## 3 Methodology
### Neutrosophic Axiomatic Design (NAD)  
Neutrosophic Axiomatic Design (NAD) is an extension of Axiomatic Design (AD) that uses neutrosophic sets to handle uncertainty, imprecision, and incomplete information in complex decision-making processes. While traditional Axiomatic Design focuses on two main principles, independence and information minimization, NAD integrates neutrosophic logic to increase flexibility and reliability in ambiguous environments. The information axiom, which concerns the ability to maintain established goals, is determined based on information content (InC). The origin of InC\({}_{i}\) is described as follows:  
\[\text{InC}_{i}=\log_{2}\bigg{(}\frac{1}{\text{probability}_{i}}\bigg{)} \tag{20}\]  
The distribution function of uniform probability, denoted (Probability\({}_{i}\)), is represented as follows:  
\[\text{Probability}_{i}=\bigg{(}\text{Common}\frac{\text{range}}{\text{ System}}\text{range}\bigg{)} \tag{21}\]  
\[\text{InC}_{i}=\text{Log}_{2}\bigg{(}\text{Common}\frac{\text{range}}{ \text{System}}\text{range}\bigg{)} \tag{22}\]  
The symbols of the components of information content, including truth members (InC\({}^{\text{Tru}}\)), false members (InC\({}^{\text{Ind}}\)), and indeterminacy members (InC\({}^{\text{Fal}}\)), are described as follows:  
\[\text{InC}^{\text{Tru}}=\log_{2}\frac{\text{Truth}-\text{membership system design}}{\text{Truth}-\text{membership Common area}} \tag{23}\]  
\[\text{InC}^{\text{Ind}}=\log_{2}\frac{\text{Indeterminacy}-\text{membership system design}}{\text{Indeterminacy}-\text{membership Common area}} \tag{24}\]  
\[\text{InC}^{\text{Fal}}=\log_{2}\frac{\text{Fality}-\text{membership system design}}{\text{Fality}-\text{membership Common area}} \tag{25}\]  
The proposed method for MCDM problems, using the NFAD approach for evaluation, is as follows: ATru represents the set of alternatives, with \(\forall k\in\text{ATru}\). The set C is the criteria, with \(\forall j\in\text{C}\); We is the weight of each C, satisfying \(\text{We}_{j}\geq 0\), \(j=1\), \(2\), \(\ldots\), n, \(\sum_{j=1}^{n}\text{we}_{j}=1\); DU is a group of decision-makers. Step 1: Apply SVTrN, with the structure <Low value (L), Medium value (M), High value (U)>, and confirmation level (CD), to represent the data. The method of representing the data is shown in Table 3.  
Step 2: To calculate the average of decision-makers' opinions, we add up the SVTrN numbers, as in Equation (13), then divide the sum by the number of decision-makers for each criterion. Step 3: To calculate the \(\mathrm{InC}^{\mathrm{Tru}}\) for each functional requirement (\(\mathrm{FR}_{\mathrm{i}}\)), we use Equation (26):  
\[\mathrm{InC}^{\mathrm{Tru}}_{\mathrm{ij}}=\left\{ \begin{array}{cc}0&\mathrm{ if}\hat{k}_{\mathrm{ij1}}>\hat{g}_{\mathrm{ij3}}\mathrm{or}\hat{k}_{\mathrm{ij3}}>\hat{g}_{ \mathrm{j1}}\\ \log_{2}\frac{\mathrm{Truth-membership\ system\ design}}{\mathrm{Truth-membership\ Common\ area}}&\mathrm{if}\hat{k}_{\mathrm{ij1}}\leq\hat{g}_{\mathrm{ij3}}\mathrm{or}\hat{k}_{\mathrm{ij3}}\leq\hat{g}_{ \mathrm{j1}}\end{array} \right. \tag{26}\]  
where \(\hat{g}_{\mathrm{j1}}\) and \(\hat{g}_{\mathrm{ij3}}\) are the low value (L) and high value (U) of \(\mathrm{FR}_{\mathrm{I}}\) and \(\hat{k}_{\mathrm{ij1}}\) and \(\hat{k}_{\mathrm{ij3}}\) are the low value (L) and high value (U) of \(\mathrm{Attu}_{\mathrm{I}}\) according to \(\mathrm{C}_{\mathrm{i}}\). Step 4: Calculate the \(\mathrm{IC}^{\mathrm{Ind}}\) value for each functional requirement \(\mathrm{FR}_{\mathrm{I}}\) using the formula in Equation (27):  
\[\mathrm{InC}^{\mathrm{Ind}}_{\mathrm{ij}}=\left\{ \begin{array}{cc}0&\mathrm{ if}\hat{k}_{\mathrm{ij1}}>\hat{g}_{\mathrm{ij3}}\mathrm{or}\hat{k}_{\mathrm{ij3}}>\hat{g}_{ \mathrm{j1}}\\ \log_{2}\frac{\mathrm{Indetermacy-membership\ system\ design}}{\mathrm{Indetermacy-membership\ Common\ area}}&\mathrm{if}\hat{k}_{\mathrm{ij1}}\leq\hat{g}_{\mathrm{ij3}}\mathrm{or}\hat{k}_{\mathrm{ij3}}\leq\hat{g}_{ \mathrm{j1}}\end{array} \right.