The current study is a cross-sectional study. The panel of experts consisted of 30 members of the academic faculty of health and medical services management, the chief of the hospital, the manager, matron, and boards and medical staff of Mashhad University of Medical Sciences with at least five years of work experience. According to the purpose of the present study and the use of multi-criteria decision-making techniques to prioritize the components affecting the Patient's experience of healthcare services, there was no question of sampling from the community, and 30 of these experts were identified. The researcher-made questionnaire was given to them in person or via their email. First, they were informed about all aspects of the research, and informed consent was obtained from all experts. The experts were also assured about the confidentiality of the information. The Ethics Committee of Mashhad University of Medical Sciences approved the study. To collect data in the pairwise comparison stage, a two-part researcher-made questionnaire was designed, based on which the contribution of each component affecting the patient experience was compared and ranked using the FAHP process. The first part includes questions on demographic variables, including gender, education level, executive position, and work experience. The second part had pairwise comparison tables including 12 dimensions related to the components affecting the evaluation of the Patient's experience. The features affecting the assessment of patient experience were extracted from Najib Jalali's study (2020) [7] titled "Designing a patient experience evaluation model in affiliated hospitals of Mashhad University of Medical Sciences.” These components include the quality of the nurse-patient relationship, providing nursing services, provision of medical services, the quality of the physician-patient relationship, the participation of the family and the nurses, emotional support, the physical environment and hoteling, quality of hospital discharge, respect for the dignity and privacy of the patient, providing information to the patient, method of pain management, and access to the necessary medications.
After completing the questionnaires, the data were entered into Microsoft Excel and analyzed using the FAHP technique. Chang's FAHP is a systematic method for selecting options and solving problems using fuzzy set theory and AHP that uses fuzzy triangular numbers. The purpose of these numbers is to determine the priority of different decision variables, while the final importance of the weights is determined using the AHP method developed based on fuzzy triangular numbers. In this method, each verbal expression is first converted into fuzzy numbers. Then, the mean matrix of the respondents' opinions for the main criteria is obtained using the geometric mean. Then the ambiguous composite expansion and the degree of preference (feasibility) of each measure compared to the rest of the requirements are calculated. Afterward, the weight vector of each criterion is normalized, and the final weight of the requirements is calculated (14). The procedure is as follows.
The object set X = {x1, x2,. .. xn} and the target set is U = {u1, u2, ...um}.
According to Chang's extent method, the analysis is performed for each target "gi," which results in the study of m extents for each set member as shown below (where Mygi (y = 1, 2,. . ., m and i = 1, 2, ...., n) is a triangular fuzzy number).
This method, according to Chang's range analysis, depends on the following synthetic fuzzy values (Si):
$${{\text{S}}_{\text{i}}=\sum _{\text{j}=1}^{\text{m}}{\text{M}}_{\text{g}\text{i}}^{\text{j}}\otimes \left[\left.\sum _{\text{i}=1}^{\text{n}}\sum _{\text{j}=1}^{\text{m}}{\text{M}}_{\text{g}\text{i}}^{\text{j}}\right)\right.}^{-1}$$
The value of \(\sum _{\text{j}=1}^{\text{m}}{\text{M}}_{\text{g}\text{i}}^{\text{j}}\)is calculated by applying the fuzzy summation law for a specific matrix so that:
$${\sum }_{j=1}^{m}{M}_{gi}^{J}$$
$${\sum }_{j=1}^{m}{M}_{gi}^{J}=\left(\sum _{j=1}^{m}lj,\sum _{j=1}^{m}mj,\sum _{j=1}^{m}uj\right)$$
$${\left[{\sum }_{i=1}^{n}{\sum }_{j=1}^{m}{M}_{gi}^{j}\right.)}^{-1}$$
$${M}_{gi}^{j}(j=\text{1,2},\dots ,m)$$
The value of \(\left[\left.\sum _{\text{i}=1}^{\text{n}}\sum _{\text{j}=1}^{\text{m}}{\text{M}}_{\text{g}\text{i}}^{\text{j}}\right)\right.\)first will be counted using the fuzzy addition law for \({M}_{gi}^{j}\left(j=\text{1,2},\dots ,m\right)\).
$$\sum _{\text{i=1}}^{\text{n}}\sum _{\text{j=1}}^{\text{m}}{\text{M}}_{\text{gi}}^{\text{j}}\text{=}\left(\sum _{\text{i=1}}^{\text{n}}\text{li}\text{,}\sum _{\text{i=1}}^{\text{n}}\text{mi}\text{,}\sum _{\text{i=1}}^{\text{n}}\text{ui}\right)\text{ }$$
And then, the inverse vector is calculated as follows:
$${\left[\sum _{i=1}^{n}\sum _{j=1}^{m}{M}_{gi}^{j}\right]}^{-1}=\left(\frac{1}{{\sum }_{i=1}^{n}{u}_{i}},\frac{1}{{\sum }_{i=1}^{n}{m}_{i}},\frac{1}{{\sum }_{i=1}^{n}{l}_{i}}\right)$$
As a second step, the degrees of possibility is calculated. After that, the degree of probability of a convex fuzzy number being more significant than k convex fuzzy numbers Mi (i = 1,2,3....,k) by
$$V\left(m\ge {M}_{1},{M}_{2},\dots ,{M}_{K})=V\left[M\ge {M}_{1}) and\right. \left(M\ge {M}_{2}\right)and\dots and \left(M\ge {M}_{K}\right)\right]=\text{min}V \left(M\ge {M}_{i}\right) ,\text{i} =\text{1,2},3,,\text{k}.$$
For j = 1,2,...,n with j ≠ i,d' (Ai) = min V(SI ≥ Sj). In the last step, normalized vectors are obtained through normalization.
$${W}^{{\prime }}={\left({d}^{{\prime }}\left({A}_{1}\right),\dots ,{d}^{{\prime }}\left({A}_{n}\right)\right)}^{T}$$
where A_i (i = 1,2,...,n) and non-phase normalization "W" is calculated as follows:
$$W={\left(d\left({A}_{1}\right), d \left({A}_{2}\right),\dots , d\left({A}_{n}\right)\right)}^{T}$$
Finally, all calculations were carried out in Excel software.