An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application

The Decision-Theoretic Rough Set model stands as a compelling advancement in the realm of rough sets, offering a broader scope of applicability. This approach, deeply rooted in Bayesian theory, contributes significantly to delineating regions of minimal risk. Within the Decision-Theoretic Rough Set paradigm, the universal set undergoes a tripartite division, where distinct regions emerge and losses are intelligently distributed through the utilization of membership functions. This research endeavors to present an enhanced and more encompassing iteration of the Decision-Theoretic Rough Set framework. Our work culminates in the creation of the Generalized Intuitionistic Decision-Theoretic Rough Set (GI-DTRS), a fusion that melds the principles of Decision-Theoretic Rough Sets and intuitionistic fuzzy sets. Notably, this synthesis bridges the gaps that exist within the conventional approach. The innovation lies in the incorporation of an error function tailored to the hesitancy grade inherent in intuitionistic fuzzy sets. This integration harmonizes seamlessly with the contours of the membership function. Furthermore, our methodology deviates from established norms by constructing similarity classes based on similarity measures, as opposed to relying on equivalence classes. This shift holds particular relevance in the context of aggregating information systems, effectively circumventing the challenges associated with the process. To demonstrate the practical efficacy of our proposed approach, we delve into a concrete experiment within the information technology domain. Through this empirical exploration, the real-world utility of our approach becomes vividly apparent. Additionally, a comprehensive comparative analysis is undertaken, juxtaposing our approach against existing techniques for aggregation and decision modeling. The culmination of our efforts is a well-rounded article, punctuated by the insights, recommendations, and future directions delineated by the authors.