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Re: [ontolog-forum] Ontology of Rough Sets

To: Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx>
Cc: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Tara Athan <taraathan@xxxxxxxxx>
Date: Fri, 14 Jan 2011 11:00:34 -0800
Message-id: <4D309D52.70507@xxxxxxxxxx>
Rich Cooper wrote:



I don’t recall any specific reference on rough sets – I think I first read something in the IEEE suite of pubs, maybe ten years ago.  


Rough sets should be fairly easy to implement in SQL, so it would be interesting to know what components you were considering, and whether they met your needs. 

Well, my needs were academic, I was using it as a learning example. So I built a concrete boat, and I am reluctant to try to float it in public.  In any case, I did not create classes named after the terms in rough set mathematics and try to formalize their definitions - I don't see any point in that. What I did do was play around with ontology design patterns inspired by rough set mathematics and multi-valued logic.

The design pattern is that rough classes are characterized, vaguely, by a pair of crisp classes. A crisp class has a definition whose restrictions arise from a finite partition of an observable quality space, which is a fairly typical ontology design pattern to begin with. The pair of crisp classes are defined using the same partitions, and the one corresponding to the lower approximation must be a subclass of the upper approximation. The rough class is a super-class of the lower approximation and a sub-class of the upper approximation.  In an application, it would be precisely defined in terms of some target quality space which is not directly observable (in the setting where the ontology is to be applied, perhaps clinical diagnosis, or sensors for fault-detection). The lower/upper approximation give a vague description of this class in terms of observable qualities. These approximations would be determined by statistics on a sample where the target quality is known, say from a research study, or by expert elicitation.

I don't think there is anything particularly profound in this - for all I know people are already doing this and calling it something else. The connection to rough set theory just gives us a vocabulary to talk about it.



If any reference info comes back to me, I’ll post it.  




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