Distrust Behavior in Social Network Large-Scale Group Decision Making and Its Application in Water Pollution Management
- The AHC method is utilized to decrease the complexity of LSGDM-SN with the FPR, in which both the trust relationships and distrust relationships among experts are incorporated into the clustering method. Then, the concept of preference similarity, trust similarity, and distrust similarity are proposed to compute the degree of overall similarity among experts. Meanwhile, the algorithm for the AHC of LSGDM-SN is presented.
- Consensus feedback based on distrust behavior and social network analysis (SNA) is presented to encourage the subset to modify its FPR based on different distrust types. In the identification process, both the distrust score and the degree of difference are incorporated to measure the distrust degree of the subset. Based on the cases of distrust behaviors, two pieces of feedback advice are provided to the subset to adjust its FPR.
- A score function of FPR is designed to choose the best alternative for water pollution management. By calculating the final score of the collective FPR, we rank all alternatives. Then, the one with the highest score is selected as the best solution for water pollution management. Finally, a framework for the proposed LSGDM-SN considering distrust behavior is depicted to visualize the decision process.
2.1. Fuzzy Preference Relation
- Socio-matrix: The matrix G = (gkq)m×m is utilized to present the relationships data among experts. If expert ek has no relationship with eq, the value of gkq is equal to 0. Otherwise, the value of gkq is 1 if there is an existing relationship between ek and eq.
- Graph: Social networks can also be represented by a graph, where the points are connected by straight lines. In the network diagram, ek→eq indicates that there is a direct relationship from ek to eq.
- Algebraic: The algebraic can denote the social relationships among experts and the relationship combinations.
3. Large-Scale Expert Clustering Based on AHC Approach
|Algorithm 1. The detailed AHC method.|
Output: subsets su1, …, sup, …, suυ.
Step 1: Regard each expert ek (k =1, …, m) as one initial subset.
Step 2: Calculating the values of pskq, tskq, dskq and oskq for each initial subset based on Equations (8)–(11).
Step 3: Selecting the maximum oskq, then classify initial subsets eq and ek into one new subset.
Step 4: Deleting subsets eq and ek in Step 3, the overall similarity is recalculated based on Definition 9.
Step 5: Steps 3 and 4 are repeated constantly. If all subsets are merged into one subset, the process is ended.
Step 6: Setting the number of subsets, output the clustering result su1, …, sup, …, suυ.
4. Consensus of LSGDM-SN Based on Distrust Behavior and SNA
4.1. Consensus Measure
4.2. Consensus Feedback Based on Distrust Behavior and SNA
4.3. Selection Process
4.4. The Proposed Framework of LSGDM-SN
5. Case Study
6. Comparative Analysis and Discussion
6.1. The Impact of Distrust Behavior on Alternative Ranking
6.2. The Impact of Weight Determination on Decision Result
6.3. Sensitivity Analysis of Consensus Threshold
6.4. The Comparison with Other Related Studies
- A novel AHC method considering preference similarity and social similarity is proposed to decrease the complexity of LSGDM-SN with FPRs. Several definitions, including preference similarity, trust similarity, and distrust similarity, are proposed to compute the degree of overall similarity among experts. Subsequently, the AHC algorithm dealing with the LSGDM-SN problem is designed.
- The consensus feedback for detecting and managing distrust behavior is presented, which encourages the subset to modify its FPR based on different distrust types. To identify the distrust behavior, both the distrust score and the degree of difference are incorporated to measure the distrust degree of the subset. Based on the value of distrust degree, two pieces of modification advice are provided to subset to modify it FPR.
- A score function is defined to derive the alternatives ranking in water pollution management. After computing the values of scores for all alternatives, we rank them. The optimal alternative is obtained based on the maximum value score. Finally, the LSGDM-SN framework considering distrust behavior is described to visualize the decision process.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|e1||(1, 0)||(0.9, 0.3)||(0.8, 0.7)||(0.6, 1.0)||(-, -)||(-, -)|
|e2||(-, -)||(1, 0)||(0.8, 0.3)||(-, -)||(0.7, 0.9)||(-, -)|
|e3||(0.3, 0.3)||(0.1, 0.6)||(1, 0)||(0.8, 0.4)||(-, -)||(-, -)|
|e18||(-, -)||(-, -)||(-, -)||(1, 0)||(0.1, 0.1)||(0.8, 0.5)|
|e19||(-, -)||(-, -)||(0.7, 1.0)||(0.4, 0.9)||(1, 0)||(-, -)|
|e20||(-, -)||(0.7, 0.2)||(0.1, 0.7)||(0.3, 0.4)||(-, -)||(1, 0)|
|τ||CLC (τ)||sup,(τ)||sup,(τ) < β||FPR|
|Collective FPR||fs(xi)||Ranking of Alternatives|
|fs(x1) = 0.505|
fs(x2) = 0.523
fs(x3) = 0.453
fs(x4) = 0.520
|x2 > ≻x4 > ≻x1 > ≻x3|
|Consensus Iteration||fs(xi)||Ranking of Alternatives|
|5||fs(x1) = 0.511|
fs(x2) = 0.519
fs(x3) = 0.451
fs(x4) = 0.518
|x2 > ≻x4 > ≻x1 > ≻x3|
|θ||τ||fs(x1)||fs(x2)||fs(x3)||fs(x4)||Ranking of Alternatives|
|0.92||0||0.509||0.527||0.453||0.512||x2 > ≻x4 > ≻x1 > ≻x3|
|0.93||1||0.506||0.526||0.448||0.520||x2 > ≻x4 > ≻x1 > ≻x3|
|0.94||3||0.509||0.519||0.455||0.517||x2 > ≻x4 > ≻x1 > ≻x3|
|0.95||4||0.504||0.518||0.457||0.521||x4 > ≻x2 >≻x1 > ≻x3|
|0.96||7||0.509||0.518||0.453||0.520||x4 > ≻x2 > ≻x1 > ≻x3|
|0.97||10||0.508||0.520||0.454||0.518||x2 > ≻x4 > ≻x1 > ≻x3|
|0.98||14||0.508||0.519||0.453||0.520||x4 > ≻x2 > ≻x1 > ≻x3|
|0.99||22||0.507||0.520||0.453||0.519||x2 > ≻x4 > ≻x1 > ≻x3|
|1||344||0.508||0.519||0.453||0.520||x4 > x2 > x1 > x3|
|Method||Clustering Method||Social Relationship||FPR||Distrust Behavior||Water Pollution Problem|
|Lu et al. ||K-means clustering||√||×||×||×|
|Liu et al. ||DM clustering||×||×||×||×|
|Wang et al. ||Louvain algorithm||√||×||×||×|
|Meng et al. ||Trust-based density peaks clustering||√||×||×||×|
|Our method||AHC method||√||√||√||√|
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Lu, Y.; Liu, G.; Xu, Y. Distrust Behavior in Social Network Large-Scale Group Decision Making and Its Application in Water Pollution Management. Water 2023, 15, 1638. https://doi.org/10.3390/w15091638
Lu Y, Liu G, Xu Y. Distrust Behavior in Social Network Large-Scale Group Decision Making and Its Application in Water Pollution Management. Water. 2023; 15(9):1638. https://doi.org/10.3390/w15091638Chicago/Turabian Style
Lu, Yanling, Gaofeng Liu, and Yejun Xu. 2023. "Distrust Behavior in Social Network Large-Scale Group Decision Making and Its Application in Water Pollution Management" Water 15, no. 9: 1638. https://doi.org/10.3390/w15091638