Integrating Rough Sets and Multidimensional Fuzzy Sets for Approximation Techniques: A Novel Approach

• Published in: IEEE access 2024, Vol.12, p.154796-154810
• Main Authors: Josen, Jomal, Mathew, Bibin, Jacob John, Sunil, Vallikavungal, Jobish
• Format: Article
• Language: English
• Subjects: Approximation; Artificial intelligence; Decision making; Effectiveness; Fuzzy sets; Generalized multidimensional fuzzy sets; Multidimensional methods; Object recognition; Problem-solving; Resource management; rough approximation through aggregation operators; rough approximation through distance measures; Rough sets; Statistical analysis; Uncertainty; α, β rough approximation; β rough approximation
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2024.3482575

This research introduces innovative rough approximation techniques for multidimensional fuzzy sets by integrating rough sets and multidimensional fuzzy sets. Departing from traditional methods that rely on predefined equivalence relations to delineate rough spaces, we propose a novel approach utilizing a function termed the 'convenient function'. The values generated by this function facilitate the establishment of lower and upper estimations, enhancing the precision of rough approximations. The adept utilization of the parameter \alpha , in conjunction with a multidimensional distance measure, allows for the attainment of desirable approximations within specified bandwidths. Additionally, we explore a more generalized version of \alpha approximation, known as \alpha - \beta approximation, along with its associated properties, thereby expanding the applicability and flexibility of the proposed methodology. Finally, we present a comprehensive case study demonstrating the efficacy of the \alpha approximation methodology in real-world decision-making processes, highlighting its practical utility and effectiveness.