# Extension of Rough Set Based on Positive Transitive Relation

## TL;DR

This paper introduces a new positive transitive relation to extend rough set theory, improving handling of incomplete information systems by maintaining transitivity and reducing computational complexity.

## Contribution

It proposes a novel rough set extension model based on positive transitive relations, addressing limitations of existing models that discard transitivity or symmetry.

## Key findings

- Enhanced performance in processing incomplete information systems
- Reduced computational complexity compared to existing models
- Better theoretical foundation for incomplete information classification

## Abstract

The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or the limitation of data comprehension, etc. An incomplete information system is mainly processed by compressing the indiscernibility relation. The existing rough set extension models based on tolerance or symmetric similarity relations typically discard one relation among the reflexive, symmetric and transitive relations, especially the transitive relation. In order to overcome the limitations of the current rough set extension models, we define a new relation called the positive transitive relation and then propose a novel rough set extension model built upon which. The new model holds the merit of the existing rough set extension models while avoids their limitations of discarding transitivity or symmetry. In comparison to the existing extension models, the proposed model has a better performance in processing the incomplete information systems while substantially reducing the computational complexity, taking into account the relation of tolerance and similarity of positive transitivity, and supplementing the related theories in accordance to the intuitive classification of incomplete information. In summary, the positive transitive relation can improve current theoretical analysis of incomplete information systems and the newly proposed extension model is more suitable for processing incomplete information systems and has a broad application prospect.

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Source: https://tomesphere.com/paper/1906.03337