Algebraic Semantics of Generalized RIFs
This work addresses contamination and data intrusion issues in rough sets and soft computing, potentially improving function selection and training methods, but it appears incremental as it builds on existing wqRIFs with new algebraic structures.
The paper tackles the problem of data intrusion and contamination in rough inclusion functions (RIFs) by generalizing weak quasi rough inclusion functions (wqRIFs) to granular operator spaces, showing that the resulting algebras are ordered hemirings with additional operators, unlike generalized RIFs.
A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing data intrusion relative to them. In this research, weak quasi rough inclusion functions (wqRIFs) are generalized to general granular operator spaces with scope for limiting contamination. New algebraic operations are defined over collections of such functions, and are studied by the present author. It is shown by her that the algebras formed by the generalized wqRIFs are ordered hemirings with additional operators. By contrast, the generalized rough inclusion functions lack similar structure. This potentially contributes to improving the selection (possibly automatic) of such functions, training methods, and reducing contamination (and data intrusion) in applications. The underlying framework and associated concepts are explained in some detail, as they are relatively new.