The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information. It can be characterized by two crisp sets, named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset. This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J . The novel approach (indicated by J MSAS) modifies the approximation space to diminish the bound- ary region and enhance the measure of accuracy. The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques. Via illustrated examples, several remarkable results using these notions are obtained and some of their properties are established. Several sorts of near open (resp. closed) sets based on J MSAS are studied. Furthermore, the connections between these assorted kinds of near-open sets in J MSAS are deduced. The advantages and disadvan- tages of the proposed approach compared to previous ones are examined. An algorithm using MATLAB and a framework for decision-making problems are verified. Finally, the chemical application for the classification of amino acids (AAs) is treated to highlight the significance of applying the suggested approximation