Abstract
This paper introduces a refined and broadened version of decision-theoretic rough sets (DTRSs) named Generalized Sequential Decision-Theoretic Rough Set (GSeq-DTRS), which integrates the three-way decision (3WD) methodology. Operating through multiple levels, this iterative approach aims to comprehensively explore the boundary region. It introduces the concept of generalized granulation, departing from conventional equivalence-relation-based structures to incorporate similarity/tolerance relations. GSeq-DTRS addresses the limitations encountered by its predecessor, Seq-DTRS, particularly in managing sequential procedures and integrating new attributes. A notable advancement is its seamless handling of continuous-scale datasets through a defined Generalized Granular Structure (GGS), enabling classification across multiple levels without necessitating reduction of attributes. A refined version of conditional probability (CP), aligned with tolerance classes, enhances the approach, supported by a meticulously designed algorithm. Extensive experimental analysis conducted on two datasets sourced from https://www.kaggle.com demonstrates the efficacy of the procedure for both continuous and discrete datasets, effectively classifying probable elements into POS or NEG regions based on their membership. Unlike traditional Seq-DTRS, it does not require reduction of attributes at each new level. Additionally, the algorithm exhibits lower sensitivity to parametric values and yields results in fewer iterations. Thus, its potential impact on decision-making processes is readily apparent.