Study on Entropy Weight Coefficient Method and Application for Water Quality Evaluation

June 2004Joumal of Northeast Agricultural UniversityVol. 11, No.1 66-68Article ID:1006- 8104(2004)-01-0066-03Study on Entropy Weight Coefficient Method and Applicationfor Water Quality EvaluationMEN Bao -huil, FU Qiang, ZHAO Xie-jing'( 1. Agricultural Department Key Open Laboratory of Agriculture Resource and Environmentin Yangtze River Upper Reaches, Chengdu Sichuan 610066 , PRC;2. Cllge of Hydraulice and Arehiteture Engineering, Northeast Agriculural University, Harbin Heilongjiang 150030, PRC )Abstract: In order to evaluate the quality of water environment, the conception of entropy is applied in informa-tion science, and the entropy weight model is built to evaluate comprehensively water quality. The indexes weights ofwater quality are determined by value of entropy. This kind of method is applied on evaluating water quality in the newwater to be built. The result shows that the water quality in it which supply water is between grade II and IV, and theresult is similar to that of gray related method.Key words: entropy weight cofficient method; water quality; gray related methodCLC number: 0236; X824; S117Document code: AIt is very important to evaluate the quality of wa-ter in environment quality assessment. Present, there1 Data Arrangement3lare about ten methods to evaluate water quality, suchas, one-item-pollution index method, and fuzzyjudgeThere are monitored points to evaluate water qu-method, and gray -related method and so on. Fuzzy-ality on a river or a lake, and every monitored pointudge method which applies subordinated degreehas evaluated indexes. Then, the characteristic valuefunction explains fuzzy character of classified boundsmatrix of evaluated indexes is X:about water quality. It can reflect reality about waterindex1|[x，X2 ... Xnquality on objective, but this method emphasizes ex-indexI|x, x。... xtreme-value action, and more information is lost, andX;=(1)the scientifiec character of weight value is not clearl".The evaluation of water quality is a multi -level andindex1m[x.Xn... X.(i=1,2, A, m; j=1,2,A, n)multi-index problem.In this paper, through using principles of the the-The evaluated indexes can be classifed twoory of inormation (especiall, the notion of entropy)網(wǎng),kinds: one is the bigger of the numerical value of in-an entropy weight model is developed to evaluate thedexes, the better of the degree of water qulityformulaquality of water. Entropy weight coeffcient which(2-1)), the other is the smaller of the numerical valueshows the variation degree among the characteristicof indexes, the better of degree of water qualityformu-values of evaluated indexes is used to determine thela(2-2). So the characteristic value in matrix(1)mustmodel weight. It has been shown that the entropybe normalized.weight model gives better results than classical ap-{Xw=Xg/maxXg (2-1)(2)proach, such as gray related method. The process|xy =minXg/Xy (2-2)about entropy weight method is explained by actuallyApplying formula(2), the normalized matrix cansurveyed data.be obtained.Received date: 2003- 03-21中國煤化工Foundation item: Supported by Hi-Tech Research and Development ProgrBiography: MEN Bao-hui(1973-), male, doctor of hydrology and water re:MYHC N M H Giter seving inigationfor rice, water conservancy design and water environment evaluate. E-mail :menbaohui@126. comNo. 1Jourmal of Northeast Agricultural University.67.a=(1-e)- 2(1-e;)(6)X'g=Fourth, calculate comprehensive evaluatedvalue W;(3)X'mX'm2...X'mw=Zapo(7)Fifth, arrange monitored point in proper order ac-2 Foundation of the Entropy Weightcording to the comprehensive evaluated value Wj.Model3 Example AnalysisFirst, calculate the characteristic value rate pw: .Five evaluated indexes have been chosen, that is,P,=X"v/Ex',(4)Il, the content of iron in water(mg'L-), I2, the con-Where: i is evaluated index;j is monitored point.tent of manganese in water(mg.L~), I3, the content ofSecond, calculate information entropy e;: .No- ionic ammonia in water(mg.L ), 14, lmn(mg.L),I5, BOD5(mg.L9). The indexes value and the actuallye.=-m 2plIp,(5)surveyed data of three crossed -sections(A, B, C)aremn,Third, calculate weight value q:shown in Table 14.Table 1 The gradation of the indices and survey dataIndexDegreeof IMIVAC0.300.50).5.00.330.810.101.00.120.160.02.20.07.074.006.0010.04.604.344.383.006.05.265.566.80The characteristic matrix (8) of the evaluated in-formula(7)(Table 3). Table 3 shows the entropy weightdex can be obtained according to the data in Table 1.model gives better results than the gray related me -[0.30 0.50 0.5 1.0 0.406 0.330 0.814 ,|0.10 0.10 0.5 1.0 0.118 0.158 0.240Table 2 The weight of evaluation indexesx,=0.02 0.02 0.2 0.2 0.060 0.072 0.066(8)Evaluated indexes1| 4.00 6.00 8.0 10.0 4.600 4.340 4.380Weight valuea 0.1996 0.2003 0.2011 0.1994 0.1996(3.00 4.00 6.0 10.0 5.260 5.560 6.800The normalized evaluated-index matrix(9)can be4 Conclusionmade by the formula(2).[1.00.60 0.6 0.3 0.7389 0.9091 0.3686According to Table 3, the entropy weight model|1.0 1.00 0.2 0.1 0.8475 0.6359 0.4167does not only judge the degree of evaluated crossed-X'j= |1.0 1.00 0.1 0.1 0333 0.2778 0.3030(9)section A, B, C, but also arrange in proper order for1.0 0.6667 0.5 0.4 0.8696 0.9217 0.9132every evaluated monitored point. The arrangement is1.0 0.750 0.5 0.3 0.5703 0.5396 0.412degree of I > degree of I > crossed -section A >According to formula(6), the weight of every eval-crossed- -section B> crossed- -section C> degree of IV>uated index can be calculated. The weight values aredegree of V. So the water quality of the three cross-shown in Table 2.中國煤化Idegreeof M andThe comprehensive evaluated value and evaluatedegreeCN MH Grosed. -ecion Aresults about every monitored point can be made byand B are close to tne aegree or山，but that of the.68.Joumal of Northeast Agriculural UniversityVol. 11Table 3 The evaluation resultNVVCEvaluated method1.00000.80380.37940.23970.67150.65560.4881Entopy weight modelD⑥⑦③④⑤mIGray related methodcrossed- -section C is approach to degree of IV. These[2] Patera A. Application of prineiples of the theory of ifirmaion inevaluated results are better than that of the documentE.management of reservoirs and water resource systems小WaterSo it is efective for entropy weight model to evaluateResources, 200, 28<(1): 29-33.the quality of water, and this method can be applied[3] Shi Cuang-xin, Yin Cheng- xin. Benefit evaluation model and itsto evaluate the environment quality of city, and wateraplicaion on small watershed control on the basis of informationresource carrying capacity in region.entropy 0 Bulletin of Soil and Water Conservation, 9999 19 (5):38-40.References[4] Guo Dong -ming, Luan Tian -xin. pplicaion of gay related[1] Tian Gui-quan. The judge -analysis method for evaluating atmo-method to evaluaing water quality 0] Water Resources & Hy-sphere environment quality []. Environment Science and Re-dropower Northeast China, 2000, 18 (9): 37-42.search, 1996, 9 (3): 45. -47.中國煤化工MYHCNMHG