3. The mathematical definition of the analysis of the soft targets

The whole analysis of the features of the soft target is based on the relation between the question and the answer. The question analyzes the status of the features of the object. Each of the answers can define the level of the security, the level of the question, and level of the features too. This fact can be seen in Figure 2.

The level of the security can be influenced by the security measures. After the repeated assessment, we can see the higher level of the security.

The whole coefficient of the object is defined in the next equations:

$$\mathbf{K}\_{\rm S} = \frac{\mathbf{L}.\mathbf{W}\_1 + \mathbf{C}\_{\rm EK}.\mathbf{W}\_2 + \mathbf{C}\_{\rm PK}.\mathbf{W}\_3 + \mathbf{C}\_{\rm IK}.\mathbf{W}\_3}{4} \tag{1}$$

KS—the final security coefficient; Wn—weight of each coefficient; L—coefficient of the locality; CEK—final coefficient of the exterior; CPK—final coefficient of the processes; CIK—final coefficient of the interior.

The weight (Wn) is set by the administrator of the software tool. We propose that these weights will be clarified after more case studies. In the current research, we evenly set these weights. The locality coefficient is defined by the map tool. The map tool has defined the risk of the locality by the administrator.

The coefficient of the interior is defined in Eq. (2). Each of the security attributes can be used in the object several times. The use of these security attributes is significant to the whole interior security. The security attributes define how many times the security attributes can be used:

$$\mathbf{I}\_{\mathbf{K}} = \frac{\mathbf{1}}{\mathbf{P}\mathbf{B}} \sum\_{i=1}^{\text{PB}} \mathbf{B}\_{\text{ib}} \left( \mathbf{B}\_{\text{i}} \in \mathbf{0}, \mathbf{100} \right) \tag{2}$$

PB—the number of the security attributes; Bi—the security attributes; IK—the criteria of the interior.

Eq. (3) defines the final interior criteria in the same category of the interior. The final interior criteria (category) are based on the sum of each of these categories of the interior criteria:

$$\mathbf{I\_{KCi}} = \frac{\mathbf{1}}{\mathbf{PK}} \sum\_{i=1}^{\text{PK}} \mathbf{I\_K} \tag{3}$$

IKCi—interior criteria (all); PK—the number of the criteria.

Figure 2.

The basics of the analysis of the soft targets.

The categories of the interior criteria are incorporated to the final coefficient of the interior. This equation is defined in Eq. (4):

$$\mathbf{C}\_{\text{IK}} = \frac{\mathbf{1}}{\mathbf{P}} \sum\_{i=1}^{\text{P}} \mathbf{I}\_{\text{KCi}} \tag{4}$$

CIK—the final coefficient of the interior; P—the number of up criteria.

The final coefficient of the interior is the sum of all the up criteria. The exterior coefficient is defined in Eq. (5):

$$\mathbf{E\_K} = \sum\_{\mathbf{k\_u}=0}^{3} \mathbf{N} \ast \mathbf{k\_u} = \mathbf{n} \ast \mathbf{0} + \mathbf{n} \ast \mathbf{1} + \mathbf{n} \ast \mathbf{2} + \mathbf{n} \ast \mathbf{3} \tag{5}$$

EK—the calculation of the value of the exterior criteria; ku—coefficient of the security level; N—the number of the attributes.

$$\mathbf{E\_{KC}} = \frac{\sum\_{\mathbf{ku}=0}^{3} \mathbf{n} \ast \mathbf{k\_u}}{\mathbf{3} \ast \mathbf{sum N}} \tag{6}$$

EKC—all of the criteria of the exterior; Sum N—the number of all attributes.

$$\text{sum N} = \sum\_{i=1}^{4} \text{N}\_{i} \tag{7}$$

The final coefficient of the exterior is defined in Eq. (8).

$$\mathbf{C\_{EK}} = \left[\frac{\mathbf{10}}{\mathbf{n}} \sum\_{\mathbf{j}}^{\mathbf{n}} \mathbf{E\_{KCj}}\right] \ast \mathbf{W} \tag{8}$$

CEK—the whole coefficient of the exterior.

Each of these equations is used in the next part of the paper (in the case study). The process coefficient is defined in Eq. (9):

$$\mathbf{P\_K} = \sum\_{\mathbf{k\_u=1}}^{\mathbf{3}} \mathbf{n\_k} \ast \mathbf{k\_u} \tag{9}$$

PK—coefficient of one process (the number of criteria); nk—the number of the criteria; ku—the level of the criteria.

$$\mathbf{P\_{KCj}} = \frac{\mathbf{10}}{\mathbf{3} \ast \mathbf{N}} \sum\_{i=1}^{n} \mathbf{P\_{Ki}} \tag{10}$$

PKCj—the complete process coefficient of the all processes in one category (processes are divided into the categories); N—the number of the processes; n—the number of the upper level of the process; PKi—each of the coefficient of one process.

The complete process coefficient is defined in Eq. (11). Each category has defined the weight according to the threats, or we can evenly set the weight:

$$\mathbf{C}\_{\rm PK} = \left[\frac{\mathbf{1}}{\mathbf{N}} \sum\_{j=1}^{k} \mathbf{P}\_{\rm KCj}\right] \ast \mathbf{W} \tag{11}$$

## The Software to the Soft Target Assessment DOI: http://dx.doi.org/10.5772/intechopen.87997

CPK—the whole coefficient of the processes; k—the criteria; W—the weight of the process.

This part of the chapter defined the mathematical definitions of the whole process of the analysis. We have defined three types of concrete analysis (processes, internal, and external) and one type of outside analysis (locality coefficient). The locality coefficient is defined according to the situation in the nearest area of the object. We can say that the locality can be changed in time without the change in the object. For example, the public event can influence the security situation in the object (e.g., the Christmas market).
