The escalating volume of healthcare waste (HCW) generated by healthcare facilities poses a pressing challenge for all nations. Adequate management and disposal of this waste are imperative to mitigate its adverse impact on human lives, wildlife, and the environment. Addressing this issue in Bosnia and Herzegovina involves the establishment of a regional center dedicated to HCW management. In practice, there are various treatments available for HCW management. Therefore, it is necessary to determine the priority for procuring different treatments during the formation of this center. To assess these treatment devices, expert decision-making employed the fuzzy-rough approach. By leveraging extended sustainability criteria, experts initially evaluated the significance of these criteria and subsequently assessed the devices for HCW treatment. Employing the fuzzy-rough LMAW (Logarithm Methodology of Additive Weights), the study determined the importance of criteria, highlighting "Air emissions" and "Annual usage costs" as the most critical factors. Utilizing the fuzzy-rough CoCoSo (the Combined Compromise Solution) method, six devices employing incineration or sterilization for HCW treatment were ranked. The findings indicated that the "Rotary kiln" and "Steam disinfection" emerged as the most favorable devices for HCW treatment based on this research. This conclusion was validated through comparative and sensitivity analyses. This research contributes by proposing a solution to address Bosnia and Herzegovina's HCW challenge through the establishment of a regional center dedicated to HCW management.