Towards a theory of granular sets
This foundational work proposes a new mathematical framework for information processing, potentially impacting various domains, but it is incremental as it builds on existing rough set theory.
The paper introduces the concept of granular sets to address classification problems in information systems, generalizing rough set theory and aiming for applications in sensor fusion and hierarchical classification.
Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called Granular set naturally arises. It is realized that in any hierarchical classification problem, Granular set naturally arises. Also when the target set of objects forms a graded set the lower and upper approximations of target sets form a graded set. This generalizes the concept of rough set. It is hoped that a detailed theory of granular/ graded sets finds several applications.