## 3 Intelligent Method for Modeling and Simulation (IM4 MnS)
### Entity Modeling with Case-Based Reasoning
#### 3.2.3 Case Retrieval  
The (P) and (T) cases contain the specifications of the environmental conditions in which the weapon system operates and the functional characteristics of the participating entities in combat situations are known. By comparing the specifications of both cases, the similarity between them can be quantified. The Jaccard similarity can be used to calculate the similarity between two sets by using the number of set elements, and it is defined as \(J(A,B)=n(A\cap B)/n(A\cup B)=n(A\cap B)/[n(A)+n(B)-n(A\cap B)]\)[26; 27]. This feature makes it possible to utilize cases that are designed using the set theory. For example, it is assumed that \(A=\{1,2\},\ B=\{1,3\}\). Then, the Jaccard similarity is \(n(A\cap B)/n(A\cup B)=\ 1/(2+2-1)=0.333\). However, this method expresses the ratio of the intersection to the union of the two sets, and the similarity can be decreased when the number of elements in the previous case increases. Hence, in this study, the Jaccard similarity was modified as the ratio of the intersection to the target case instead of the union set of the previous and target cases, and it is defined as \(J^{\prime}(A,B)=Sim(A,B)=n(A\cap B)/n(B)\). The similarity of environmental conditions is calculated by the weighted sum of each similarity of the expected environment (\(E\)) and the functional demands (\(F\)) of the participants. Each weighted value has a value between 0 and 1, and the sum of the values is 1. Equation (1) indicates the similarity of the environmental condition (EC), and is based on Equation (2). \[Sim\big{(}EC^{P},EC^{T}\big{)}=\ \lambda_{1}^{OE}Sim\big{(}E^{P},E^{T}\big{)}+ \lambda_{2}^{OE}Sim\big{(}F^{P},F^{T}\big{)},\ \ \big{(}0\leq\lambda_{1}^{EC},\lambda_{2}^{EC}\leq 1 \,\ \lambda_{1}^{EC}+\lambda_{2}^{EC}=1\big{)} \tag{1}\]\[J^{\prime}\Big{(}E^{P},E^{T}\Big{)}=Sim\Big{(}E^{P},E^{T}\Big{)}=\frac{n\Big{(}E^{P }\ \cap\ E^{T}\Big{)}}{n(E^{T})},\quad J^{\prime}\Big{(}F^{P},E^{T}\Big{)}=Sim \Big{(}F^{P},E^{T}\Big{)}=\frac{n\Big{(}F^{P}\ \cap\ F^{T}\Big{)}}{n(F^{T})} \tag{2}\]  
The designed model in the combination with the modules based on the template can represent multiple variants of the model using certain modules according to the structural and functional characteristics. The case similarity for the organization of the modules can be quantified by comparing the configuration modules and their properties. The properties can be categorized into qualitative and quantitative types. The qualitative (QL) similarity is calculated using the Jaccard similarity that was modified in this study, and the quantitative (QN) similarity is determined by averaging the ratio of the Euclidean distance to a large value for each QN property. Consequently, the similarity of the module configurations is calculated by the weighted sum of these similarity values. Equation (3), which is based on Equations (4) and (5), determines the similarity of configuring modules and their properties. Equation (4) provides the similarity score for the sets of QL values of the modules that are involved in the previous case and the target case using the modified Jaccard similarity. In the same way, Equation (5) offers the similarity score for the sets of QN values of the previous and target modules using the average of the ratio of the Euclidean distance for the corresponding QN values.