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Re: [ontolog-forum] Ontology of Rough Sets

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Sat, 15 Jan 2011 08:27:45 -0800
Message-id: <20110115162813.4D7CA138D69@xxxxxxxxxxxxxxxxx>

Hi Chris,


A Boolean variable is bivalent – it can take on True or False as its value.  A multi-valent variable can be True False or Unknown, as you define it.  Rough sets are multivalent because their boundaries are not crisply defined.  They can be in the set, out of the set, or in the bracketing upper and lower boundaries.  


The meaning of the upper and lower boundaries depends on how the boundaries are defined.  They can be used to model and process uncertainties of various kinds.  


There is a long history of multivalent architectures, tagged architectures, and various other ways investigated for finding a set in a discovery process.  Most of it was in EE areas, where sensors can provide mixed logic and scalar measures.  Especially in electronic warfare, multivalent variables are often used to delay making the True or False decision until more information is available about the boundary sets.  






Rich Cooper


Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher Menzel
Sent: Friday, January 14, 2011 6:01 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Ontology of Rough Sets


On Jan 14, 2011, at 4:16 PM, Rich Cooper wrote:



Agreed, rough set theory is a different view of sets, not probabilistic, not fuzzy,


Rough sets differ formally from fuzzy sets in some important ways, but they are certainly kissin' cousins.  Both were designed to deal with vagueness and imperfect knowledge, and the idea of the boundary region of a rough set is meant to do the same sort of work that fuzzy membership was designed to do. Indeed, it is possible alternatively to define rough sets in terms of a rough membership function, which turns out to be a generalization of fuzzy membership.

not ambiguous, but bounded and multivalent.


Rough sets have boundary regions; I don't know what you mean by saying they are bounded. And I have no idea what you have in mind in calling them multivalent.




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