Fuzzy set theory, allows for degrees of membership and introduces membership functions to model imprecise information. Q-fuzzy set theory extends this by incorporating linguistic quantifiers for a flexible representation of uncertainty. Intuitionistic fuzzy set theory, adds a separate degree of non-membership for a more comprehensive portrayal of uncertainty. Refined intuitionistic fuzzy set theory, further enhances precision by subdividing membership and non-membership values, addressing the limitation of singular assignments in representing uncertainty. This research delves into the foundational aspects of refined intuitionistic Q-fuzzy set (RIQFS) and investigates several key properties associated with this specialized mathematical framework, like subset, equal set, null set, and complement set within the framework of refined intuitionistic Q-fuzzy set. The investigation also involves conceptualizing basic set-theoretic operations, including union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference. Furthermore, the analysis explores fundamental laws, elucidating each with illustrative examples to facilitate a clearer understanding.