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A number of numeric measures like rough inclusion functions (RIFs) are usedin general rough sets and soft computing. But these are often intrusive bydefinition, and amount to making unjustified assumptions about the data. Thecontamination problem is also about recognizing the domains of discoursesinvolved in this, specifying errors and reducing data intrusion relative tothem. In this research, weak quasi rough inclusion functions (wqRIFs) aregeneralized to general granular operator spaces with scope for limitingcontamination. New algebraic operations are defined over collections of suchfunctions, and are studied by the present author. It is shown by her that thealgebras formed by the generalized wqRIFs are ordered hemirings with additionaloperators. By contrast, the generalized rough inclusion functions lack similarstructure. This potentially contributes to improving the selection (possiblyautomatic) of such functions, training methods, and reducing contamination (anddata intrusion) in applications. The underlying framework and associatedconcepts are explained in some detail, as they are relatively new.

Algebraic Semantics of Generalized RIFs