# On Fuzzy and Case-Based Dynamic Software Development Process Modeling and Simulation Approach
## 4 Materials and Methods--On the Fuzzy CMMN Model for SDP Simulation
### Fuzzy Inference in the SDP Model  
The SDP is a dynamic and knowledge-intensive BP because of HFs within process activities. As it is very difficult to predict how HFs influence one another in the implementation of an activity, we take them as fuzzy variables. The influence of the HF on the SDP can be expressed as \(HF(f_{1},f_{2},\ldots,f_{n})\), where \(f_{i}\) denotes a particular attribute of a resource. In this research, we emphasize such resource attributes as motivation (\(f_{1}\)), experience (\(f_{2}\)), and availability (\(f_{3}\)). Consequently, a linguistic variable of HF consists of linguistic attributes \(f_{i}\)--such as motivation (\(f_{1}\)), experience (\(f_{2}\)), and availability (\(f_{3}\))--whose value set \(T\) can, in turn, be divided into meaningful crisp intervals, and whose linguistic meaning denotes the human linguistic attribute level as Excellent (5), Good (4), Moderate (3), Low (2), or None (1). We chose these HF variables because it is already established that motivation, experience, and availability can make a difference in the performance of any human-related activities. For example, employee motivation is considered a force that drives employees towards achieving specific goals and objectives [42; 43]. In [42], the authors observed that a significant and positive relationship exists between employee motivation and employee performance. Employee experience level turns human resources management in an organization into a more strategic process that engages the employee through meaning and providing value [44]. Availability is the parameter that shows how much time a resource can be used for task execution. It is very important to include the possibilities of HFs in BP simulation in order to achieve more precise values of task execution time and to see the impact of deviation from the estimated time. In this paper, HF motivation (\(f_{1}\)), experience (\(f_{2}\)), and availability (\(f_{3}\)) are not measured, as this is not the main aim of this study. However, since it is important to estimate these factors, their values are randomly generated, and the total HF is inferred using ANFIS. ANFIS is an FIS implemented within the framework of adaptive neural networks [45]. It is based on a set of fuzzy IF-THEN rules (e.g., (1)), with the MFs appropriate to generate specified input-output pairs:  
\[R_{i}:if\ \Big{(}x_{1}\ \textit{is}\ A_{1}^{(i)}\big{)}\ldots\textit{and} \ldots\Big{(}x_{n}\ \textit{is}\ A_{n}^{(i)}\Big{)}\ \textit{then}\ f_{i}=a_{i}^{T}\cdot x+b_{i}\, \tag{1}\]where \(x\in\mathbb{R}^{n}\) is a vector of inputs in the presumption characterized by an appropriate MF, and \(a_{i},b_{i}\) are the coefficients of linear Takagi-Sugeno consequents. Training ANFIS means determining parameters belonging to the components of the premise (i.e., input parameters) and the consequences (i.e., output) of using an optimization algorithm [45]. The principal schema of ANFIS consists of five layers, as follows [45]:  
Layer 1. Fuzzification: inputs ((\(x_{1}\), \(x_{2}\)), \(n=2\)) are fuzzified using trapezoidal MFs whose parameters--\(c_{1}\), \(c_{2}\), \(c_{3}\), \(c_{4}\)--are both adaptive and adapted during the learning. As the values of the parameters change, the MF of the linguistic term \(A_{n}^{(i)}\) also changes [45]. Layer 2. Evaluation of the rule strength: each node provides the rule strength, \(w_{i}\) (Equation (2)) [45]:  
\[w_{i}=\prod\mu_{i}(x), \tag{2}\]  
Layer 3. Normalization: the strengths of all rules, \(w_{i}\), are normalized (\(\overline{w}_{i}\)) (Equation (3)) [45]:  
\[\overline{w}_{i}=\frac{w_{i}}{\sum_{i}w_{i}}, \tag{3}\]  
Layer 4. Application of the rule (\(R_{i}\)) to obtain the output \(f_{i}\)[45]. Layer 5. Computation of the global model response (\(f\)) is given in Equation (4) [45]:  
\[f=\sum_{i}\overline{w}_{i}f_{i}, \tag{4}\]  
After training is complete, ANFIS performance is determined by various statistical tests [46].