**4. Approach towards Topology Design**

Associative fusion rules allow changing the sequence in which information sources are fused without altering the fusion result. Therefore, associativity is a beneficial property with regard to the topology design of distributed information fusion systems. Assuming associativity, a system designer or a design algorithm can focus on other criteria for designing a fusion system, such as spatial availability of sources or consistency as well as the redundancy of sources. In this section, we analyse the presented fusion rules regarding the associativity property and its impact on topology design. Following this, a two-layer fusion topology based on the MCS fusion rule (6) is presented. Consistency as a design criterion both increases the specificity of fusion results due to the minimum-operator [6] and to facilitate source defect detection algorithms [21,22]. This motivates the dive into the MCS fusion topologies in this article.

Some flaws and shortcomings of this consistency-based approach are discussed, which leads to several adjustments to overcome those. This includes the introduction of redundancy as a design criterion.

First, both fusion node and fusion topology are defined, and some notations introduced:

**Definition 4** (Fusion Node)**.** *A fusion node fn is a self-contained module encapsulating a fusion operator. A node takes information items as input and outputs a single fused information item. As a node is a self-contained module, a fusion node and its fusion operator have to satisfy the following additional properties:*


*Idempotency as a property is not required since idempotency restricts the fusion node in the case where a reinforcement effect is desired (e.g., via the product operator as a t-norm). A fusion node with an associative fusion operator is beneficial since it allows splitting the fusion node.*

*A fusion node is a modular part of a fusion topology. In order to facilitate the fusion process of the grander topology, it may output auxiliaries denoted as* [*AUX*]*. Consequently, a node is also required to be able to process* [*AUX*] *as input if necessary.*

**Definition 5** (Fusion Topology)**.** *Interconnected fusion nodes build up a fusion topology. Fusion nodes may be interconnected parallelly, serially, hierarchically, cascadingly, or in more complex structures. A fusion topology organises a feed forward flow of information. Recursive interconnections are excluded. A fusion topology is constructed in layers l* ∈ N>0*. In each layer, fusion nodes are indexed consecutively with k* ∈ N>0*. The k-th fusion node in layer l is denoted by fn*(*k*,*l*)*, its output information item by I*(*k*,*l*)*, and its auxiliary output by* [*AUX*](*k*,*l*)*.*

Given the above definitions, Figure 3 shows a three-layer example topology to help visualise the introduced notations.

**Figure 3.** An example for a three-layer fusion topology. Fusion nodes are denoted with *fn*(*k*,*l*) and their output information items with *I*(*k*,*l*) together with auxiliary information [*AUX*](*k*,*l*). The index *l* denotes the layer. Within a layer *l*, the nodes are numbered consecutively by *k*.

The MCS-based design presented in this article focuses on a two-layer topology by grouping consistent or redundant information sources into fusion nodes. For an easier reading of the article, fusion nodes are also denoted as *fn*(*k*) in a two-layer topology. Since this approach considers associative fusion rules, the basic two-layer design can be easily extended into a multi-layer version.
