Research on prediction of internet public opinion based on grey system theory and fuzzy neural network

Abstract

Under smart city environment, the internet public opinion management is more difficult, therefore the combined prediction model based on grey system theory and fuzzy neural network is constructed. Firstly, the internet public opinion characteristics under smart city is discussed. Secondly, the mathematical model of the grey system theory is studied. the basic structure and mathematical model of fuzzy neural network are analyzed, and then the training algorithm is designed. Finally, simulation analysis of internet public opinion is carried out, simulation results show that the new method can improve prediction correctness of internet public opinion effectively, and the internet public opinion controlling level can be improved.

Keywords

Prediction internet public opinion grey system theory fuzzy neural network

1 Introduction

With rapid development of internet and information technology, the network has become the important carrier of internet public opinion. The internet public opinion has become the fourth media after newspaper, radio and television. The internet public opinion not only promotes the development of democratic politics, but also spread all kinds of contradictions and problems in realistic society, therefore the new challenge is put forward for the government. In recent years, the core ideas of smart city is that the information process ability can be greatly improved, application field and intelligent level are also improved. One hand, the smart city can promote the development of internet public opinion, on the other hand, it can bring out difficult of managing internet public opinion. Under smart city environment, the internet has become the main media of transmitting information, the internet of smart city not only bring out convenience of information transmission, but also has a large amount of complex information, therefore the internet public opinion is easily out of control, and then some unexpected events will happen.

In addition, the number of netizen has increased in recent years, they can express their opinions and ideas online. The internet public opinion is a new method of controlling the information by government, if the internet public opinion is poorly controlled, the situation that the public opinion is out of control, therefore it is important to control the internet public opinion [1]. The internet public opinion spread quickly, and has wide audience range, and has strong interaction ability, under smart city environment, the netizen has the characteristics of spontaneity, irrationality, and emotion, then the internet public opinion and rumor are difficult to be recognized, therefore the authenticity of public opinion faces great test, in recent years, the rumors have become important sources of social unstable factors, therefore the internet public opinion should be real time monitored, then the developing trend of internet public opinion can be correctly grasped, then the positive effect of internet public opinion can be reflected effectively, it is necessary to carry out the prediction analysis for it, the grey system theory and fuzzy neural network are combined to construct the prediction model for internet public opinion prediction under smart city environment, then the reliable prediction results can be obtained.

2 Internet public opinion characteristics under smart city

Under smart city environment, the innovation of government public opinion governance idea is the necessary requirement of modern society government. The smart city has the characteristics of innovativeness and intelligence, the government has strong innovation ability under smart city environment, then the government governance can keep pace with complex internet public opinion [2]. The government should adhere to the idea of citizen-centered, and response to the appeal of internet users. With depth of smart city construction, the whole world has gradually become interconnected network, and the communication method of people is increasingly transparent. The equal dialogue between government and internet user should be achieved. The smart city framework is shown in Fig. 1.

Fig.1

Diagram of smart city framework.

The full perception of smart city and interaction of internet require government not only predict developing trend of internet public opinion and recognize the complexity and dynamic characteristics of internet, but also forwardly absorbs different organization and group to participant collaboration, then all kinds of resources can be integrated effectively, the self perception and governance capacity deficit of government can be broken, then the synergistic governance effect “one add one is larger than two” can be formed.

Firstly, in macroscopic terms the government can carry out multi subject cooperation governance model, which can provide the multi subject for development of network public opinion. The network governance is the multi subject cooperation governance for social affairs, the new type coordination relationship between government and society is constructed through citizen participation channel, then cooperative cooperation governance mechanism among government department, government and social organization is constructed.

Secondly, for effective governance of internet public opinion of government, all aspects of society should be fully developed, and the whole process linkage governance from prediction to response for internet public opinion, then the effective governance can be achieved. Firstly, the cooperation advantage of every department for government can be fully developed, which can provide the good policy environment and technical support for orderly development of internet public opinion. The resources of every department can be summarized through constructing internal linkage governance mechanism among multi subject cooperation governance of publicity departments, public security departments, and emergency departments. The internet public opinion can be monitored daily, sorted and studied, then the negative internet public opinion can be contained effectively. In addition, for society the social members should carry out self monitoring and self controlling, for example, the relevant department of internet industry, nongovernmental organization should strengthen the education training, then the guidance function of internet public opinion can be played, and the positive energy can be transferred, and the harmonious and orderly network environment can be established.

The positive and negative public opinion transmitting model should be constructed for predict of them. The state transition of public opinion spread model is shown in Fig. 2.

Fig.2

State transition of public opinion spread model.

In Fig. 1, N is overall number of people, S is the people who do not know public opinion, B is the people who know and do not spread the public opinion, G is the people who know and do not spread the positive public opinion, I is the people who spread the negative public opinion, R is the people who spread the positive public opinion, T is the extremist, L is the patriot, P is the isolator, g is the spread ratio of positive public opinion, b is the spread rate of negative public opinion, α is the RI conversion rate, β is the IR conversion rate, θ is the probation rate of extremist, γ₁ is the arrest rate of extremist, γ₂ is the release rate of extremist, μ is the disappointment rate of patriot.

State transition model of B population can be expressed by following equation:

$\begin{matrix} N \frac{d b (t)}{d t} = - b (t) Na (t) {i (t) \\ + s (t) + b (t) Ns (t) [r (t) + t (t)]} \end{matrix}$ (1) where s (t) is the proportion of people who do not known the public opinion to the total number of people; b (t) is the proportion of people who know and do not spread the negative public opinion to the total number of people, i (t) is the proportion of people who know the negative public opinion to the total number of people, t (t) is the proportion of extremist to total number of people, r (t) is the proportion of people who know the positive public opinion to total number of people.

And the dynamical differential equations of spread model of public opinion are expressed by:

$\begin{matrix} \frac{d s (t)}{d t} = - b [i (t) + t (t)] d (t) - g [r (t) + l (t)] t (t) \\ + θ t (t) + γ_{2} g (t) + μ l (t) \end{matrix}$ (2) $\frac{d b (t)}{d t} = - b [i (t) + t (t)] b (t) + b [i (t) + t (t)] s (t)$ (3)

$\begin{matrix} \frac{d i (t}{d t} = - b [i (t) + t (t)] i (t) - β s (t) + b [i (t) + t (t)] \\ b (t) + br (t) \end{matrix}$ (4) $\frac{d t (t)}{d t} = - θ t (t) - γ_{1} t (t) + a [i (t) + t (t)] i (t)$ (5) $\frac{d p (t)}{d t} = - r_{2} p (t) + γ_{1} t (t)$ (6) $\frac{d g (t)}{d t} = - g [r (t) + l (t)] h (t) + g [r (t) + l (t)] s (t)$ (7)

$\begin{matrix} \frac{d r (t)}{d t} = - g [t (t) + l (t)] r (t) - α r (t) \\ + g [r (t) + g (t)] g (t) + β i (t) \end{matrix}$ (8) $\frac{d l (t)}{d t} = - μ l (t) + g [t (t) + l (t)] r (t)$ (9)

3 Mathematical model of the grey system theory

The grey system theory was put forward in 1982, which is used to solve the problem with less information and less data sample. The grey system theory is used to analyze the nondeterminacy problem when a small amount of information is known, while a majority of the information is unknown, the helpful information can be selected through forming a small amount of the known information, accurate represent and valid supervisory control of the evolution can be achieved. And the key characteristic of the grey system theory has no excessive requirement for the sample, and the data is not suitable to any distribution. The grey system theory casts off the limitation of the conventional exact mathematics, therefore it can be convenient to be used, and therefore it has great feasibility in the internet public opinion predication of smart city [3].

The grey prediction model can be defined by $V = E \times W$ (10) where V denotes the prediction vector of the m subjects, V = [v₁, v₂, ⋯, v_m] ^T, and the series of internet public opinion is obtained according to value of V; W denotes the weight vector of n prediction indexes, W = [w₁, w₂, ⋯, w_m] ^T, and the following equation should be satisfied: $\sum_{i = 1}^{n} w_{i} = 1$ . E denotes the prediction matrix for different prediction index, the corresponding expression is expressed as follows $E = [\begin{matrix} e_{1} (1) & e_{1} (2) & \dots & e_{1} (n) \\ e_{2} (1) & e_{2} (2) & \dots & e_{2} (n) \\ ⋮ & ⋮ & ⋮ \\ e_{m} (1) & e_{m} (2) & \dots & e_{m} (n) \end{matrix}]$ (11) where e_i (k) denotes the relational coefficient between kth index and kth optimal index for ith subject predicted, which is expressed as follows [4] $e_{i} (k) = \frac{min_{i} min_{k} | C_{k}^{*} - C_{k}^{i} | + λ max_{i} max_{k} | C_{k}^{*} - C_{k}^{i} |}{| C_{k}^{*} - C_{k}^{i} | + λ max_{i} \underset{k}{max | C_{k}^{*} - C_{k}^{i} |}}$ (12) where λ denotes the amending coefficient, λ = 0.5, $C_{k}^{*}$ denotes the optimization value of kth index of ith prediction object.

4 Mathematical model of fuzzy neural network

Fuzzy neural network has many advantages in internet public opinion prediction, which has preferable knowledge representation capacity and fault tolerance ability, and it can convey and accumulate the information well. The fuzzy neural network can be applied to predict internet public opinion of smart city, the fuzzy membership degree is used to express the developing trend of internet public opinion of smart city, the neural element and connecting weight are used to express the distribution of internet public opinion of smart city, then the correct knowledge can be obtained, which is in favor of accumulating the information, and the prediction precision of internet public opinion of smart city be improved [5].

Fuzzy neural network has five layers, which concluding input layer, fuzzification layer, fuzzy relational layer, relational layer after fuzzification, and outputting layer. The corresponding structure of fuzzy neural network is shown in Fig. 2.

Input layer: the input variables is input into this layer, and then is input into the next layer of neural network, the input variables constitute the input vector, and the input vector is defined by the following form [6]: $x = [x_{1}, x_{2}, \dots, x_{n}]^{T}$ (13) The membership degree function is expressed by: $\begin{matrix} α_{j} (x) = φ_{j} (\frac{∥ x - c_{ij} ∥}{σ_{ij}}) = e^{- \frac{{∥ x - c_{ij} ∥}^{2}}{σ_{ij}^{2}}}, \\ j = 1, 2, \dots, \sum_{i = 1}^{n} N_{i} \end{matrix}$ (14) where, c_ij and σ_ij are the center and width of membership function, N_i is the scale of ith inputting vector.

(2) Fuzzification layer: for node in fuzzification layer there is a language variable, and the solution of input membership function can be obtained, and the membership function is expressed by: $m_{j} = e^{\frac{x - c_{ij}}{σ_{ij}^{2}}}, j = 1, 2, \dots, \sum_{i = 1}^{n} N_{i}$ (15)

(3) Fuzzy relational layer: fuzzy sum of inputting variables from fuzzification layer can be carried out in the fuzzy relational layer, and can obtain the fuzzy relational vector, which is expressed by

$\begin{matrix} β_{j} = min {m_{1}, m_{2}, \dots, m_{k}}, \\ j = 1, 2, \dots, N_{A}, k = 1, 2, \dots, N_{n} \end{matrix}$ (16)

where $N_{A} = \prod_{i = 1}^{n} N_{i}$ .

(4) Relational layer after fuzzification: normalized calculation for relational vector is carried out in this layer, and the computing expression is expressed by $\bar{β_{j}} = \frac{β_{j}}{\sum_{i = 1}^{N_{A}} β_{i}}, j = 1, 2, \dots, N_{A}$ (17) $\sum_{i = 1}^{N_{A}} \bar{β_{j}} = 1$ (18)

(5) Outputting layer: weighted linear sum of relational strength is calculated in this layer, and the corresponding expression is expressed by [7] $y = \sum_{i = 1}^{N_{A}} ω_{i} {\bar{α}}_{i} = ω^{T} Λ$ (19) where, ω_i is the connecting weight between nodes, ω is the connecting vector between nodes, ω = [ω₁, ω₂, ⋯, ω_{N
_A}] ^T, $Λ = [\bar{α_{1}}, \bar{α_{2}}, \dots, \bar{α_{N_{A}}}]^{T}$ .

5 Training algorithm of fuzzy neural network

In order to avoid algorithm fall into local optimal, the traditional particle algorithm is improved The chaos is ergodic, which is combined with traditional algorithm, the chaos variable is acquired based on logistic mapping, and the computation formula is listed as follows [8]: $y_{i + 1} = u \cdot y_{i} \cdot (1 - y_{i})$ (20) where, y_i+1 and y_i are the ith and i + 1th time iteration results of variable y, u is controlling variable. Therefore the chaos optimization lead to the diversity of particle swarm, the any particle formed in the searching space is used to replace the undesirable particle, and the algorithm procedure is listed as follows [9]:

Step 1. the particle swarm is initialized, the basic parameters of chaos particle algorithm are selected.

Step 2. the velocity and location of updated particle is computed according to velocity and location of particle, and object function value of different particle is acquired, 20% of optimal particles are stored.

Step 3. the chaos optimal method is used to map the current particle swarm on interval [0,1], and the computation formula is listed as follows: $y_{1}^{(k)} = \frac{p_{g}^{(k)} - q_{min}^{(k)}}{p_{g}^{(k)} - q_{max}^{(k)}}$ (21)

where, $q_{min}^{(k)}$ and $q_{max}^{(k)}$ denote the upper and bottom limits of kth time iteration particle searching.

Step 4. the chaos series $y (k) = (y_{1}^{(k)}, y_{1}^{(k)}, \dots,$ $y_{M}^{(k)})$ are confirmed according to M iteration, y (k) is inversely mapped on original interval, and the $p_{g}^{(* k)} = (p_{g 1}^{(* k)}, p_{g 2}^{(* k)}, \dots, p_{gM}^{(* k)})$ is generated, and the computation formula is listed as follows: $p_{gn}^{(* k)} = Z_{min}^{(k)} + (Z_{max}^{(k)} - Z_{min}^{(k)}) y_{n}^{(k)}, n = 1, 2, \dots, M$ (22)

Step 5. the new solution is confirmed according to the series $p_{gn}^{(* k)}$ , when the new solution is better than the original solution, the new solution is used as the optimal value of chaos optimization, otherwise, k = k + 1, return to Step 4.

Step 6. $p_{i}^{(k)}$ and $p_{g}^{(k)}$ are updated, when the predefined precision meets the requirement, the searching process will be over, the last value is output, otherwise, return to Step 7.

Step 7. the searching space decreases, and other 80% of particles form the new swarm, return to Step 2, and the calculation expression is listed as follows [10] ${\begin{matrix} Z_{min}^{(k)} = max {Z_{min}^{(k)}, p_{i}^{k} - r \cdot (Z_{max}^{(k)} \\ - Z_{min}^{(k)})} \\ Z_{max}^{(k)} = min {Z_{max}^{(k)}, p_{i}^{k} - r \cdot (Z_{max}^{(k)} \\ - Z_{min}^{(k)})} \end{matrix}, 0 < r < 1$ (23)

6 Combined prediction algorithm combing grey system theory and fuzzy neural network

Step 1. the prediction precision a_it at t moment of ith method is computed, and the computation formula is listed as follows [11]: $a_{it} = {\begin{matrix} 1 - | (x_{t} - {\hat{x}}_{it}) / x_{t} |, | (x_{t} - {\hat{x}}_{it}) / x_{t} | < 1 \\ 0, | (x_{t} - {\hat{x}}_{it}) / x_{t} | ⩾ 1 \end{matrix}$ (24)

Step 2. the induced ordered weighted arithmetic mean value at t moment of m kinds of prediction method is computed, which is calculated by the following formula:

$\begin{matrix} f_{it} = (< a_{1 t}, x_{1 t} >, < a_{1 t}, x_{1 t} >, \dots, \\ < a_{1 t}, x_{1 t} >) = \sum_{i = 1}^{m} l_{i} x_{a - index (it)} \end{matrix}$ (25)

Step 3. the error of combined prediction model is confirmed, which is computed by the following formula [12]: $e_{t} = x_{t} - f_{it} = x_{t} - \sum_{i = 1}^{m} l_{i} x_{a - index (it)}$ (26)

Step 4. the optimal model is established by using minimum quadratic sum of error of combined prediction model, the objective function is expressed by $min S (L) = \sum_{t = 1}^{N} e_{t}^{2}$ (27) $s . t . \sum_{t = 1}^{m} l_{i} = 1, l_{i} ⩾ 0$ (28)Step 5.L = [l₁, l₂, ⋯, l_m] ^T is calculated, and the weighted coefficients of every prediction method are acquired.

Step 6. the combined prediction model is used to predict the internet public opinion of smart city.

7 Internet public opinion prediction simulation of smart city

A smart city in China is used to carry out the internet public opinion prediction simulation, the prediction sample of public opinion selects from real data in from 2007 to 2016. Firstly, the logarithmic transformation preprocessing is carried out for these original public opinion data, then the smooth property of original data series can be improved then the combined prediction model is applied in predict the rumors of internet public opinions. The prediction programmer is compiled by MATLAB software, and the prediction results are shown in Table 1.

Table 1
China prediction results rumors from internet public opinion in from 2007 to 2016

Year Real number of rumors Prediction number of rumors Error/%

2007 43204 432102 0.02

2008 48495 48107 0.08

2009 49554 49281 0.06

2010 50346 50115 0.05

2011 52359 52185 0.03

2012 55962 55495 0.08

2013 57843 57602 0.04

2014 56943 56032 0.16

2015 54065 53889 0.03

2016 52045 51895 0.03

Year	Real number of rumors	Prediction number of rumors	Error/%
2007	43204	432102	0.02
2008	48495	48107	0.08
2009	49554	49281	0.06
2010	50346	50115	0.05
2011	52359	52185	0.03
2012	55962	55495	0.08
2013	57843	57602	0.04
2014	56943	56032	0.16
2015	54065	53889	0.03
2016	52045	51895	0.03

As seen from Table 1, the prediction value based on grey system theory and fuzzy neural network has less prediction error, then it has better precision, the prediction value of rumors coincide with the real value. The prediction analysis results show that the combined prediction model based on grey system theory and fuzzy neural network is good tool of predicting internet public opinion. In addition, the simulation results show that the prediction results of rumors increases from 2007 to 2013, because the number of internet users increase in this period, the prediction results from 2013 to 2016 decreases, because the smart city construction is carried out in this period, then the controlling level of internet public opinion increases.

The combined prediction method based on grey system theory and fuzzy neural network is applied to predict the rumors of internet public opinion from 2017 to 2022, and the corresponding prediction results are shown in Table 2.

Table 2

Prediction results of rumors of internet public opinion in from 2017 to 2024

Year	Combined prediction results of grain yield/ million tons
2017	50763
2018	48657
2019	46247
2020	44592
2021	43668
2022	42186

As seen form Table 2, the rumor number of this smart city in from 2017 to 2022 are predicted, the prediction results can provide valid guidance for establishing internet public opinion controlling measurements.

The trained prediction model based on grey system theory and fuzzy neural network is used to spread the spread trend of a unexpected event, and the event happens on June 1, 2017, which is defined as coordinate value of 1, the coordinate value of 2 denotes the Jun 2, 2017, and so on. And the predicting simulation results are shown in Fig. 4.

As seen from Fig. 3, the negative public opinion exists the maximum value for simulation results from people who spread the negative public opinion, people who do not spread the negative public opinion and the extremists, in addition, the adjacent area of the maximum value is the High tide of public opinion diffusion.

Fig.3

Structural diagram of fuzzy neural network.

Fig.4

Prediction trend simulation results of the expected event.

8 Conclusions

Under smart city environment, the internet public opinion is more complex and changeable, which has the characteristics of uncertainty, interactive quality, and latent, therefore it is necessary to correctly predict it for judging the developing trend of internet public opinion event, and the effective guidance is carried out for it. The combined prediction model is established through combining the grey system theory and fuzzy neural network, and the training algorithm is designed, simulation results show that the combined prediction model has higher prediction precision.

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