## 3 Materials and Methods
### The Utilization of Fuzzy Logic in Multi-Criteria Decision-Making
\[\overset{\approx}{\widetilde{r}}_{i}=\left(\overset{n}{\underset{i=1}{ \overset{\approx}{\widetilde{a}}_{ij}}{\overset{\approx}{\widetilde{a}}_{ij}}} \right)^{\frac{1}{K}}=\left[\overset{\approx}{\widetilde{a}}_{i1}\otimes \overset{\approx}{\widetilde{a}}_{i2}\otimes\ldots\otimes\overset{\approx}{ \widetilde{a}}_{i\text{{{}}}n}\right]^{\frac{1}{K}} \tag{15}\]  
Step 4: The attributes' IT2F weights (\(\overset{\approx}{\widetilde{w}}_{i}\)) can be obtained from the values of \(\overset{\approx}{\widetilde{r}}_{i}\) using the following equation:  
\[\overset{\approx}{\widetilde{w}}_{i}=\overset{\approx}{\widetilde{r}}_{i} \otimes\left[\overset{\approx}{\widetilde{r}}_{1}\oplus\ldots\oplus\overset{ \approx}{\widetilde{r}}_{i}\oplus\ldots\overset{\approx}{\widetilde{r}}_{n} \right]^{-1} \tag{16}\]  
Defuzzification of IT2F weights (\(\overset{\approx}{\widetilde{w}}_{i}\)) can be executed following the procedure outlined in (17). Here, the values \(w_{01,2,3,4}\) denote the arithmetic mean of the upper and lower bounds of the IT2F weight (\(\overset{\approx}{\widetilde{w}}_{i}\)). \[w_{i}=\frac{\int xu(x)dx}{\int u(x)dx}=\frac{-w_{01}\cdot w_{02}+w_{03}\cdot w_ {04}+\frac{1}{3}(w_{04}-w_{03})^{2}-\frac{1}{3}(w_{02}-w_{01})^{2}}{-w_{01}-w_{ 02}+w_{03}+w_{04}} \tag{17}\]  
The QFD Technique, Conventional Model Limitations, Optimization Strategies, and Emerging Areas of Application  
The Quality Function Deployment (QFD) technique was originally created by [PERSON] [69] as a systematic tool for planning and product development, enabling the explicit definition of customer requirements, the so-called voice of customers, and their conversion into measurable product and process characteristics [70, 71, 72]. Additionally, it systematically evaluates the proposed product or process capabilities concerning their effectiveness in meeting identified customer needs [73]. QFD introduced innovation to conventional product planning approaches in two ways. Firstly, it has allowed the customer's perspective to be adequately considered. Secondly, the QFD procedure necessitates the involvement of interdisciplinary expertise, enablingproduct planning and design and process planning to provide a coherent response to customer requirements [52; 69]. QFD provides a systematic approach to meeting current and anticipated customer demands and expectations while also facilitating operational decisions across various stages of product development. As a result, QFD allows for proactive addressing of quality issues, promotes more cost-effective production, and fosters simultaneous engineering, ultimately leading to improved overall product and process performance. [PERSON] [74] highlights the key benefits of QFD, which include focusing on customer needs from early product development stages, the identification of crucial elements for product and process development, and maintaining consistency in product engineering and process planning. The House of Quality (HoQ) [75] is an essential tool for implementing the QFD process. It documents all analytical procedures involved in QFD execution and serves as a conceptual map, enabling inter-functional planning and communication [76]. This includes identifying customer requirements (WHAT); transforming them into quality attributes (HOW) as intended responses to the values expected by users; discovering and modeling correlations between quality and requirement attributes; and prioritizing quality attributes based on their effectiveness in meeting the specified requirements while considering detected autocorrelations. Today, QFD extends beyond conventional applications owing to its adaptability to a wide range of contexts. The principles of QFD analysis, originally used to translate user requirements into engineering product characteristics, are now being effectively utilized to tackle numerous engineering issues. Table 4 presents insights from an extensive literature review, illustrating the potential uses of the QFD method across various fields.