Algebraic Semantics of Generalized RIFs

TL;DR

This paper introduces a generalized algebraic framework for weak quasi rough inclusion functions in granular operator spaces, aiming to reduce data intrusion and improve the selection of rough set measures.

Contribution

It extends wqRIFs to general granular operator spaces, defining new algebraic operations and showing their structure as ordered hemirings, which is novel in rough set theory.

Findings

Generalized wqRIFs form ordered hemirings with additional operators.

Generalized rough inclusion functions lack similar algebraic structure.

Framework potentially improves measure selection and reduces data contamination.

Abstract

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.