Hepatitis is an infectious disease typified by inflammation in internal organ tissues, and it is caused by infection or inflammation of the liver. Hepatitis is often feared as a fatal illness, especially in developing countries, mostly due to contaminated water, poor sanitation, and risky blood transfusion practices. Although viruses are typically blamed, other potential causes of this kind of liver infection include autoimmune disorders, toxins, medicines, opioids, and alcohol. Viral hepatitis may be diagnosed using a variety of methods, including a physical exam, liver surgery (biopsy), imaging investigations like an ultrasound or CT scan, blood tests, a viral serology panel, a DNA test, and viral antibody testing. Our study proposes a new decision-support system for hepatitis diagnosis based on spherical q-linear Diophantine fuzzy sets (Sq-LDFS). Sq-LDFS form the generalized structure of all existing notions of fuzzy sets. Furthermore, a list of novel Einstein aggregation operators is developed under Sq-LDF information. Also, an improved VIKOR method is presented to address the uncertainty in analyzing the viral hepatitis categories demonstration. Interesting and useful properties of the proposed operators are given. The core of this research is the proposed algorithm based on the proposed Einstein aggregation operators and improved VIKOR approach to address uncertain information in decision support problems. Finally, a hepatitis diagnosis case study is examined to show how the suggested approach works in practice. Additionally, a comparison is provided to demonstrate the superiority and efficacy of the suggested decision technique.

Energy sustainability is described as an ability to get the energy supplies without diminishing the ability of future generations to provide themselves with any energy. Preceded by the mentioned notion, this paper will be focused on bipolar hesitant fuzzy soft sets (BHFSS) related to the problem of energy sustainability. It actually was a proposed new mathematical method able to conquer ambiguity and uncertainty while determining the different choices in energy-related decisions. In this way, it lead to more informative and better choices to be made, thus leading to the utilization of sustainable energy systems. The paper introduced basic operations and comparison rules for BHFSS. Furthermore, algebraic norms-based aggregation operators were proposed to make the model more robust and flexible so that it was adaptable to a wide range of energy sustainability decisions. Main characteristics of the BHFSS aggregation operators were discussed in detail. Last but not least, this paper also provided a comparison of the BHFSS-based approach with one of the most popular multi-criteria decision-making (MCDM) approaches known as compromise solution (CoCoSo). This comparison confirmed how BHFSS can control for uncertainty and how it can reflect preferences in a mapped way, which afforded it strengths in uses like choosing renewable power and strategy for lowering $C{O}_2$ emissions.