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
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5  5 7 1 2
From: ontologforumbounces@xxxxxxxxxxxxxxxx
[mailto:ontologforumbounces@xxxxxxxxxxxxxxxx] On Behalf Of Tara Athan
Sent: Saturday, January 15, 2011
4:07 PM
To: [ontologforum]
Subject: Re: [ontologforum]
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.645652.
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!
Tara