An Improved Analytic Hierarchy Process and Application in Grain Production

June2012 Vol.19 No.2 66-70心ScienceDirect，Journal of Northeast Agricultural University (English Edition)Available online at www.sciencedirect.comAn lmproved Analytic Hierarchy Process and Application in GrainProductionGao Chun-yul"?, and Wang Wen-long2' College of Science, Northeast Agricultural University, Harbin 150030, China' College of Science, Northeast Foresty University, Harbin 150040, ChinaAbstract: Value analysis of grain production infuencing factors is a complex decision problem. This paper introduced a modifedAnalytic Hierarchy Process (AHP) accumulation factor, namely Solving Weight by AHP's Accumulation Factor Sequence EvaluatingData. We used the arithmetical average to replace the expert marking, so that the possible decision mistakes by the subjctivejudgments could be avoided. We computed the case with this method, which obtained atribute value of 17 influencing factors of thepotential food production in Heilongjiang Province, and the result of which was reasonable.Key words: Analytic Hierarchy Process (AHP), accumulation factor, potential food productionCLC number: S11;0223Document code: AArticle ID: 1006-8104(2012)-02-0066-05of grain production for the exports, and accelerateIntroductionthe development to grain production in HeilongjiangProvince.The safety problem of grain is the most importantthing to China population, the key isue of ensuring Method Descriptionsthe grain safety is to protect the main production area;as a main grain production area and an importantAnalytic Hierarchy Process (AHP) accumulation factorcommodity grain base, Heilongjiang Province holds ais an improved AHP method which has developedcrucial position in grain production. In company withsince the eighties of last century. The method usesthe transfer of the main production area to the north, power function product instead of linear summationstudying the development countermeasure and probingwhen thinking about the importance quantizationinto questions of grain production have operationscheme (Engle, 1987). Although accumulation factorsignificance to the development of Heilongjiang method retains merits of the traditional AHP andgrain production. We put forward the problems ofalso overcomes reverse phenomena of AHP whenHeilongjiang grain production and made suggestionsdecision system is changing, it needs the markingto resolve the problems. Studying the problems of by many experts that would lead to subjectivegrain in Heilongjiang could provide reference to judgments. Correlation coefficient method is aconstitute policies of main grain production area andcommonly used objective method of value assignmentgenerate regional development advantage of grainbut the calculation process is complex (Liu, 1997).production, offer foundation to study the problemsThis paper attempted to use Solving Weight by中国煤化工Received 12 May 2011Gao Chun-yu (1976-), femalc, lecturer, engaged in the research of mathematic ecology. E-MYHCNMH GE-mail: xuebaoenglish@ neau.edu.cnGao Chun-yu et al. An Improved Analytic Hierarchy Process and Application in Grain Production.67.AHP's Accumulation F actor Sequence Evaluatingthe arithmetic average of the minimum and maximumData to give a reasonable weight. The improvedinto nine, the factors were identified as one to ninemethod is a relatively simple objective method(a total of nine grades), that is to say the ninth levelof value assignment, it has the characteristics ofcorresponding to the maximum and minimum valuesrank preservation of accumulation factor as well ascorresponding to the first level, the other filledeliminating the deviation effect brought by subjective between one to nine. The results were recorded as x,factor.which shall be the property value of the i indicator.Solving Weight by AHP's Accumulation FactorSequence Evaluating Data method is firstly to sort Calculated property sub-criteria level valueson the index layer to obtain the actual value of eachand contribution coefficientsindex and establish power function y=xx.x.",As the criteria layer can contain multiple layers andthen calculates arithmetic mean of indexes x, x2,each layer of sub-criteria should be a number of.. x, of index layer, and then divides the Intervalfactors which have on the target layer with the trendconstituted by the arithmetic average of the minimumfactors to reflect, so the order of property values in theand maximum into nine, then calculates attribute valuecalculation is started from the bottom to the top. Weof each layers, then takes logarithm of power function,could choose the arithmetic average property value ofand converts into a linear. Index values a|, a2, ", a, .subordinates index layer factors as the property valueare obtained after regression, the request for the weightof the sub-criteria, that was the k criterion of attributeturns into i, a=Za, Detailed calculation is as thefollowings (Li et al, 2005).values: uj=Pk(Pk was the number of indicatorlayers included in the sub-criteria; xij served as thePreparation of meat pattiesproperty value of the k sub-layer.According to specific issues, we selcted appropriateindicators to make a structure chart by guidelines forDerivation of the contribution coefficient ofrelations between the decision-making and clarifyeach index level and weight by application toprogram layer and attribute layer.accumulation factorFirst of al, we tested the original data, if it followedFirst, we established the power function u;*=ITx*, andnormal distribution and then the factors of index layerwould be recorded cI, C2, .. c,. After trending of the used regression method to find a; (a; worked as theraw data, we standardized all the data that betweencontribution coefficient of the k sub-layer), and then0 to 1 and eliminated various factors dimension onexamined it withF test and T test. Ifa=Za, a;="ithe index, so we got the data denoted by the order ofprecedence marked as xi,x2,”, xn.became the weight of the j index layer. We used thevalue of k criterion to make sure the calculation resultObtain of index layer attribute valueus (u;=Zax;xj), at the same time, flll in the blanks 1Starting from the index layer, we needed to determinethe atrbute value of factors of layers, which should to 9 with data sizes of uk array (Bai et al, 2008).reflect the elements of each program on the importanceBy repeating the above two steps, we got the weightof the extent of the amount (Bai et al, 2006). Weof each index and finally got the important value of thecalculated arithmetic mean of indexes x,x2, ", xn oftarget level (gene中国煤化工one index).index layer, then divided the Interval constituted byAt the same timefYHc N M H GIe layeryi,http: /publish.neau.edu.cn8●Journal of Northeast Agricultural University (English Edition)Vol.19 No.2 2012hi, " Yp (p meant the number of rule layer).chemical fertilizer fold scalar, irigation, crop acreage,cropping index, forestry, animal husbandry and fisheryOrders of Affecting Heilongjiangand water conservancy in the number of food cropGrain Production Factorsyield per unit area, the affected area, the per capitaannual net income of rural households, the annualHeilongjiang is an important commodity grainaverage temperature, annual precipitation, annualproduction base and its food production has a directsunshine hours, the expenditure of forestry (Niuimpact on national economic development in China.et al, 2010), water and meteorological department,Studying the affecting size of various factors on foodthe total power of farm machinery, the expendituresproduction potentiality can correctly guide the agri-of basic construction, three expenditures of sciencecultural investment which plays an important guidingand technology, personnel number in science androle in rational development of food production plans,technology activities and scientific and technologicalpromotion of the high-quality food in Heilongjiangachievements in agriculture (the number of publishand efficient production.ed paper) (Huang et al, 2011). The hierarchicalTo rank food production affecting factors and factorstructure model about this issue is demonstrated insequence actively seeking assignments using theFig. 1.weight value of AHP potential impact on, the targetThis paper standardized the data from 1992 tolevel is the food production potentiality y。"yh (Zhou2007 (a total of 16 years) to eliminate the affection ofet al, 2006). The inspection factors of criteria layerdimension to the results, then used the prior 14 yearsyst include four areas (Qi and Xiao, 2009; Chen etof data to multiple regression, with two years of dataal, 2009): namely agricultural productive condition,to test the model fitting results. After the handle ofnon-human controlled factors, natural conditions anstandardized data, we could process each criterion andthe role of technology. Index layer c; is composed ofits corresponding index attribute value. We could usespecific goals and data reflecting criteria law (Wang,the Matlab to implement this process. Calculation was2009; Lv and Liu, 2011). The selection factors are as the followings.Affecting factors on food production protentiality| Conditions for agricutural production Non-human control facor|Natural conditions| Role of science and technology|拿营含|营急|”Fig. 1 AHP structure modelObtaining logarithms of basic data on 17xw-Min{x}formula was.indicators中国煤化bhere s sid thatx;=logc, further standardized them from 0 to 1, thethe criterialMYHCNMHGors1≤s≤4,iE-mail: xuebaoenglish@ neau.edu.cnGao Chun-yu et al. An Improved Analytic Hierarchy Process and Application in Grain Production.69.said the afcting factors 1≤i≤17, and x showedindex value after the first treatment of the i indicatorTable 2 Weight of index layerof each factor.Index layer factorsSortContributionWeightcofficientCalculated weights of each index layer BAffected area (million1.3420.177211By using the two indicators x and x2 we establishedhectares)Agricultural forestrythe power function y,n=x,i°x,2", s=1, 2, 3,4 towater department0.7500.163172calculate the weights of the first and the secondexpenditure (million)indicator. First, we calculated arithmetic mean of划，Grain sown area (ilion1160.131795x and then divided the Interval constituted by theRural per capita annual net0.8410.118311 .family income (dollars)arithmetic average of the minimum and maximumGrain yield per unit area0.6570.077628into nine, and madey,=k, k=1, 2, ..9. After that, we(kg 1 ha)calculated the logarithm ofy,n=x,f "x,2“, and convertedAgricultural machinery power1.3070.063183(kilowatts)it into a linear regression. We used SAS sofware toCapital expenditure (million)0.2270.049037calculate regression cofficient and marked it as Q; andIrigated area (ffective)0.4720.048025a|amillion hectaresa2, so weight could been shown asa= a.ta2 a,+a2'Hours of sunshine (hours)0.8550.044049Annual rainfall (mm)00.7890.039332The average annualCalculated weight values of layer B relative totemperature (degrees0.7250.027287. Celsius)the target layerAScientific and technological21.2140.027255Established the exponential function yr,"vy2”, in whichactivities (person)ys,i=apx,+azxXs2, s=1, 2, 3, 4. The calculation pro-Technology promotion130.6950.019811(million)cess was the same as the step of index layer attributeOff pure chemical ferilizer1.2010.013904value.consumption (tons)Animal husbandry and fisheryUsing each criterion with the correspondingand water conservancy in the0.843index to precede regression analysis, we couldnumber of (people)obtain the contribution factor of each index, thMultiple crop indexl60.498Published scientificcontribution coefficient would be treated to get weight170.127papers (articles)value of each criterion and index which is shown inTables 1 and 2.ConclusionsTable 1 Weight of guidelinesFrom the weight table of rule layer, we found thatCriteria layerthe factors of potential impact on food productionfactorscoefficientwere non -human controllable factors, technologicalNon-human control0.4710.413850 .factors, natural conditions and agricultural productionfactorRole of science andconditions, the degree of influence decreased in0.9170.353141technologysuccession (Guo et al, 2007). Based on the com-Natural conditions1.0430.148081parison of the weight of target layer and rule layer,some views were, put forward. The factor affectingConditions foragricultural0.3200.084928potential food pro中国煤化工was stilproductionsome non-human:fYHCNMHGsdisaster.http: /publish.neau.edu.cnJournal ofNortheast Agricultural University (English Edition)Vol.19 No.2 2012area and crop yields.Mathematics in Practice and Theory, 38(24): 1-4.However, the conditions of agricultural productionCh Y, Liu H, Hao H 1, et al.2009. Analysis of temporal and spatialhad lttle influence on potential food production,variation, driving factors and trend prediction of grain yield in Gansuwhich indicated that the popularity of agriculturalProvince. Agriculural Research in the Arid Areas, 27(4): 225-229.modernization in agricultural production inChenG Y, Guo Y L, Zhang Y z, e1 al.2009. Analysis of temporal andHeilongjiang Province was not good enough. Andspatial variation, driving factors and trend prediction of grain yieldthis also reminded the authorities that if we wantedin Gansu Province. Agriculnural Research in the Arid Areas, 27(4):to enhance the potential of food production in209-212.Heilongjiang Province, to quicken the modernizationEngle RF, GrangerC W J. 1987. Co-integration and error crrection:of agriculture, and to improve agricultural productionconditions, there was still a long way to go, but thereGuo s M, Ma s, Chen Y J. 2007. Effect factors on grain productwould have a huge room for growth (Chen et al.,in main grain product areas of China. Research of Agricultural2009; Wang et al, 2008).Modernization, 28(1): 83-87.After the analysis of table, we could see thatHuang z FuL F, DuJ, et al. 2011. Analysis on infuencing factors ofalthough the natural conditions had some impacts ongrain production in China. Journal of Anhui Agricultural Sciences,potential food production, its influence was lttle com-39(21): 158-160.pared with the previous. The target weight sum of theLiu Q z.1997. The product method of AHP and a ideal weapon indexorder of 1 to 7 reached 73.4528% of the total weight,founction. Mahematics in Proctice and Theony, 27(4): 209-304.but it appeared fault-layer-phenomenon in data.LIF G, BaiJY, Zhao HJ. 2005. The study of solving weight by AHP" sFrom the original data table, we could see thataccumulation factor sequence evaluating data. Operations Researchnatural conditions in the past decade fluctuatedand Management Science, 14(6): 60-63.slightly. In addition to non-human controlled factors,LvX G, Liu X H.2011. Analysis of the level of grain production factorsscience and technology had grecat impact on potentialby AHP. Hubei Agricutural Sciences, 50(13): 2798-2800.food production, which fully demonstrated the role ofNiu CM, Wen x F, Wang F. 2010. Infuence factor analysis of grain-technology in food production process was essential.production in Yanchi County based on factor analysis method.Solving Weight by AHP's Accumulation FactorResearch of Soil and Water Conservation, 17(6): 278-282.Sequence Evaluating Data was a good sort methodQi Y ), Xiao Y C.2009. Analysis of the factors infuencing grainfor the analysis of food production capacity in Hei-production of Chongqing. Journal of Southwesi Agriculturallongjiang Province. This method was not only simpleUniversity: Social Science Edion, 7(5): 30-33.and reasonable for the data processing, but also wasWang z Y, Yu H M, Wang L, et al.2008. Analysis on the contributiona simple calculation method. And it could avoid therate of the factors of influencing grain production and somepossible mistakes by the subjective judgments to apolicy suggestions. Journal of Anhui Agricultural Science, 36(4):great extent. Besides, the results agreed well with the1690-1692.actual situation, and the method was reliable.Wang z, Li S C.2009. On the impact factors for Chinese grainproduction-based on principal component analysis and co-integrationReferencesanalysis. Journal of Tianjin University: Social Sciences, 11(5):BaiJ Y, SongJS, Li F G. 2006. Analysis of accumulation factors399.401.in the calculation of weights and application. Sci-Technology andZhou J M, Xu F, LiJH, et al.2006. Analysis on the efective factors ofManagemen, 36(2): 45-48.the grain potential productivity and the deficiency between demandBaiJ Y,MJ, LiF G. 2008. Application of analytic hicrarchy processand supply in Fujian Province. Fujian Journal of Agriculturalusing accumulation factor to evaluate weight factors in soring cities.Sciences, 2中国煤化工CNMHGE- mail: xuebaoenglish@ neau.edu.cn