---3 fuzzy comprehensive evaluation method for water quality assessment

The so-called fuzzy evaluation, is based on the evaluation criteria and measured values, through the fuzzy transformation of things to evaluate a method. A thing often has a variety of attributes, so the evaluation of things must consider a variety of factors at the same time, but many problems often difficult to use a simple numerical expression, that is often with fuzziness, then should use fuzzy comprehensive evaluation. According to the quantity of evaluation factors, the type of comprehensive evaluation of fuzzy mathematics can be divided into single factor evaluation and comprehensive evaluation (multi-factor evaluation) two methods.

The core of fuzzy comprehensive evaluation method is to determine the membership function, the method is based on fuzzy mathematics, the quantitative analysis of the evaluation object, then according to the measured value of the index and the standard evaluation category, through the matrix transformation, the evaluation of the object analysis to calculate an evaluation result. On the basis of fuzzy comprehensive evaluation method, many methods based on fuzzy theory have been developed and widely used in all fields. Considering the complexity and fuzziness of water environment, it has become a hot research direction to combine fuzzy theory and other water quality evaluation methods in water quality evaluation.

The process of evaluating water quality by fuzzy comprehensive evaluation method is as follows:

The application of fuzzy comprehensive evaluation can be summed up in the following steps:

1) Set up a set of pollutants for each single factor index u= {u1, U2, ..., un}, Element UI (i= 1, 2,......, N) is the measured value of each pollution that affects environmental quality.

2) Establish a set of water quality grading standards, k= {k1, K2,......, KM}, wherein the element kj= (1, 2,......, M) is the water quality grading standard for each pollutant.

3) Establish fuzzy relation matrix R. That is r= [Rij] fuzzy relationship matrix in water quality evaluation, is to reflect the evaluation factor to the level of water membership of a transformation relationship. If the "lower half ladder" is used to calculate the membership degree Rij (0< Rij < 1), the analytic formula of membership degree is:

Type: SJ, sj+1 represents the standard value of adjacent two-level water quality; CI represents the measured value of an evaluation factor in a water sample.

The fuzzy relationship matrix R can be computed in turn:

4) Establish a weighted fuzzy matrix W.

A is the contribution of various pollution factors to environmental pollution, as well as the synergy between the multi-factor, antagonism effect on environmental pollution, to make a weighted distribution of an n-koriyuki vector (or line matrix), namely: W = [W1, W2,..., Wn] Among them, the use of pollutant concentration over-weighted method to calculate the weight of each pollution factor:

Wi =ci/s I

Type: Ci is the measured concentration of the pollutants of the first I; S I is the arithmetic mean of the standard values of water quality of the pollutants at the first level. wi≥0,i=1,2,......, N

For fuzzy transformations, the Wi value should meet the normalization requirements, namely:

5) Calculate fuzzy comprehensive evaluation matrix B.
After R and A have been established, B can be obtained according to the principle of fuzzy transformation, namely:

...... Type I comprehensive evaluation

Type: B = [B1, b2 ... bm] is the result of comprehensive evaluation;

6) Finally, the final water quality evaluation level is obtained by the maximum membership principle.

Considering the uncertainty of water environment and combining the weight of pollution factor, the fuzzy comprehensive evaluation method can objectively reflect the condition of the effluent environment. The advantage of this method is that by evaluating target object, we can not only get the influence of various evaluation factors, but also can analyze the main pollution factors affecting water quality. However, due to the current criteria for determining the degree of membership has not been unified, the general situation is determined by man-made subjective, so often evaluation results will be large differences, which is the method used in water quality evaluation of one of the bottlenecks .

---3 fuzzy comprehensive evaluation method for water quality assessment