Granularity and Rational Approximation: Rethinking Graded Rough Sets

Abstract

AbstractThe concept of rational discourse is typically determined by subjective, normative, and rule based constraints in the context under consideration. It is typically determined by related ontologies, and coherence between associated concepts employed in the discourse. Classical rough approximations, and variants of variable precision rough sets (VPRS) including graded rough sets embody at least some aspects of potentially useful concepts of rational approximation, but can be very lacking in application contexts, and rough set theoretical frameworks for cluster validation. While the literature on knowledge from general rough perspectives is rich and diverse, not much work has been done from the perspective of rationality in explicit terms. In this research, the gap is addressed by the present author in variants of high granular partial algebras. Specifically, the nature of optimal concepts of rational approximations is examined, and formalized by her in such frameworks. Graded rough sets are generalized from a granular perspective, and the compatibility of the introduced concepts are studied over it. Further aspects of algebraic semantics of granular graded rough sets are examined. Some incorrect results in graded rough sets in the literature are also corrected.KeywordsGeneral rough setsRational approximationGraded rough setsMereologyContaminationHigh granular partial algebrasIngredient grading problem