*4.3. Robustness*

The MCS fusion topology based on consistencies in the historic training data is prone to unexpected inconsistencies in information items. Due to the minimum operator used in the first level fusion nodes (see (15) and Figure 4), intermediate fusion results are altered significantly if items are less consistent then they are expected to be, that is <sup>h</sup> ≤ *<sup>α</sup>*<sup>r</sup> . Even in large groups of sources, a single information source producing an unexpectedly inconsistent item may change the outcome significantly. An example of such an occurrence inside a fusion node using *α*<sup>r</sup> = 1 is given in Figure 5.

**Figure 5.** Information items of a fusion node with consistency level *α*<sup>r</sup> = 1. Left plot (**a**) shows possibility distributions with expected consistent behaviour. In the right side plot (**b**), a single defective information item with unexpected behaviour (marked in red) causes h(**I**) < *α*<sup>r</sup> . Fusion with (15) results in dissimilar possibility distributions.

Unexpected inconsistent behaviour of reliable sources occurs in two situations.

• First, incomplete information and epistemic uncertainty in the training data may lead to assessing a group of sources as consistent prematurely. Information sources may produce different (in)consistent behaviours depending on the training data's true value and its position on the frame of discernment. Take, for example, a conditionmonitoring scenario of a technical system in which sensors state the condition on a discrete frame of discernment *X* = {*error1*,*error2*, *normal*}. Two sensors may both detect two of the conditions (e.g., *error1*, *normal*); however, only one is able to detect the third condition (*error2*). If training data does not include data regarding *error2*, then with Algorithm 1, both sensors are falsely identified as consistent and grouped into a fusion node. If *error2* occurs later, then the sensors behave unexpectedly inconsistently. This problem relates to *spurious correlations* in probability theory [70], which describes

that, in large datasets, it is particularly likely that correlations are found between variables incorrectly.

• Second, defective sources are a cause of unexpected inconsistent behaviour. Defective sources are sources that are trustworthy and therefore have a high reliability but nonetheless start to supply incorrect information [71]. Source defects appear in different forms: Information can change suddenly, drift continuously or incrementally, or can be characterised by an increasing number of outliers [72,73]. Countermeasures are majority-guided fusion rules as applied by Ehlenbröker et al. and Holst and Lohweg [21,23]. This requires redundant and reliable sources in a fusion node.

In the following, we propose three adaptations to the distributed MCS-based fusion topology. These adaptations aim to increase the robustness of the topology in the case of incomplete training data and defective sources.

