Key points are not available for this paper at this time.
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 settheoretic 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.
Saeed et al. (Sat,) studied this question.