Abstract: a new method of calculating weight is

Abstract: Given
that results of traditional assessing methods presently used are extreme values
and of poor resolution, a set pair analysis based on triangular fuzzy number is
established and a new method of calculating weight is constructed by using the weighted
average method. The case study shows that the method presents the evaluating
grade as a confidence interval which makes it more feasible and suitable to
practical conditions.

Keywords: set pair analysis;
triangular fuzzy number; super-standard multiple weight method; confidence
interval; lake eutrophication.

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1       
Introduction  

Sustainable
management of water resources requires a more detailed understanding of
spatiotemporal trends and variability of hydrological variables; Despite
dramatic improvements in water quality as a result of large-scale efforts to
reduce nutrient enrichment, cultural eutrophication and concomitant high algal
blooms continue to be the leading cause of water pollution for many freshwater
and coastal marine ecosystems and are a rapidly growing problem in the
developing world 1. Given that the demand for freshwater resources is
expected to increase dramatically, protecting diminishing water resources has
become one of the most pressing environmental issues and will likely become
more complicated as pollution further degrade water quality 2. Water quality
assessment is the back-bone of lake water management and pollution control, it
provides water resource managers with much needed information to understand the
state of the water bodies in order to make sound decisions for proper
management of this vital resource.

Many
credible water quality assessment methods have been designed and used,
including; single factor evaluation method, comprehensive water quality
evaluation method, fuzzy evaluation method, grey evaluation method, artificial
neural network method, parameter method, biological evaluation method and
nutritional status evaluation method, set pair analysis method etc 3. All of
these methods were widely used in water quality evaluations of individual water
bodies, and of watersheds. These existing methods were used to provide
information that formed an important foundation for promoting the rational
development, planned use, and protection of water resources 4.  In recent years the comprehensive evaluation
methods are extensively used in China because the methods allows a more
thorough investigation of water quality and a more continuous depiction of the
eutrophication processes, however, 
several problems are inherent in these methods. These methods include
the fuzzy comprehensive evaluation which has been proved effective in solving
problems of fuzzy boundaries and controlling the effect of monitoring errors on
assessment results 5. However, there are still some limits when applying fuzzy
comprehensive evaluation method to water quality assessment; For example, when
the method emphasizes extreme value action, more information is lost and the
scientific character of weight value is not clear etc 6. Set pair analysis
model has higher objectivity and reliability compared with the traditional
fuzzy comprehensive evaluation model 7. Nevertheless; it does not deal with
the weight of the evaluation index 8. 
Weight plays a key role in the comprehensive evaluation mathematical
model, reflecting the position and role of each index in the procedure of
comprehensive decision making, and directly influencing the result of the
comprehensive evaluation. For the same measured data, the low content and high
standard allowable concentration largely affect the pollution comparatively
9.  It is difficult to establish a
unified evaluation model, which promotes the further study on the water quality
assessment methods 10. 

This
paper presents a new method based on confidence interval in evaluation of lake eutrophication
that uses the resolving power of the set pair analysis model (SPA) and the
triangular fuzzy number (TFN) to deal with certain-uncertainty information in
lake assessment. It clearly defines the scientific character of weight value
using the weighted average method and furthermore gives the final evaluating
grade as a confidence interval which has a commonly held interpretation in the
scientific community and more widely has advantages of high resolution and
information utilization.

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