Appointment scheduling for outpatient services is a challenge in the healthcare sector. For addressing this challenge, most studies assumed that patients unpunctuality and the duration of service have constant values or a specific probability distribution function. Consequently, there is a research gap to consider the uncertainty of both patients unpunctuality and the duration of service in terms of fuzzy sets. Therefore, this research aims to consider fuzzy values for both unpunctuality and duration of service have to improve an outpatient Appointment scheduling (the time interval between two patients) in a referral clinic with the objective of reducing the total weight of waiting time, idle time, and overtime. Four different fuzzy linear programming models and 36 scenarios have been developed based on the show, no-show of patients, single-book, and double-book by using GAMS software. These four models are as follows: (1) probability of no-show equal to zero, (2) probability of no-show equal to 20%, (3) probability of no-show equal to zero and with double-book factor, and (4) probability of no-show equal to 20% and with double-book factor. The results of the first, second, third, and fourth models, respectively, present the scenarios considering 10, 5, 15, and 15 minutes for the time interval between two patients that have the minimum total weight of patient waiting times, physician idle times, and physician overtime. By considering these findings, the investigated referral clinic can improve its Appointment systems performance. Moreover, other similar clinics can apply the proposed model for improving their Appointment systems' performance.