Fuzzy cluster analysis of air quality in Beijing district

The principle of fuzzy clustering analysis is applied in this article, by using the method of transitive closure, the main air pollutants in 17 districts of Beijing from 2014 to 2016 were classified. The results of the analysis reflects the nearly three year’s changes of the main air pollutants in Beijing. This can provide the scientific for atmospheric governance in the Beijing area and digital support.


Introduction
In recent years, with the acceleration of urbanization, the control of air pollution has become a top priority in urban development and one of the hot spots in society [1][2][3]. Beijing is the political, cultural and economic center of China and the construction of Beijing is an important part of the country's development strategy of "common prosperity and economic revitalization".
In the evaluation of atmospheric conditions, the methods used mainly include systematic clustering analysis, grey clustering analysis and fuzzy clustering analysis [4][5][6]. Clustering problem is according to the actual situation and a certain standard to identify the proximity between the objects, and to put close to each other objects, the fuzzy clustering analysis is based on the study of the attributes of the object itself to construct the fuzzy matrix, on this basis, according to certain membership to determine the relationship between classification [7]. The influence of human activities on the air environment is very complex, there are a lot of things and phenomena are fuzzy quality, in air environment impact assessment on the recognition and measurement of exist a lot of fuzziness, so only choose a reasonable method, can perfect to reflect the situation of air environmental quality. Taking Beijing as an example, through to the 17 to collect the average density of major pollutants in years, guided by the principle of fuzzy mathematics, and the annual average concentration of major pollutants were analyzed, and the scientific classification, for Beijing city governance and environmental comprehensive control to provide advice, for the urban environment and urban management to provide scientific basis for air [8].
In 1965, L. A. Zadeh, an American expert on cybernetics, first proposed the concept of fuzzy sets, which marked the birth of fuzzy mathematics. Fuzzy mathematics is to study and deal with ambiguity phenomenon, a kind of mathematical theory and method. The so-called fuzziness refers to the uncertainty and uncertainty in objective things, the root of which lies in the intermediary transition between objective things. Fuzzy mathematics is an emerging subject which has wide application in pattern recognition, artificial intelligence and so on [9][10][11].

Principle and method of fuzzy clustering analysis
The fuzzy clustering analysis is divided into the following steps represents the m attribute eigenvalues of the i-th sample object to be classified, so that an original data matrix is obtained, denoted as In order to compare the data of different dimensions, it is necessary to make a standardized transformation of the original data in general, and the common methods are as follows ①Standard deviation transformation

Establish fuzzy similarity matrix
For any two objects is determined according to the degree of similarity between them, and then the n order fuzzy similarity matrix is established. There are several ways to determine the similarity coefficients: ①Scalar product method The value of the parameter c in the formula is properly chosen so that the similarity coefficient

Calculation transitive closure of fuzzy similar matrices
The square of the fuzzy similarity matrix R is computed by the square method in turn The transitive closure of R is

Clustering
Make a dynamic clustering map based on transitive closure.
. 1  2  5  17  3  4  6  7  8  9  10  11  12  13  14  15  16 , , , , . has been affected by a lot. In the suburbs of Beijing, the Mentougou district and Shunyi district appear in the same category for three consecutive years. Huairou district, Miyun district and Yanqing district in the far suburbs appear in the same category in 2014 and 2016. In the suburbs, the Changping district and the Pinggu district in the far suburbs have changed over the three years, indicating that the air quality of the two regions has fluctuated greatly in the past three years. Therefore, the government departments can rationally arrange the air test site through the classification of each district and the change of each district over time to control the air pollution.