A Novel Decision-Making Framework for Addressing Digitalization Solutions in the Medical System Under Generalized Fuzzy Rough Information

Background and Context Setting

The traditional decision-making models often fall short when it comes to handling the kind of uncertainty and fuzziness inherent in the medical sector's digitalization efforts. The existing literature on fuzzy sets and their extensions has laid a strong foundation for addressing such uncertainties. These mathematical models provide a framework for reasoning that is closer to human natural decision-making, making them apt for applications in complex systems like healthcare (Dutta et al., 2023). Despite the progress, there remains a gap in the application of these theories to the specific challenges of digitalization in healthcare, particularly in creating a cohesive and practical decision-making framework that incorporates the latest developments in fuzzy set theory. In the context of digitalization solutions within the medical system, fuzzy sets play a crucial role in enhancing decision-making processes. Medical decision-making often involves dealing with imprecise, incomplete, or uncertain information. For example, symptoms may not always present in a clear-cut manner, or patient responses to treatments may vary widely. Fuzzy sets help in modeling such uncertainties, enabling the development of systems that can make informed decisions even when inputs are ambiguous or partially known. However, as the complexity of medical systems and the volume of available data have grown, traditional fuzzy set theory has evolved into more sophisticated models to better address these challenges:

1. Intuitionistic Fuzzy Sets (IFSs): Proposed by Atanassov, these extend the concept of fuzzy sets by incorporating the degree of non-membership in addition to the degree of membership. This is particularly useful in medical decision-making where the lack of evidence for a condition (non-membership) is as crucial as the evidence for it (membership). For instance, in diagnosing a disease, both the presence and absence of certain symptoms can provide valuable information.

2. Pythagorean Fuzzy Sets (PFSs): Further extending the idea of IFSs, PFSs allow the sum of the squares of membership and non-membership degrees to be at most 1, rather than the sum itself. This provides a larger space to express uncertainty and has been found useful in complex decision-making scenarios where a more nuanced understanding of uncertainty is needed, such as evaluating the risk of potential side effects of treatments based on incomplete clinical data.

3. q-Rung Orthopair Fuzzy Sets (q-ROFSs): These sets offer an even more generalized framework for dealing with uncertainty, where the membership and non-membership degrees are governed by a parameter q, defining an Ortho pair structure. This flexibility makes q-ROFSs particularly adept at handling highly uncertain and imprecise information, as often encountered in predicting patient outcomes where multiple, unpredictable factors influence the prognosis.

The evolution from traditional models to more complex systems like IFSs, PFSs, and q-ROFSs reflects the ongoing effort to better model and manage the intrinsic uncertainty in medical information. By enabling a more accurate and nuanced representation of uncertainty, these advanced fuzzy set theories significantly enhance the decision-making capabilities of digital health solutions. They facilitate more personalized medicine, allowing healthcare providers to tailor treatments to individual patient profiles, improve diagnostic accuracy, and optimize resource allocation, ultimately leading to better patient outcomes and more efficient healthcare systems (Dutta et al., 2023).