RDTTM: Dynamic Risk-Defined Trust Transitivity in Social Networks

TL;DR

Social Network Group Decision-Making (SNGDM) is often hindered by the rigid way trust is propagated through a network. The Risk-defined Trust Transitivity Model (RDTTM) breaks this rigidity by introducing a risk-attitude parameter ($heta$). This allows the model to adjust how quickly trust decays or distrust grows across a referral chain, providing a more personalized and human-like decision-making process.

Problem & Motivation: The "One Size Fits All" Trust Fallacy

In digital ecosystems like CouchSurfing or E-commerce platforms, we rely on the "friends of friends" logic to make decisions. However, current mathematical models for trust transitivity have a major flaw: they assume everyone views risk the same way.

If a friend you trust 80% recommends a specialist they trust 80%, a conservative person might only trust that specialist 50% (high attenuation), while a risk-taker might trust them 70%. Existing SOTA methods (like those by Wu et al.) often use fixed "uninorm" operators that reflect a single, typically conservative, risk profile. Furthermore, they often ignore inconsistency—the scenario where an evaluator provides conflicting high trust and high distrust scores simultaneously.

Methodology: The RDTTM Framework

The paper introduces a structured approach to move from sparse social data to a concrete group decision.

1. Four-Tuple Information Space

Instead of a single "trust score," the model uses a tuple $\lambda =(t,d)$, where $t$ is trust and $d$ is distrust. This expands into a space covering:

• Trust & Distrust: Direct values.
• Hesitancy: When $t+d<1$ (uncertainty).
• Inconsistency: When $t+d>1$ (conflicting data).

2. Risk-Defined Propagation ($P_{h}eta$)

This is the core innovation. The operator propagates trust along a path based on a parameter $heta$:

• High $heta$: Reflects a conservative DM. Trust drops sharply across each hop in the network.
• Low $heta$: Reflects a risk-taking DM. Trust is preserved more effectively across referrals.

Fig 1. A typical expert trust network where nodes calculate indirect trust via propagation paths.

3. Path Centrality Aggregation

Since there are often multiple paths between two people (e.g., $e_{4}o{e}_{3}o{e}_{1}o{e}_2$ vs. $e_{4}o{e}_{5}o{e}_2$), the model uses Closeness Centrality. Paths involving more "central" or influential experts are given higher weights during aggregation.

Experiments: Sensitivity to Risk

The authors tested RDTTM on a "Trusted Service Selection" problem (choosing a computer supplier). The results were striking:

• At $heta=1.25$ (Risk-taking), Supplier $o_1$ was the winner.
• At $heta=10$ (Conservative), Supplier $o_4$ was the winner.

Fig 2. The ranking of suppliers shifts completely as the Decision Maker's risk attitude (1/θ) changes.

This proves that previous "fixed" models were only providing a partial view of the truth. By adjusting $heta$, the RDTTM can simulate various human behaviors, outperforming the static nature of previous SOTA methods.

Critical Insight & Conclusion

The true value of this paper lies in its Inductive Bias toward human psychology. Trust is not a physical constant; it is a subjective perception of risk. By mathematically defining the Knowledge Degree (KD) based on Euclidean distance and linking it to a tunable Risk Attitude, the authors have bridged a gap between social psychology and fuzzy mathematical logic.

Limitations: The model currently assumes that the DM knows their own $heta$ value. In future iterations, an automated way to "learn" a user's risk profile from historical decisions would make the system significantly more powerful for large-scale social networks.