Upgraded Tuned Liquid Column Damper (UTLCD) is an interesting variant of Tuned Liquid Column Damper, which was developed recently. UTLCD consists of a conventional Tuned Liquid Column Damper (TLCD) integrated into an undamped Tuned Mass Damper (TMD). Based on this device, a hybrid type of UTLCD (HUTLCD) is developed to minimize the vibration response of earthquake-induced buildings. HUTLCD is constituted of two independent components, including an active UTLCD (AUTLCD) and a passive UTLCD (PUTLCD). These individual components are connected in parallel to a high-rise building. In this research, the Hedge-Algebras theory (HA) is utilized to design controllers for AUTLCD. This study also uses a new algorithm, Balancing Composite Motion Optimization (BCMO), which has recently been introduced to solve optimization problems. The performance of HUTLCD is compared with that of a pure AUTLCD or a pure PUTLCD, which have the same weight as the HUTLCD. The results achieved from the present work confirm that the HUTLCD is more effective than the pure PUTLCD for the vibration reduction capacity and is better than the pure AUTLCD for both aspects of the vibrational control capacity (for most cases compared with) and saving control energy (for all cases considered). Moreover, the HUTLCD is not more robust than the AUTLCD as the structural stiffness rises, but the HUTLCD still offers higher control effectiveness compared with the AUTLCD or PUTLCD when the structural stiffness decreases. In addition, although the data used to design the optimum HA-based controller is the El Centro earthquake, this controller maintains a high efficiency level for numerous other earthquakes.