Q-Neutrosophic Spherical-Cubic Soft Algebra for Enhancing Residential Space Art Design Courses Quality in IoT-Enabled Smart Factories

This paper introduces a new mathematical model called Q-Neutrosophic Spherical-Cubic Soft Evaluation Algebra (Q-NSCSEA) to support the improvement of educational practices in residential space art design courses. These courses are increasingly integrated with smart factory environments powered by the Internet of Things (IoT). The model combines ideas from Q-neutrosophic logic, spherical sets, cubic soft sets, and algebraic quasigroup structures to form a powerful mathematical system. It helps evaluate and compare student design projects based on artistic, functional, and industrial standards. Our approach builds a structured neutrosophic system using truth (T), indeterminacy (I), and falsity (F) values to describe the level of aesthetic quality, uncertainty in design structure, and failure to meet IoT-smart production requirements. Several new mathematical definitions and operations are proposed, including neutrosophic union, intersection, and project composition under quasigroup behavior. Realistic numerical examples are provided to demonstrate how the model works in educational design assessments. The proposed model supports better decision-making for educators and designers by linking abstract creative ideas with real-world smart manufacturing constraints.