A novel algorithmic multi-attribute decision-making framework for the evaluation of energy systems using rough approximations of hypersoft sets

Selecting the best power source that is legal, affordable, environmentally friendly, and able to ensure long-term viability is a difficult but vital task. Existing frameworks based on traditional fuzzy and soft sets are unable to adequately capture the complexity of the optimal energy system selection (ESS). These decision models may also be complex, especially when rough data and integrity need to be taken into account. In this study, the imperative concepts of rough set and hypersoft set are integrated into a novel theoretical framework called hypersoft rough set (HSRS). The former provides a broad theoretical framework to address information-based ambiguities and uncertainties, while the latter can be thought of as a trustworthy aid for incomplete data analysis using approximate methods. Elementary notions of HSRS, its relevant approximation space, lower and upper approximations, and operations are characterized along with essential properties and results. A rigorous algorithmic strategy for assessing the feasibility of ESS based on the operations of HSRS is suggested to assist decision-makers in identifying appropriate strategies to address the electric power deficit. Potential benefits of the newly suggested approach include improved versatility in modeling complex decision-making scenarios, better discriminating ability, suitability for handling abnormalities in data, and parametrization. The algorithm's adaptability is evaluated through a practical application to a real-world problem about the identification of the best ESS in Pakistan. The outcomes show that the suggested approach effectively ascertains the ideal ESS. Compared to the methods currently in use, the analytical framework that has been suggested seems to be more robust.