# Algebraic Semantics of Generalized RIFs

arXiv: https://arxiv.org/abs/2109.12998 · HTML: https://mlsanity.com/paper/2109.12998/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 52 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 5 of 5)

- [Dialectical Rough Sets, Parthood and Figures of Opposition-1](https://mlsanity.com/paper/1703.10251/) (2017)
- [General Rough Modeling of Cluster Analysis](https://mlsanity.com/paper/2106.04683/) (2021)
- [Contamination-Free Measures and Algebraic Operations](https://mlsanity.com/paper/1512.02140/) (2015)
- [Generalized Ideals and Co-Granular Rough Sets](https://mlsanity.com/paper/1704.05477/) (2017)
- [Pure Rough Mereology and Counting](https://mlsanity.com/paper/1701.08301/) (2017)

## Built on by (most cited first, 1 of 1)

- [Granular Generalized Variable Precision Rough Sets and Rational Approximations](https://mlsanity.com/paper/2205.14365/) (2022)

## Abstract (arXiv)

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.