Unascertained measurement evaluation model of environmental effection on Nujiang development
PANG Yan-jun(庞彦军), LIU Li-min(刘立民), LIU Kai-di(刘开第)
(School of Science, Hebei University of Engineering, Handan 056038, China)
Abstract: The uncertainty of index system was descried using membership function, and the knowledge information in index membership about object classification was studied. A comprehensive evaluation model of unascertained measurement was established according to the analysis of contribution of index to sample classification and the conversion method of membership degree from index to sample. The results indicate that this model can be used to evaluate the environmental effect of water conservancy and hydropower development of nujiang.
Key words: hierarchical structure; membership degree; index distinguish weight; unascertained measure
CLC number: X824 Document code: A Article ID: 1672-7207(2011)S1-1058-04
1 Introduction
The index system of environmental evaluation exhibites a hierarchical structure, the chararter of which is the uncertainty of levels in evaluating the base index and the nonlinear relation between the upper and lower indexes. The comprehensive environment evaluation has important application background, and it is necessary to concern its rationality and accuracy. The requirement for environment effect evaluation is to predict and evaluate the effection after implementing the projects so as to recognize the environmental risk and propose solving schemes. It takes environmental factors to macroscopic decision, which is not only an important way and system guarantee in consorting economic development and environment protection, but also a main form of environmental evaluation recently[1].
The environmental effect evaluation of water conservancy and hydropower development consists of effects of the natural ecological environment and social environment and the contribution of project to social and natural resources utilization, which poseseses 30 lower effction indexes[2-3]. Because of the different importance of each index to the environment effect, the importance weight of each index can be determined using analytic hierarchy process(AHP)[4]. However, there is unascertainty in determining the lower effcet index to evaluation level and the nonlinear relation between the upper and lower indexes, and any environment evaluation method should consist of two links to describe the unascertainty information and treat nonlinear relation.
In this work, the uncertainty of the evaluation method was described using the membership function, and the knowledge information in index membership about object classification was studied. A comprehensive evaluation model of unascertained measurement was established according to the analysis of contribution of index to sample classification (name the index distinguish weight) and the conversion method of membership degree from index to sample.
2 Classification weight of index
Suppose Q is sample space, I={I1, I2, …, Im} is the index space, xj is the monitoring value of Q about index Ij, then Q can be denoted as m dimensional vector Q=(x1, x2, …, xm). Suppose C=(C1, C2, …, Cp) is the evaluation scale-space, if C1>C2>…>Cp or C1<>2<…<>p, it can say C is ordered.
2.1 Single index unascertained measurement
Suppose μijk is the membership degree of index j measured value of xj to class ck, then (μj1, μj2, …, μjp) is the single index unascertained measurement vector of sample space Q, and the matrix is expressed as:
(1)
which is the single index unascertained measurement evaluation matrix of sample space Q.
2.2 Index distinguish weight
Suppose
(2)
(3)
(j=1, …, m) (4)
where vj is the comparable value of index j about object Q, αj is the distinguish weight of index j about object Q.
It can be seen as one measurement to distinguish the category of Q for various membership degree of index and to distinguish it in extent. For instance, if αj=0, then μj1=μj2=…=μjp by the properties of entropy, and it indicates the membership degree of index j is redundant to object classification.
3 Multiple indexes comprehensive measure- ment
3.1 Effective value
The expression:
(5)
is identified as the k-class effective value of index j. Usually, the k-class effective value of different index j has no comparability because of the different importance for different indexes possess to object Q.
3.2 Comparable value
Let βj(Q) be the importance weight of index j to object Q, then
(6)
is the comparable effective value of index j of k-class membership degree and written as k-class comparable value for short. The k-class comparable value of different indexes j has comparability and direct additivity.
3.3 Comparable sum
Let
(7)
then, Mk is the k-class comparable sum of object Q.
3.4 Comprehensive measure
Let
Δ
(8)
then, it is the membership degree of object Q to class Ck.
3.5 Grade criterion of recognition
Suppose the evaluation space {C1, C2, …, Cp} is ordered and satisfies C1>C2>…>Cp, λ is confidence level (λ>0.5, and λ=0.6 or 0.7 generally), then the 
evaluation level C0 of object Q by using the confidence criteria is determined[5].
Here,
(9)
Let nl be the point value of level Cl (l=1, 2, …, p), then the following should be the integrate score of object Q.
Here,
(10)
Therefore, the samples of the same grade by scores can be scheduled.
4 Example
Ref.[6] gives the hierarchical structure of index evaluation system for environmental effect on nujiang development. In this part, the memberhsip degree vector of 30 lower indexes to the evaluation levels (here, C1 denotes better, C2 good, C3 general, C4 invalid) combined with the analytic hierarchy process and expert evaluation method (see Table 1) is determined, and the environmental effect on nujiang development is evaluated.
4.1 Calculate membership degree vector of primary index
In the following, B1 is taken as an example.
(1) The single index measure evaluation matrix of B1 is expressed as:
and the distinguish weight vector of C1j (j=1, …, 4) about B1 is α(B1)=(0.251 7, 0.251 7, 0.270 8, 0.225 85).
(2) The importance weight vector of indexes C11-C14 to index B1 is λ(B1)=(0.35, 0.35, 0.11, 0.19).
(3) The comparable value matrix of C1j about B1 is
Table 1 Evaluation of index system, index membership degree and weight of environment effect on Nujiang development
(4) The membership degree vector of B1 is μ(B1)=(0, 0.412 0, 0.300 0, 0.288 0).
Then, the membership degree vectors of B2, B3 and B4 are obtained simultaneously. Therefore, the single index evaluation matrix of upper index Q is expressed as:
4.2 Calculate membership degree vector of objects
The membership degree vector of environmental effect Q from the determination process is obtained, μ(Q)=(0.167 8, 0.449 0, 0.246 0, 0.137 2).
4.3 Recognition
From the analysis above, it is known that if λ=0.6, then the environmental effect Q is ascribed to a “better” level; if λ=0.8, then the environmental effect Q is ascribed to a “general” level. Therefore, the the environmental effect Q is ascribed between the “general” and “better” level. For instance, the quantized value {100, 85, 70, 50} of evaluation set {C1, C2, C3, C4}, the score of environmental effect Q is n(Q)=79.035 and is ascribed between “general” and “better” level.
5 Conclusions
(1) From the grade recognition and the score, the environmental effect for water power development in middle and lower reaches of nujiang is non-ideal, and should be decided carfully.
(2) From the evaluation matrix U(Q), the natural and ecological environment B1 is ascribed to “better” level with the confidence less than 0.42, indicating it will destroy the natural and ecological environment. The social and economic effects B3 is ascribed to “better” level with the confidence more than 0.87, indicating it concerns economic influence more than the protection of natural and ecological environment.
References
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[4] Satty T L. The analytic hierarchy process[M]. New York: McGraw Hill, 1980: 287.
[5] CHENG Qian-sheng. Attribute recognition theoretical model and its application[J]. Journal of Peking University, 1997, 33(4): 23-30.
[6] FU Peng, CHEN Kai-qi, XIE Yue-bo, et al. Method for environment impact assessment of hydropower development considering social factors[J]. Journal of Hydraulic Engineering, 2009, 8(2): 1012-1017.
(Edited by FANG Jing-hua)
Received date: 2011-04-15; Accepted date: 2011-06-15
Foundation item: Project(60874116) supported by the National Natural Science Foundation of China; Project(F2009000857) supported by the Natural Science Foundation of Hebei Province, China
Corresponding author: LIU Li-min; Tel: +86-15833109511; E-mail: liulm2001@163.com
