Disturbance Observer-Based Control: Weighted Aggregated Aczel-Alsina Sum Product Assessment Based on Power Operators for Managing Fuzzy 2-Tuple Linguistic Neural Networks

Disturbance observer–based control (DOBC) is a valuable strategy for enhancing control system performance by compensating for disturbances. The core idea is to design an observer that accurately estimates external disturbances affecting the system, and then use this estimation to adjust the control input accordingly. This article introduces a novel approach involving fuzzy 2-tuple linguistic (F2-TL) sets, incorporating algebraic and Aczel-Alsina operational laws. Additionally, we propose several operators: the F2-TL Aczel-Alsina power averaging (F2-TLAAPA) operator, the F2-TL Aczel-Alsina power weighted averaging (F2-TLAAPWA) operator, the F2-TL Aczel-Alsina power geometric (F2-TLAAPG) operator, and the F2-TL Aczel-Alsina power weighted geometric (F2-TLAAPWG) operator. These operators are used to aggregate information into a singleton set, and we discuss their fundamental properties, including idempotency, monotonicity, and boundedness. Moreover, we explain the WASPAS (weighted aggregated sum product assessment) technique, applying the proposed methods and illustrating them with relevant examples. The article also explores the application of these techniques to multi-attribute decision-making (MADM) problems, demonstrating their value. Finally, to validate the introduced methods and highlight the superiority of the proposed approach, we compare the ranking results obtained using our methods with those from existing techniques.