Roughness in rings via cubic sets with applications

This paper introduces a novel hybrid structure called rough cubic sets in the context of ring theory, combining the concepts of roughness and cubic sets. We systematically investigate the fundamental operations and properties of rough cubic sets, with particular emphasis on their algebraic characteristics in rings. The study further explores the notion of rough cubic ideals in rings, establishing their essential properties. As a practical application of the developed theory, we propose an innovative approach to solving multiple attribute decision-making problems within the rough cubic set environment. Our results demonstrate both the theoretical richness of this new structure and its potential for practical applications in decision sciences.