A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory
Abstract
:1. Introduction
2. Literature Review
3. Technical Process
- Step 1:
- Literature Review and Issue Identification
- Collect and analyze the relevant literature and research results on online rumor management.
- Identify key issues and challenges within the current research landscape.
- Step 2:
- Problem Definition and Hypothesis Formulation
- Define the primary research question and establish corresponding hypotheses.
- Outline the research framework and develop an analytical model as the foundation.
- Step 3:
- Model Development and Objective Setting
- Create a multi-agent intervention model that includes self-media and netizens.
- Determine the optimal intervention time and its influencing factors.
- Establish relevant objective functions and constraints.
- Step 4:
- Model Formalization and Mathematical Approaches
- Formalize and transform the intervention model using mathematical techniques.
- Explore mathematical theories suitable for addressing uncertainties.
- Step 5:
- Model Application and Insights
- Apply the model to real-world cases and evaluate its effectiveness.
- Provide comprehensive insights and analyze factors affecting intervention timing.
- Step 6:
- Conclusion and Future Directions
- Summarize the key findings and conclusions drawn from the study.
- Discuss study limitations and propose directions for future research.
4. Problem Description
5. Model Building
5.1. Parameter Introduction
indicates the timing of the regulatory intervention, ; | |
indicates the time when the online rumor began to be published, ; | |
indicates the proportional coefficient of the spread rate of online rumors to the attention of online rumors, ; | |
indicates the highest threshold for the spread rate of online rumors; | |
indicates the proportional coefficient of the variable intervention cost to the regulatory authority and the duration of the online rumor’s publication, ; | |
indicates the proportion of users who forwarded true information related to category i online rumors by category k entities, , ; | |
indicates the correlation coefficient between the bonuses of the subject of category k and the proportion of users who retweet true information related to the online rumors in category i, , ; | |
indicates the degree of consumption of the fixed intervention costs for the regulatory authorities; | |
indicates the highest threshold value for the total cost consumption of the regulatory authority. |
5.2. Multi-Objective Functions
5.2.1. Minimize the Spread Rate of Online Rumors
5.2.2. Minimize the Total Cost of the Intervention
5.3. Opportunity Constraints and Multi-Objective Models
5.3.1. Opportunity Constraints on the Propagation Rate of Online Rumors
5.3.2. Constraints on the Opportunity to Intervene in the Degree of Total Cost Consumption
5.3.3. Timing Constraints on Interventions
5.3.4. Multi-Objective Model
- is the constraint on the propagation rate of online rumors;
- is the constraint on the degree of consumption of the total cost of the intervention.
5.4. An Equivalent Form of the Model
6. Comparative Experiments
6.1. Parameter Settings
6.2. Solve and Analyze
6.2.1. Analysis of Results Obtained When the Participants Have the Same Weight
- a.
- The Role of Self-Media
- b.
- Impact of Passive Media Response
- c.
- Influence of Netizen Participation
- International Hot Spots: In the absence of external influences, regulators should act during the birth period for optimal impact and cost-effectiveness. Once self-media and netizens engage, intervention should be delayed until the rumor’s decline (extinction period).
- Livelihood-Related Rumors: Independent of external participation, early intervention during the rumor’s birth is advised. With the involvement of self-media and netizens, an even earlier intervention is preferable.
- Anecdotal Rumors: When self-media actively disseminates true information, intervention should occur at the rumor’s inception. If self-media is passive but netizens are active, regulators should act during the rumor’s decline. Specifically, if self-media is negatively responsive while netizens are positively engaged, an early extinction-period intervention is ideal. Conversely, with passive netizen reactions, the middle extinction period is recommended.
6.2.2. Analysis of Results Obtained When Participants Have Different Weights
- a.
- Influence of Negative Responses from Self-Media and Netizens
- b.
- Impact of Active Responses from Self-Media and Netizens
- International Hot Spot Online Rumors: The optimal intervention time for international hot spot online rumors shifts from the birth period to the extinction period. This change suggests that interventions become more effective later in the rumor’s life cycle, when self-media responds negatively and netizen participation is high.
- Anecdotal Online Rumors: Similarly, the best timing for intervening in anecdotal online rumors moves from the diffusion period to the extinction period. This indicates that delaying an intervention until the later stages could be more beneficial when these actors are engaged.
- Online Rumors Related to People’s Livelihoods: The intervention timing for rumors concerning people’s livelihoods has seen a slight adjustment, shifting from the middle to the early birth period. Although this shift is less dramatic compared to the other types of rumors, it underscores the importance of early intervention in such cases.
- a.
- Intervention without Other Entities’ Involvement
- b.
- Decision Making Based on the Focus of the Intervention
- c.
- Role of Self-Media and Netizen Involvement
6.3. Effectiveness of Models
6.4. Revelation and Analysis
- The Impact of Self-Media and Netizens: The involvement of self-media and netizens significantly influences the optimal timing for interventions. For international hot spot rumors, the optimal intervention period shifts from the birth period to the extinction period. In contrast, for rumors concerning people’s livelihoods, this shift is less pronounced, moving from the middle to the early birth period. Notably, self-media’s active engagement drastically changes the best intervention timing of anecdotal rumors from the extinction to the birth period.
- Optimal Timing with Self-Media and Netizens’ Involvement: Regardless of whether regulatory authorities prioritize governance effectiveness or cost-efficiency, the presence of self-media and netizens dictates that the best time to intervene in international hot spot rumors is during their extinction period. For rumors related to people’s livelihoods, early intervention, right at the beginning of their emergence, proves most effective.
- Anecdotal Rumors Without External Participation: When anecdotal rumors circulate without the participation of self-media or netizens, the regulatory focus—whether on governance effectiveness or cost reduction—significantly affects the optimal intervention timing. Focusing on governance leads to an intervention during the extinction period, whereas prioritizing cost reduction shifts this to the diffusion period.
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
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Internet Rumor Category i | ||||||||
---|---|---|---|---|---|---|---|---|
International hot spots () | 0.1 | 0.1 | 0.2 | 0.2 | 0.8 | 0.4 | 0.1 | 0.1 |
Livelihood issues () | 0.3 | 0.3 | 0.3 | 0.3 | 0.8 | 0.4 | 0.1 | 0.1 |
Anecdotes () | 0.2 | 0.2 | 0.1 | 0.1 | 0.8 | 0.4 | 0.1 | 0.1 |
Name | Value |
---|---|
0.3 | |
0.95 | |
0.95 | |
0.6 | |
0.6 |
Positive | Negative | |
---|---|---|
0.8 | 0.2 |
Internet Rumor Category | Example 1 | Example 2 | Example 3 | Example 4 | Example 5 |
---|---|---|---|---|---|
International hot spots | 12.5937 (Extinction period) | 16.4724 (Extinction period) | 35.1824 (Extinction period) | 34.9921 (Extinction period) | 1.9470 (Birth period) |
Livelihood issues | 1.6679 (Birth period) | 2.3015 (Birth period) | 1.7970 (Birth period) | 2.3690 (Birth period) | 6.7716 (Birth period) |
Anecdotes | 5.9085 (Birth period) | 19.1390 (Extinction period) | 17.9021 (Extinction period) | 21.5345 (Extinction period) | 28.8501 (Extinction period) |
Name | Focus on the Effect of Governance | Focus on Low Cost |
---|---|---|
0.8 | 0.2 | |
0.2 | 0.8 |
Internet Rumor Category | Example 1 | Example 2 | Example 3 | Example 4 | Example 5 |
---|---|---|---|---|---|
International hot spots | 35.9649 (Extinction period) | 35.7093 (Extinction period) | 38.7049 (Extinction period) | 35.9429 (Extinction period) | 1.9465 (Birth period) |
Livelihood issues | 1.6679 (Birth period) | 2.3015 (Birth period) | 1.7969 (Birth period) | 2.3693 (Birth period) | 6.7732 (Birth period) |
Anecdotes | 5.6603 (Birth period) | 19.9189 (Extinction period) | 18.6368 (Extinction period) | 19.9598 (Extinction period) | 13.4819 (Extinction period) |
Internet Rumor Category | Example 1 | Example 2 | Example 3 | Example 4 | Example 5 |
---|---|---|---|---|---|
International hot spots | 35.9293 (Extinction period) | 39.6701 (Extinction period) | 37.4099 (Extinction period) | 15.4117 (Extinction period) | 1.9476 (Birth period) |
Livelihood issues | 1.6679 (Birth period) | 2.3011 (Birth period) | 1.7969 (Birth period) | 2.3691 (Birth period) | 6.7704 (Birth period) |
Anecdotes | 5.4278 (Birth period) | 18.2858 (Extinction period) | 17.1017 (Extinction period) | 18.4918 (Extinction period) | 7.9616 (Diffusion period) |
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Jin, M.; Liu, F.; Ning, Y.; Gao, Y.; Li, D. A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory. Mathematics 2024, 12, 2457. https://doi.org/10.3390/math12162457
Jin M, Liu F, Ning Y, Gao Y, Li D. A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory. Mathematics. 2024; 12(16):2457. https://doi.org/10.3390/math12162457
Chicago/Turabian StyleJin, Meiling, Fengming Liu, Yufu Ning, Yichang Gao, and Dongmei Li. 2024. "A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory" Mathematics 12, no. 16: 2457. https://doi.org/10.3390/math12162457
APA StyleJin, M., Liu, F., Ning, Y., Gao, Y., & Li, D. (2024). A Mathematical Optimization Model Designed to Determine the Optimal Timing of Online Rumor Intervention Based on Uncertainty Theory. Mathematics, 12(16), 2457. https://doi.org/10.3390/math12162457