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## Re: [ontolog-forum] Ontology of Rough Sets

 To: "[ontolog-forum]" Tara Athan Sat, 15 Jan 2011 16:07:11 -0800 <4D3236AF.6070807@xxxxxxxxxx>
 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! Tara
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 Current Thread Re: [ontolog-forum] Ontology of Rough Sets, (continued) Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, AzamatAbdoullaev Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, Christopher Menzel Re: [ontolog-forum] Ontology of Rough Sets, Tara Athan Re: [ontolog-forum] Ontology of Rough Sets, Christopher Menzel Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, Christopher Menzel Re: [ontolog-forum] Ontology of Rough Sets, AzamatAbdoullaev Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, Tara Athan <= Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, AzamatAbdoullaev Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, AzamatAbdoullaev Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, Christopher Menzel Re: [ontolog-forum] Ontology of Rough Sets, Rich Cooper Re: [ontolog-forum] Ontology of Rough Sets, John F. Sowa Re: [ontolog-forum] Ontology of Rough Sets, Christopher Menzel Re: [ontolog-forum] Ontology of Rough Sets, Christopher Menzel