Granular knowledge and rational approximation in general rough sets – I

Abstract

Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic.

Keywords:

• Rough sets
• rational approximations
• ideals and filters
• rationality of objects
• rationality types
• co-granular rough sets
• substantial parthood
• mereology

Acknowledgments

The present author would like to thank the referees for useful comments that led to improvements in the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported by Woman Scientist Grant No. WOS-A/PM-22/2019 of the Department of Science and Technology.