A multi-robotic task assignment and decision analysis system refers to an advanced framework in robotics and artificial intelligence where multiple robots are coordinated to perform a set of tasks efficiently and intelligently. This article designs innovative approaches to fix uncertainty during task allocation in a multi-robotic system under a hybrid fuzzy framework and decision-making models. To achieve this goal, we expose a modified theory of circular q-rung orthopair fuzzy set (Crq-ROFS), which is a broader framework of intuitionistic fuzzy sets and q-rung orthopair fuzzy sets. We formulated feasible operations of Schweizer-Sklar t-norm and t-conorm in light of circular information about q-rug orthopair fuzzy (Crq-ROF). We also delved into a family of mathematical approaches of Schweizer-Sklar t-norm and t-conorm, namely, Crq-ROF Schweizer-Sklar weighted average (Crq-ROFSSWA) and Crq-ROF Schweizer-Sklar weighted geometric (Crq-ROFSSWG) operators with dominant propositions. The theory of the multi-attribute decision-making (MADM) problem offers authentic and reliable solutions by aggregating human judgment. An experimental case study discussed evaluating an ideal solution under consideration of multi-criteria or attribute information. A comparison method is conducted to showcase the reliability and effectiveness of the pioneering approaches with existing approaches.