## 4 Methods
### Fuzzy AHP  
Fuzzy AHP is a powerful technique that considers uncertainty in human judgment. Two functions, the triangular membership function (TMF) and the trapezoidal membership function (TRMF), are most commonly used in FAHP. According to the literature, \begin{table}
\begin{tabular}{c c} \hline \hline
**Criteria** & **Sub-Criteria** \\ \hline \multirow{4}{*}{Learnability (A1)} & Familiarity(A11) \\  & Learning time(A12) \\  & Minimal Action(A13) \\ \hline \multirow{4}{*}{Efficiency (A2)} & No. of Taps(A21) \\  & Task Completion Rate(A22) \\  & Response Time(A23) \\  & Ease of Use(A24) \\  & Connection(A25) \\ \hline \multirow{4}{*}{Memorability (A3)} & Saving(A31) \\  & Retain(A32) \\  & Reminder(A33) \\ \hline \multirow{4}{*}{Aesthetic (A4)} & Attractive(A41) \\  & Appeal(A42) \\  & Organized(A43) \\ \hline \multirow{2}{*}{Error (A5)} & Presence of Error(A51) \\ \hline \multirow{4}{*}{Navigation (A6)} & Search(A61) \\  & Intuitive(A62) \\  & Involvement(A63) \\ \hline \multirow{4}{*}{Readability (A7)} & Legible(A71) \\  & Understandable(A72) \\ \hline \multirow{4}{*}{Cognitive Load (A8)} & Essentiality(A81) \\  & Presentation(A82) \\ \hline \multirow{4}{*}{Provision for Physically Challenged users (A9)} & Weak Muscle Control(A91) \\  & Low Vision(A92) \\  & Hearing Impairment(A93) \\ \hline \multirow{4}{*}{Satisfaction (A10)} & Provision(A101) \\  & Finding Correct Information(A102) \\ \cline{1-1}  & Improvement(A103) \\ \cline{1-1}  & Recommendation(A104) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Usability criteria and associated sub-criteria for assessing T2 DM mHealth application. various studies have employed TMF or TRMF to assess ambiguity and vagueness in expert judgments. TMF is used in this study because of its popularity and its ease of computation. TMF turns expert-provided qualitative data into TFN. To overcome the uncertainties involved within the AHP methodology, the FAHP methodology, which is an extension of the traditional AHP method, utilized fuzzified comparison ratios that were described by TMF. The concept was to describe the weights of the nine-level judgment scales using triangular fuzzy numbers (TFNs) for depicting the relative significance of the criteria associated with the hierarchy [39]. Figure 2 depicts a TFN represented by the real numbers including \(l\), \(m\), and \(u\) and involving parameters such that \(l<m<u\), where \(l\) is the least value, \(m\) indicates the promising value, and \(u\) is the maximum value related to the membership function \(\mu_{\widetilde{A}}(x)\). The linguistic variables for indicating the relevance associated with each criterion are shown in Figure 3. The following equation represents a TFN's membership function:  
\[\mu_{\widetilde{A}}(x)=\left\{ \begin{array}{ll}\frac{x-l}{m-l},&l\leq x\leq m \\ \frac{u-x}{u-m},&l\leq x\leq u\\ 0,&\text{otherwise}\end{array} \right. \tag{1}\]  
The respective lower and upper limit of the fuzzy number \(\widetilde{A}\) are represented by \(l\) and \(u\), with \(m\) denoting the fuzzy number's mid-value. Based on decision-maker (DM) assessments, the AHP approach was utilized to calculate criteria weights [40]. In the AHP method, which examines qualitative and quantitative criteria, pairwise comparisons are used. To deal with uncertainty issues, the regular AHP approach was expanded to include theory related to fuzzy sets, resulting in the FAHP. The essential steps employed in the FAHP are set out below:  
**Step 1. ** Generating the fuzzy pairwise comparison matrices  
Fuzzy pairwise comparison matrices were created for each level, as illustrated in Table 2, utilizing crisp data acquired from experts on a well-defined fuzzy linguistic scale. Following that, using synthetic extent values, the extent analysis approach was employed to produce the priority weights. The fuzzy criterion assessment matrix was created by a pairwise comparison of the different attributes pertaining to the overall objective.