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Re: [ontolog-forum] Ontology of Rough Sets

 To: "'[ontolog-forum] '" "Rich Cooper" Fri, 14 Jan 2011 14:16:02 -0800 <20110114221606.C9EBB138D85@xxxxxxxxxxxxxxxxx>
 Azamat,   Agreed, rough set theory is a different view of sets, not probabilistic, not fuzzy, not ambiguous, but bounded and multivalent.  (more=>>   Sincerely, Rich Cooper EnglishLogicKernel.com 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 AzamatAbdoullaev Sent: Friday, January 14, 2011 1:32 PM To: [ontolog-forum] Subject: Re: [ontolog-forum] Ontology of Rough Sets   That's indeed an original idea. The rough sets as well as fuzzy sets, extending the classical sets as new mathematical tools,  are designed to cope with the things/concepts which are too ambiguous, vague and uncertain, like ontology is. But the big challenge of ontology O is that its rather a relation than a set, to be specified by two mathematical objects known in the theory of relations as the ground/set G (the domain, a sequence of classes/sets) and the figure/graph F (the Cartesian product),    Sets relating names to values?  That is, if G is the set of domains and F is the set of objects ranging over G’s domains, then that is equivalent to a two column table of names and values.  Maybe I am missing something in your statement – please explain if you don’t mind spending the time to do so.     described as a couple of the mathematical things, O = (G(O), F(O)). Further the context is to be reified as the world states, W, with its model, M and language, L, as it was done in the Reality book, http://www.igi-global.com/bookstore/TitleDetails.aspx?TitleId=859&DetailsType=Chapters   - nice book!   -Rich     Azamat Abdoullaev    ----- Original Message ----- From: Sent: Friday, January 14, 2011 5:50 AM Subject: Re: [ontolog-forum] Ontology of Rough Sets   Tara,   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.     If any reference info comes back to me, I’ll post it.     -Rich   Sincerely, Rich Cooper EnglishLogicKernel.com 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: Thursday, January 13, 2011 3:31 PM To: Rich Cooper Cc: '[ontolog-forum] ' Subject: Re: [ontolog-forum] Ontology of Rough Sets   Rich Cooper wrote: Hi Tara,   Are you are visualizing the slice of an orange while I’m visualizing the remainder of the orange with the slice removed? Must be, because I don't catch how the application you outline below fits the mathematical theory of rough sets that I have read about. Can you provide a reference?   Without that visualization shift, I can’t fit my imaging into your response “a rough set would be a sub-lattice with top node of the upper approximation and bottom node being the lower approximation”.      My view of a rough sets application is that we have many overlapping ways of sensing objects with instruments (blood tests, MRI …) that can detect and report on what was found.  The trajectory, or process, (e.g., life cycle of a disease) of the said object shows up in different instruments at different phases of its existence.  Before computers, statisticians could only dismiss outliers, but with computers in everything, we can look at the outliers as valid data points.  There must be subtleties yet unmined in those signatures.    Rough sets provide a way of modeling that kind of dynamic signal and differencing.  Potentially they can help explain nuances of the data that weren’t detectable with less analysis.     Sensors are often modeled as probabilistically detecting or not detecting objects, but remember that sensors only detect COLUMNS, of object properties - attributes.  So the probabilistic view may not make practical analysis of data outliers.     So I would still like to see an ontology of rough sets, if there is one available.     Thanks, -Rich   Sincerely, Rich Cooper EnglishLogicKernel.com 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: Thursday, January 13, 2011 1:17 PM Cc: '[ontolog-forum] ' Subject: Re: [ontolog-forum] Ontology of Rough Sets   I'm more inclined to think of a lattice of crisp sets, and a rough set would be a sub-lattice with top node of the upper approximation and bottom node being the lower approximation. One of the interesting things, to me, of this set theory is two orthogonal partial orders: 1. the usual containment (U1 (upper approx of set 1) contained in U2, L1 contained in L2) -> RSet1 contained in RSet2 2. roughness (U1 contained in U3, L3 contained in L1) -> RSet1 is rougher than RSet3 And actually this was why I started to look into the theory in the first place- because I was considering a domain with more than one partial order - graphs. Tara Rich Cooper wrote: `Tara, John,`` ``Also, the lower and upper bounds on a rough set parallels some of the``lattice properties John has suggested for ontologies.  Would it be accurate``to characterize rough sets in that way - as a specification of the GLB and``LUB in a lattice of rough sets, based on data collected in the rough sets so``far?  `` ``Musingly,``-Rich`` ``Sincerely,``Rich Cooper``EnglishLogicKernel.com``Rich AT EnglishLogicKernel DOT com``9 4 9 \ 5 2 5 - 5 7 1 2``-----Original Message-----``From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx``[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Tara Athan``Sent: Thursday, January 13, 2011 10:53 AM``To: [ontolog-forum]``Subject: Re: [ontolog-forum] Ontology of Rough Sets`` ``OK, let's be careful.`` ``There is a mathematical set theory called "rough set theory", that was ``introduced in the 1980's`` ``PAWLAK, Z. 1982. ROUGH SETS. International Journal of Computer & ``Information Sciences, 11(5), pp.341-356.`` ``and has been studied quite a bit since. Here are some more recent articles:`` ``PAWLAK, Z. and A. SKOWRON. 2007. Rudiments of rough sets. Information ``Sciences, 177(1), pp.3-27.``PAWLAK, Z. and A. SKOWRON. 2007. Rough sets and Boolean reasoning. ``Information Sciences, 177(1), pp.41-73.``PAWLAK, Z. and A. SKOWRON. 2007. Rough sets: Some extensions. ``Information Sciences, 177(1), pp.28-40.`` ``It might be a good idea to emphasize at this point that sets and ``concepts are not the same thing. A set is determined by its membership, ``a concept is determined by its definition. The extension of a concept is ``a set, but the same concept can have extensions with different ``membership in different contexts, such as at different times (this may ``be an abuse of the term "context", I'm not sure.) However, if we, ``implicitly or explicitly, specify the context so that a concept has a ``unique extension, then we can work with sets through their defining ``concepts.`` ``Rough set theory uses the notion of "indiscernability", where there is ``an attribute which can be measured to some precision or "granularity" ``and this precision does not fully describe reality. The universe of ``discourse is clustered into groups that indiscernible with respect to a ``set of attributes.``"Crisp" sets consist of unions of these clusters. But it is also ``possible to have sets, as determined by listing their membership, which ``cannot be defined precisely by specifying regions in the quality spaces ``of the available attributes because there are indiscernible clusters ``that fall partly within and partly outside of the set.`` ``Such sets are rough sets, and they have two approximations:``an lower approximation, which consists of the greatest crisp subset,``a upper approximation, which consists of the smallest crisp superset.`` ``Given only the available attributes of an individual x, and the upper ``and lower approximations of a rough set, then the question "Is x a ``member of rough set B" has three possible answers, definitely yes, ``definitely no, or maybe. Thus rough sets intuitively carry a 3- valued ``logic, although the mathematics is more nuanced - see``POLKOWSKI, L. 2003. A note on 3-valued rough logic accepting decision ``rules. Fundam. Inf., 61(1), pp.37-45.`` `` ``So we can also wonder about the extension of the "rough" notion to ``ontologies.`` ``That approach has been explored:``INUKAI, Y., A. GEHRMANN, Y. NAGAI and S. ISHIZU. 2007. ROUGH SET THEORY ``USING SIMILARITY OF OBJECTS DESCRIBED BY ONTOLOGY [online]. [Accessed ``Jan 13, 2011]. Available from: ``http://journals.isss.org/index.php/proceedings51st/article/viewFile/504/294.`` ``Or we may ask a different but related question: Instead of an atomic ``concept being a Boolean unary predicate, what if it is a 3-valued unary ``predicate? I'm not sure if there are published papers addressing this ``question.`` ``If there are other perspectives on this issue, it would be interesting ``to hear about it from other list members.`` ``Tara`` `` ``John F. Sowa wrote:``  ` `Folks,`` ``We have to make a clear distinction between ontology and the tools,``languages, logics, and reasoning methods used with any ontology.``The subject line of this thread could be very misleading.`` ``Ever since Aristotle, categories and hierarchies of categories``have been useful for ontology -- primarily because the study``of existence leads to a study of what kinds of things exist.`` ``A's syllogisms and his method of definition by genus and``differentiae have also been useful.  But many people (starting``with Aristotle himself) have noted that prototypes rather``than strict definitions are better for some applications.`` ``In general, there is *no* specific logic or reasoning method``that is either essential or irrelevant to ontology.  The``choice depends entirely on specific applications -- or even``on very narrow questions or problems about an application.`` ``Re rough sets:  This is an important topic, but I would be``very cautious about any way of thinking that combines the``word 'ontology' with any particular reasoning method.`` ``That is in fact why I have been unhappy with the phrase``"Web Ontology Language" used as a scrambled acronym for OWL.``It suggests to many novices, that the word 'the' belongs in``front of that phrase -- but that idea is hopelessly misguided.`` ``Ontology is *orthogonal* to any and all versions of logic,``reasoning methods, and implementation tools.  Any specific``language or tool tends to channel thinking into certain paths``that may be useful for some applications.  But ways of thinking``that are specialized for one kind of application can often be``inappropriate or even misguided for other applications.`` ``John`` `` `` ``_________________________________________________________________``Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  ``Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  ``Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx``Shared Files: http://ontolog.cim3.net/file/``Community Wiki: http://ontolog.cim3.net/wiki/ ``To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J``To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx`` `` ``  ``    ` ` `` ``  ` `-- ``Tara Athan``Owner, Athan Ecological Reconciliation Services``tara_athan at alt2is.com``707-272-2115 (cell, preferred)``707-485-1198 (office)``249 W. Gobbi St. #A``Ukiah, CA 95482` `-- ``Tara Athan``Owner, Athan Ecological Reconciliation Services``tara_athan at alt2is.com``707-272-2115 (cell, preferred)``707-485-1198 (office)``249 W. Gobbi St. #A``Ukiah, CA 95482` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
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 Current Thread Re: [ontolog-forum] Ontology of Rough Sets, Tara Athan Re: [ontolog-forum] Ontology of Rough Sets, Ronald Stamper Re: [ontolog-forum] Ontology of Rough Sets, John F. Sowa 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, Tara Athan 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, 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