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Re: [ontolog-forum] Ontology of Rough Sets

To: <tara_athan@xxxxxxxxxx>, "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Sat, 15 Jan 2011 17:13:16 -0800
Message-id: <20110116011318.A67CB138D51@xxxxxxxxxxxxxxxxx>

Hi Tara,


YES, it is starting to look like an ontology.  Can you suggest some instances and a definition, the simpler the better?  


Or something to deepen the discussion.  I suggest inference over rough sets – not statistical inference, but how rough sets combine with crisp and rough alike.  


When two linear signals are added, with both independently noisy at the same noise energy,  adding them cancels 3db of energy from the noise in the sum by signal averaging.  So arrays of noisy sensors can be integrated at that level.  


But what happens to algebraic expressions mixing rough and crisp sets in calculations?  Does it result in biases that can be worked with?  


Thanks for the enlightenment,




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 Tara Athan
Sent: Saturday, January 15, 2011 4:07 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Ontology of Rough Sets


Rich Cooper wrote:

Hi Azamat,


But there is more.  We have definitions for four kinds of sets - fuzzy, probabilistic, rough, and crisp sets.  How many more KINDS of definitions (i.e., aspects like fuzzy, probabilistic, ..) are there in principal?  


I.e., with those four examples, is there a way to describe the “signature” of how various aspects of reality are chosen to model sets?  If so, can the number four (4) be increased?  What limit could be placed on the increase, if any?

Following: COLYVAN, M. 2008. Is Probability the Only Coherent Approach to Uncertainty? Risk Analysis, 28(3), pp.645-652.

Kinds of Uncertainty
1. Epistemic Uncertainty: Incomplete knowledge about some determinate fact.
   There are a number of different flavors of this type of uncertainty, but
   they are all amenable to probabilistic interpretation.
   For example, with rough sets arising from coarsening of a reference scale,
   the probability of a certain element belonging to the rough set has the pattern
   |  Member of          | Probability     |
   | lower approximation |      1          |
   | boundary set        | between 0 and 1 |
   | complement of       |      0          |
   | upper approximation |                 |


2. Linguistic Uncertainty
   Vagueness- (also called fuzziness) using terms that admit borderline cases, such as "adult"
   Context Dependence - such as "tall"
   Ambiguity - using terms with multiple meanings, such as "bank"
   Underspecificity - using unwanted generality
      ("there are rainy days ahead")
I'm no expert on linguistic uncertainty, so I can't verify if these four cases really cover everything.

But I have some expertise in epistemic uncertainty, and as a Bayesian, I do agree with the statement above. But I imagine there are some statisticians who disagree. And the disagreement hinges on the ambiguity of "probability"; the Bayesian and the frequentist definitions.

A frequentist would split uncertainty into systemic uncertainty and bias, and would only agree on a probabilistic interpretation of the latter.

This is starting to look like an ontology!

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