## Appendix D
The goal is broken down into themes,which are then utilized to compute the data of different fields of origin and formats that are required for an actionable actor in the decision-making process. All things considered, a generic mathematical formula might be used to characterize the theme breakdown process:

\[\mathbf{i=f(d)}\] (A2)

for each sub-set of desired indicators, where:

* **i:** is the vector/edge of specific indicators,
* **f:** is the computational method, including mathematical or algorithmic processes, or is a mathematical model or is a complex transfer function, and
* **d:** is the vector of input data, which is necessary for the calculation of the relevant indicators [25]. Combining Equations (A1) and (A2) and applying them to the general mathematical formula (1), the process of thematic decomposition could be generalized by the form:

\[\mathbf{M_{i,p}}\mathbf{:W^{(j)}}_{(i,p)}=\mathbf{f_{(i,p)}}\left[\mathbf{SDC _{(i,p)}}\right]\] (A3)

where:

* **i** is the grade of thematic decomposition of initial mission \"\(\mathbf{M_{0}}\mathbf{:W^{(j)}}\)\" into sub-missions \"\(\mathbf{M_{(t,a)}}\): \(\mathbf{W^{(j)}}\)\", where \(\mathbf{t\in\mathbb{N}}\)*,
* **p** is the number of participant actionable actor(s) or sub-actor(s), where \(\mathbf{p\in[1,2,3,\)\(\ldots,n]}\),
* **n** is the max number of participant actionable actor(s) or sub-actor(s), where \(\mathbf{n\in\mathbb{N}}\)*,
* **SDC** is a special data core, which includes the operational information, and
* **j** is the maximum number of questions, where \(\mathbf{j\in\mathbb{N}}\)*. _E3. Thematic Decomposition of a Mission as a Representative Example_

As previously noted, j-questions for each participating actionable actor can completely characterize each mission. Additionally, in accordance with the MDMP approach, an expert might break down a mission into smaller missions for each participant who is an actionable actor based on the goals of the original mission by applying the process of thematic and geographic decomposition. The Subject Matter Expert (SME), who determines how to accomplish the decomposition of a task using typically empirical criteria while taking into account the time available and the preparedness of the involved actionable players is the key to the success of this analysis. The incremental examination of each theme breakdown relates to a particular actionable actor and an area of interest where the mission (sub-mission of the primary goal) will be carried out. An operational officer in this field is required to identify the best options, to direct and provide orders to the participating actionable actor, or to seek more operational data in order to carry out precise evaluations. The process of thematic deconstruction involves breaking down each subject into its component sub-subjects (1 st level), then further breaking down each sub-subject (2 nd level) into its component sub-subjects (n-level), etc. This structure, where \(\mathbf{n\in\mathbb{N}}\)*, is an acyclic network that resembles an n-tree. Therefore, at the top of this n-tree structure, there is the initial mission \"\(\mathbf{M_{0}}\mathbf{:W^{(j)}}\)\", which is branched, thematically and geographically, downward into further n sub-missions for each actionable actor until reaching the last elementary thematic decomposition (leaf in the tree structure). Each sub-mission is a vector, which begins from \"\(\mathbf{M_{0}}\mathbf{:W^{(j)}}\)\" and ends with \"\(\mathbf{M_{(t,a)}}\mathbf{:W^{(j)}}\)\", where \(\mathbf{t\in\mathbb{N}}\)* and it could be named as a terminal node in case there is no more decomposition (analysis). Otherwise, the node could be divided into more thematic sub-missions, until the entire procedure stops at elementary decomposition. Thus, suppose that we are at the 1 st level of decomposition and the initial mission \"\(\mathbf{M_{0}}\mathbf{:W^{(j)}}\)\" is fully described by replying to the j-question \(\mathbf{W^{(j)}}\).