index can be evaluated by k levels and a matrix is obtained that contains m×k index standard values:

Fig.1.Positional relationship among points x and M and domains［a，b］and［c，d］.

where yihis the standard value of the ith index at the hth level，and h=1，2，…，k.

The attraction domain matrix Iaband the range domain matrix Icdare determined based on matrix Yand the measured data in the target irrigation district（Wei et al.，2013）:

The matrix composed by point Mihofin the attraction domain［aih，bih］is determined:

The positional relationship between points xijand Mihis determined according to Eqs.（7）through（9），and then the relative difference degreeis calculated according to Eqs.（2）through（4）.Finally，the relative membership degreeof index xijto level h can be obtained according to Eq.（1）.

The relative membership degree matrix of index xijto level h can be express as

The comprehensive relative membership degree of sample j to level h is calculated based on the formula provided by Meng et al.（2012）:

The comprehensive relative membership degree matrix U′before normalization processing is obtained based on Eq.（11）:

The comprehensive relative membership degree matrix U after normalization processing of Eq.（12）is obtained:

The level eigenvalue vector H can be expressed as

H is used to evaluate the level of the samples（Chen，2005）.

3.Case study

3.1.Indices and levels

Using data obtained from the Beitun Irrigation District from Wang（2011）and with reference to irrigation water use efficiency obtained in experimental research，five indices were used to characterize the agricultural water use efficiency and benefits:（1）the canal water utilization coefficient ηc，which represents the utilization of all of the canal water and is multiplied by the water use efficiency of the main canal，branch canal，lateral canal，agricultural drainage，and sublateral canal；（2）the field water utilization coefficient ηf，which is the ratio of the net irrigation water volume to the water volume in the sublateral canal；（3）the crop water productivity Wp，which is the ratio of the yield to the evapotranspiration；（4）the effective irrigation rate in farmland ηe，which is the ratio of the effective irrigation area to the cultivated area；and（5）the water-saving irrigation area ratio Ap，which is the ratio of the water-saving irrigation area to the cultivated area.

The agricultural water use efficiency and benefits in an irrigation district are classified into five levels:level 1，level 2，level 3，level 4，and level 5.These five levels，which are different from those in Wang（2011），represent high efficiency，relatively high efficiency，medium efficiency，relatively low efficiency，and low efficiency.The standard values of the five indices in each level are listed in Table 1.

3.2.Calculation process

The index values for evaluating agricultural water use efficiency and benefits in the Beitun Irrigation District in different years are listed in Table 2.

Table 1Evaluation standard of efficiency and benefits of agricultural water use in Beitun Irrigation District.

Table 2Index values for evaluating efficiency and benefits of agricultural water use in Beitun Irrigation District.

According to Tables 1 and 2，we can obtain

The attraction domain matrix，the range domain matrix，and the matrix composed by point Mihare determined based on matrix Y and the actual situation in the Beitun Irrigation District:

The positional relationships between xijand Mihare determined according to the matrixes Iab，Icd，and M.Thenandare calculated.We can obtain

According to the consistency theorem used to determine the importance of indices（Chen，2002），pairwise comparison of the importance of indices，and the relation table between the tone operators and relative membership degree，the weight vector of the five indices before normalization processing is determined，as follows:

The weight vector after normalization processing is as follows:

The relative membership degrees in the Beitun Irrigation District in different years were calculated，using the data from 2007（j=2）as an example to explain the solution process.We can determine that the relative membership degree column matrix when j=2 is u32=［0.350 0.600 0.717 0.750 0］Tbased on matrix U3.

Using the values p=1 and α=2，when j=2 and h=3，Eq.（11）can be expressed as

Substituting the values of u32and ω into the above equation，we can obtain2u′3=0.660.Similarly，we can obtain2u′1=0，2u′2=0.080，2u′4=0.203，and2u′5=0.004.The comprehensive relative membership degree vector when j=2 is as follows:2u′=［00.0800.660 0.2030.004］T

A similar calculation is made when j=1，3，and 4，and the comprehensive relative membership degree matrix is obtained before normalization processing，as follows:

After normalization processing，the matrix U is obtained as follows:

The level eigenvalue vector of efficiency and benefits of agricultural water use in the Beitun Irrigation District is obtained according to Eq.（15）:

The weight vector of six indices provided by Wang（2011）is as follows:

The weight of the irrigation water utilization coefficient is removedfromtheweightvectormentionedabove，andamodified weightvectoroftheremainingfiveindicesthatisthesameasthose selected in this study can be obtained.The normalized modified weight vector after normalization processing is as follows:

ωm=［0.1690.284 0.4070.0700.070］

Substituting the normalized modified weight vector into Eq.（11），the comprehensive relative membership degree is calculated，and then the level eigenvalue vector is obtained，as shown in Table 3.

Table 3 shows that the level eigenvalue is stable within a certain range after the change of the weights，which suggeststhat the variable fuzzy assessment model used in this study is little influenced by human disturbance and the results are reasonable and objective.

Table 3Results of evaluation obtained from different weight vectors.

In order to obtain more reasonable results，the variable fuzzy assessment models with different parameter values of α and p were used to calculate the level eigenvalues based on the weight vector in this study，and the evaluation results are shown in Table 4.

3.3.Results analysis and discussion

From Table 4，it can be observed that the level eigenvalue of agricultural water use efficiency and benefits in the Beitun Irrigation District is stable over a small range when the model parameters are altered，which proves that the evaluation results obtained in this study are highly reliable.Table 4 shows that the comprehensive evaluation indices from 2006 to 2008 were all at the third level（medium efficiency），while the index in 2009 increased slightly，falling between the second level（relatively high efficiency）and third level，indicating an improvement in efficiency and benefits of the agricultural water use in the Beitun Irrigation District，which is attributed to some water-saving measures.These measures including improving the supporting facilities for irrigation water distribution in the Beitun Irrigation District，rapidly developing efficient water-saving projects，and efficiently controlling seepage losses in water conveyance and irrigation.

There are some differences between the variable fuzzy evaluation model and the traditional one.The variable fuzzy evaluationmodelcanadoptseveralweightvectors（twoweightvectors were used in this study:one determined by the variable fuzzy method，andtheotherobtainedfromWang（2011）orchangethe model type（one linear model and three nonlinear models were usedinthisstudy）bychangingparameters（α and p）onthe basis oftheprimarymodel.Thelevelsofthesamplesweredetermined after the comprehensive analysis of more evaluation results，and these levels are more reasonable and reliable than the levels determined from only one evaluation result（Li et al.，2012）.

4.Conclusions

The variable fuzzy assessment model for evaluation of agricultural water use efficiency and benefits in an irrigation district was introduced in this paper.This model can determine the relativemembershipdegreeandrelativemembershipfunctionin eachindex'sstandardinterval，andobtainareasonableevaluationresult through the change of model parameters.The model was appliedtotheBeitunIrrigationDistrict.Theresultsshowthatthe water use efficiency and benefits in the Beitun Irrigation District from2006to2008wereallatthethirdlevel（mediumefficiency），but increased a little bit in 2009，reaching a level between the second level（relatively high efficiency）and third level.The model has some practical value in the evaluation of water use efficiency and benefits of in irrigation districts.

Table 4Evaluation results of agricultural water use efficiency and benefits.

References

Braud，I.，Tilmant，F.，Samie，R.，Goff，I.L.，2013.Assessment of the SiSPAT SVAT Model for irrigation estimation in south-east France.Procedia Environ.Sci.19，747-756.http://dx.doi.org/10.1016/j.proenv.2013.06.083.

Chen，H.M.，Ning，Y.C.，Sun，X.D.，2011.Production safety evaluation model based on principal component analysis.Procedia Eng.26，1949-1955. http://dx.doi.org/10.1016/j.proeng.2011.11.2389.

Chen，S.Y.，2002.Fuzzy Recognition Theory and Application of Complex Water Resources System Optimization.Jilin University Press，Changchun（in Chinese）.

Chen，S.Y.，2005.Engineering variable fuzzy set theory and model:The fuzzy mathematical foundations of hydrology and water resources.J.Dalian Univ.Technol.45（2），308-312（in Chinese）.

Cruz-Blanco，M.，Lorite，I.J.，Santos，C.，2014.An innovative remote sensing based reference evapotranspiration method to support irrigation water management under semi-arid conditions.Agric.Water Manag.131（1），135-145.http://dx.doi.org/10.1016/j.agwat.2013.09.017.

Huang，X.，Li，H.L.，Qiu，L.，2013.Variable fuzzy set based model for evaluation of reservoir water quality.Water Resour.Hydropower Eng.44（7），21-24（in Chinese）.

Kaneko，S.，Tanaka，K.，Toyota，T.，Managi，S.，2004.Water efficiency of agricultural production in China:Regional comparison from 1999 to 2002. Int.J.Agric.Resour.Gov.Ecol.3（3-4），231-251.http://dx.doi.org/ 10.1504/IJARGE.2004.006038.

Li，Q.，Zhou，J.Z.，Liu，D.H.，Jiang，X.W.，2012.Research on flood risk analysis and evaluation method based on variable fuzzy sets and information diffusion.Saf.Sci.50（5），1275-1283.http://dx.doi.org/10.1016/ j.ssci.2012.01.007.

Lin，Y.C.，Zeng，Z.H.，Ren，C.Z.，Hu，Y.G.，2012.Water use efficiency and physiological responses of oat under alternate partial root-zone irrigation in the semiarid areas of northeast China.Procedia Eng.28，33-42.http:// dx.doi.org/10.1016/j.proeng.2012.01.679.

Martin，P.H.，LeBoeuf，E.J.，Daniel，E.B.，Dobbins，J.P.，Abkowitz，M.D.，2004.Development of a GIS-based spill management information system. J.Hazard.Mater.112（3）， 239-252.http://dx.doi.org/10.1016/ j.jhazmat.2004.05.014.

Meng，L.H.，Chen，Y.N.，Xu，X.M.，Li，W.H.，2012.Assessing water resources carrying capacity in Tarim River Basin using a variable fuzzy model.Bull. Soil Water Conserv.32（2），162-167（in Chinese）.

Singh，R.，Kroes，J.G.，van Dam，J.C.，Feddes，R.A.，2006.Distributed ecohydrological modeling to evaluate the performance ofirrigation system in Sirsa district，India:I.Currentwatermanagementanditsproductivity.J.Hydrology 329（3-4），692-713.http://dx.doi.org/10.1016/j.jhydrol.2006.03.037.

Sun，L.P.，Qian，W.Y.，2009.An improved method based on principal component analysis for the comprehensive evaluation.Math.Pract.Theory 39（18），15-20（in Chinese）.

Wang，G.H.，2011.Evaluation of water use efficiency and benefit of Beitun Irrigation District.Water Sav.Irrig.36（6），60-62（in Chinese）.

Wang，J.H.，Qian，J.Z.，Li，R.Z.，Chen，T.H.，2007.Improvement and application of fuzzy probabilistic method.Syst.Eng.-Theory Pract.27（5），173-176（in Chinese）.

Wei，R.J.，Liang，C.，Ren，C.，Zhao，L.，2013.Variable fuzzy recognition method of water resources security evaluation in Songhua Dam.South-to-North Water Transfers Water Sci.Technol.11（2），1-5.http://dx.doi.org/ 10.3724/SP.J.1201.2013.02001（in Chinese）.

Ye，L.T.，Sun，S.H.，Wang，Y.R.，Yu，P.，2011.Evaluation of utilization efficiency and benefit of irrigation water for Lizigu Irrigation areas in Tianjin City.Rural Water Hydropower China 53（2），105-108（in Chinese）.

Zhang，Q.，2009.Research on the thin coal mining equipment decision model and method based on catastrophe evaluation theory.Adv.Intelligent Soft Comput.62（2），511-516.http://dx.doi.org/10.1007/978-3-642-03664-4_56.

Zhang，X.B.，Fan，S.G.，2001.Estimating crop-specific production technologies in Chinese agriculture:A generalized maximum entropy approach. Am.J.Agric.Econ.83，378-388.

Zhao，R.H.，Chen，S.Y.，2008.Application of fuzzy variable set model to evaluation of rural hydro-modernization.J.Hydraulic Eng.39（2），218-223（in Chinese）.

This work was supported by the National Natural Science Foundation of China（Grant No.51279059），the Excellent Innovation Talents Plan of Hohai University，and the Fundamental Research Funds for the Central Universities.

*Corresponding author.

E-mail address:sgcln@126.com（Guang-cheng Shao）.

Peer review under responsibility of Hohai University.

http://dx.doi.org/10.1016/j.wse.2014.06.002

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