# An Adaptive Dempster-Shafer Theory of Evidence Based Trust Model in Multiagent Systems
## 5 Simulation
### Manage Trust Certainty with Entropy
#### 5.2.3 Comparison and Discussion  
Here, we discuss trust certainty from the perspective of entropy of evidence. The previous literature studied certainty from the observed trust, namely, the amount of positive or negative feedback. For instance, ref. [20,66] analyzed certainty from the perspective of probability-certainty density function [65], and the estimated certainty was employed to generate evidence. That is to say, a piece of trust represented by belief, disbelief, and the unknown should derive from the amount of positive and negative feedback, and the estimated uncertainty will be employed to obtain the trust of the unknown. We provide another perspective to make use of certainty; we first analyzed multiple conditions that result in uncertainty, including lacking certainty, randomness, incompleteness, and varying performances. BPAs could represent this observation according to the Dempster-Shafer theory of evidence. However, how much we could rely on (or trust) the generated evidence when making decisions is a great challenge, and one of the significant aspects is the certainty of the evidence estimated by entropy.  
Shannon entropy [61] is a well-known information-theoretic measure of uncertainty that is based on a discrete probability distribution over a finite set of alternatives. However, entropy is said to be inappropriate for certainty estimation of the observed evidence represented by the binary event \((r,s)\)[20,66]. From one aspect, Shannon entropy's value ranges from 0 to \(\infty\), which does not fit our intuition. From another aspect, the confidence placed in a probability estimation is required. Finally, the defined Shannon entropy cannot be employed to capture the probability estimation's uncertainty represented by binary events (positive and negative feedback). In this paper, we used entropy to estimate the certainty of the observed evidence represented by BPAs, and this certainty is an essential part of making full use of BPAs. First, entropy models bits of missing information, which can also be interpreted as the information provided by the evidence, and more information conveyed by the evidence should be more valuable. Second, the estimated entropy value is in the range of 0 to 1, which can be employed to exhibit the evidence's certainty. Last but most importantly, in our opinion, the uncertainty of a trust derived from two events \((r,s)\) consists of two main aspects: the conflict between each judgment (conflict between \(r\) and \(s\)) and the uncertain part of the judgment (assigned to uncertainty). Then the entropy definition (Definition 6) [60] is designed to capture the certainty of BPAs from these two aspects that fit well to learn uncertainty. Furthermore, as exhibited in this section, the comparison results have proved the two essential qualities of certainty. That is, certainty rises with increasing experiences beyond a fixed conflict (Section 5.2.1), and uncertainty rises with the increasing conflict under a fixed amount of interactions (Section 5.2.2). Thus, the entropy is appropriate for measuring the uncertainty of the generated evidence by the Dempster-Shafer theory of evidence.