A New Perspective on Formation of Haze-Fog: The Fuzzy Cognitive Map and Its Approaches to Data Mining
Abstract
:1. Introduction
2. Previous Research on the Formation of Haze-Fog
2.1. Physical Chemistry Mechanism in the Formation of Haze-Fog
2.2. Statistical Analysis of the Formation of Haze-Fog
2.3. Data Mining Methods for the Formation of Haze-Fog
2.4. Proposed Problems
- C = {C1, C2, …, Cn} is the set of n nodes of a graph, which represents a set of concepts of a system, in general.
- W: (Ci, Cj) → wij is a function of n × n to a pair of concepts (Ci, Cj) taking value in the range −1 to 1, with wij denoting a weight of directed edge from Ci to Cj, if i ≠ j, and wij equal to zero if i = j. Thus, W (n × n) = (wij) is a connection matrix.
- A(t) = {A1(t), A2(t), …, An(t)} is a sequence of concepts activation degrees at the moment t. A(0) indicates the initial vector and specifies initial values of all concept nodes and A(t) is a state vector at certain iteration t.
- f is a transformation function, which includes recurring relationship on t ≥ 0 between A(t + 1) and A(t).
- bivalent
- trivalent
- logistic
3. A New Perspective: The Fuzzy Cognitive Map for Haze-Fog Formation
3.1. The Construction of the Fuzzy Cognitive Map for Haze-Fog Formation
3.2. The Evolution Mechanism of the Fuzzy Cognitive Map to Haze-Fog Formation
4. The Approach to Data Mining of the Fuzzy Cognitive Map for Haze-Fog Formation
5. Experiments and Results
- recombination method—single-point crossover;
- mutation method—random mutation;
- selection method—roulette wheel;
- probability of recombination: 0.8;
- probability of mutation: 0.5;
- population_size: 200 chromosomes;
- max_generation: 500,000;
- max_fitness: 0.9; and
- the parameters of the FCM:
if (the forecast value is in the interval of corresponding actual intensity) |
the number of valid forecast in the right interval plus one; |
else |
the invalid number in a wrong interval plus one. |
6. Conclusions
- (1)
- Physical chemistry methods model the actual physics and chemical reactions of pollutants under the influence of the meteorological conditions. However, with more complex nature of reactions, the methods fail to describe and simulate the nonlinear processes involved in the haze-fog formation.
- (2)
- Statistical analysis methods incorporate the factors that are involved in the formation of haze-fog by using the measurements from equipment and the linear analysis of the contributing factors for the formation of haze-fog. They are important cognitive bases for the formation of the haze-fog. However, statistical analysis cannot describe the nonlinear dynamic process responsible for the formation of haze-fog.
- (3)
- Data mining methods can be used to discover the nonlinear relationships in the formation of haze-fog. However, at present, because of the limitation of the model such as in Meng et al. [43], not considering the correlations among the contributing factors and the dynamic changes in data, the results in existing data mining methods are unsatisfactory.
- (1)
- Quantitatively dynamic models need to be further developed for the formation of haze-fog under increasingly complex scenarios.
- (2)
- The relationships among the factor concepts in the formation of haze-fog need to be well recognized and modeled.
- (3)
- The dynamic and nonlinear changes need to be further simulated for forecasting the formation of haze-fog.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Inputs: Sample Data from the Process of Haze-Fog Formation |
Step1. Initialize parameters of genetic algorithm and the FCM within the known range. Step2. Generate initial population based on operator. Step3. Calculate fitness function according to the time series data. Step4. Evolve the population. Step5. Return to Step 3, until the fitness function is maximized (i.e., the end of mining conditions) after finite iterations. |
Outputs: The Relationship Degrees in the Fuzzy Cognitive Map for Haze-Fog Formation |
Haze Intensity | [0, 0.25) | [0.25, 0.50) | [0.50, 0.75) | [0.75, 1] | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Forecast Result | FCM | MRM | FCM | MRM | FCM | MRM | FCM | MRM | ||
Haze Intensity (Actual Number) | ||||||||||
[0, 0.25) (4) | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ||
[0.25, 0.50) (2) | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | ||
[0.50, 0.75) (1) | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | ||
[0.75, 1] (3) | 0 | 1 | 0 | 0 | 1 | 0 | 2 | 2 |
Haze Intensity | [0, 0.25) | [0.25, 0.50) | [0.50, 0.75) | [0.75, 1] | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Forecast Result | FCM | MRM | FCM | MRM | FCM | MRM | FCM | MRM | ||
Haze Intensity (Actual Number) | ||||||||||
[0, 0.25) (6) | 5 | 5 | 1 | 1 | 0 | 0 | 0 | 0 | ||
[0.25, 0.50) (7) | 0 | 0 | 7 | 7 | 0 | 0 | 0 | 0 | ||
[0.50, 0.75) (2) | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | ||
[0.75, 1] (5) | 0 | 1 | 0 | 0 | 1 | 1 | 4 | 3 |
Haze Intensity | [0, 0.25) | [0.25, 0.50) | [0.50, 0.75) | [0.75, 1] | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Forecast Result | FCM | MRM | FCM | MRM | FCM | MRM | FCM | MRM | ||
Haze Intensity (Actual Number) | ||||||||||
[0, 0.25) (11) | 10 | 10 | 1 | 1 | 0 | 0 | 0 | 0 | ||
[0.25, 0.50) (10) | 1 | 1 | 8 | 8 | 1 | 1 | 0 | 0 | ||
[0.50, 0.75) (3) | 0 | 0 | 0 | 0 | 3 | 2 | 0 | 1 | ||
[0.75, 1] (6) | 0 | 1 | 0 | 0 | 1 | 1 | 5 | 4 |
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Peng, Z.; Wu, L. A New Perspective on Formation of Haze-Fog: The Fuzzy Cognitive Map and Its Approaches to Data Mining. Sustainability 2017, 9, 352. https://doi.org/10.3390/su9030352
Peng Z, Wu L. A New Perspective on Formation of Haze-Fog: The Fuzzy Cognitive Map and Its Approaches to Data Mining. Sustainability. 2017; 9(3):352. https://doi.org/10.3390/su9030352
Chicago/Turabian StylePeng, Zhen, and Lifeng Wu. 2017. "A New Perspective on Formation of Haze-Fog: The Fuzzy Cognitive Map and Its Approaches to Data Mining" Sustainability 9, no. 3: 352. https://doi.org/10.3390/su9030352