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bakim
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 Posted: Tue Oct 14, 2008 8:59 pm Post subject: Ideas to incorporate/integrate both the spatial and temporal |
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Hello all,
A fine greeting to all,...
I would like to know the opinion and comment from various experts who
are actively engaged in Fuzzy logic rule based modeling, about the
possibility of integrating both the spatial and temporal data in
generating a rule set and developing a fuzzy model.
I have explore some of the possibilties but i am not certain about the
procedure I have adopted. I am working on an Environmental assessment
modeling based on Fuzzy logic rule based concept. One of the parameter
I have considered as an input variable is Rainfall, which is varying
temporally ( daily, monthly, yearly ) apart from other input
parameters like landuse, soil, slope, vegetation cover etc, which vary
spatially. The problem, I have is to asses how can I integrate both
the spatial and temporal variables in developing the Fuzzy Knowledge
base, (Rules and membership function).
If someone has experience such problem and has a ideas how to handle
such problem of temporal and spatial integration in Fuzzy rule based
modeling, I would be highly thankful to get the expert feedback and
directions and comments.
Thanks in advance,
Best Regards
Truly,
Bakim |
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Dmitry A. Kazakov
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| Posted: Wed Oct 15, 2008 8:10 am Post subject: Re: Ideas to incorporate/integrate both the spatial and temp |
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On Tue, 14 Oct 2008 13:59:35 -0700 (PDT), bakim wrote:
| Quote: | I would like to know the opinion and comment from various experts who
are actively engaged in Fuzzy logic rule based modeling, about the
possibility of integrating both the spatial and temporal data in
generating a rule set and developing a fuzzy model.
I have explore some of the possibilties but i am not certain about the
procedure I have adopted. I am working on an Environmental assessment
modeling based on Fuzzy logic rule based concept. One of the parameter
I have considered as an input variable is Rainfall, which is varying
temporally ( daily, monthly, yearly ) apart from other input
parameters like landuse, soil, slope, vegetation cover etc, which vary
spatially. The problem, I have is to asses how can I integrate both
the spatial and temporal variables in developing the Fuzzy Knowledge
base, (Rules and membership function).
|
You should say where you see any problem. Rainfall is not time dependent,
it is a value. It would be likely a fuzzy value over some numeric domain
like milliliter of water per square centimeter. That this value is the
result of some function of some place on the Earth and clock is irrelevant
to the issue, as you consider the rainfall as an input. (It could be
different, if the inputs were rather the location coordinates and clock.)
Clearly, the decision made depends on the rainfall. It does not matter
whether this water fell at 15 or 16 October, again assuming that the time
is not an input. The laws of physics do not change with the calendar.
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de |
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bakim
Guest
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| Posted: Wed Oct 15, 2008 3:27 pm Post subject: Re: Ideas to incorporate/integrate both the spatial and temp |
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On 15 Okt., 09:33, "Dmitry A. Kazakov" <mail...@dmitry-kazakov.de>
wrote:
| Quote: | On Tue, 14 Oct 2008 13:59:35 -0700 (PDT), bakim wrote:
I would like to know the opinion and comment from various experts who
are actively engaged in Fuzzy logic rule based modeling, about the
possibility of integrating both the spatial and temporal data in
generating a rule set and developing a fuzzy model.
I have explore some of the possibilties but i am not certain about the
procedure I have adopted. I am working on an Environmental assessment
modeling based on Fuzzy logic rule based concept. One of the parameter
I have considered as an input variable is Rainfall, which is varying
temporally ( daily, monthly, yearly ) apart from other input
parameters like landuse, soil, slope, vegetation cover etc, which vary
spatially. The problem, I have is to asses how can I integrate both
the spatial and temporal variables in developing the Fuzzy Knowledge
base, (Rules and membership function).
You should say where you see any problem. Rainfall is not time dependent,
it is a value. It would be likely a fuzzy value over some numeric domain
like milliliter of water per square centimeter. That this value is the
result of some function of some place on the Earth and clock is irrelevant
to the issue, as you consider the rainfall as an input. (It could be
different, if the inputs were rather the location coordinates and clock.)
Clearly, the decision made depends on the rainfall. It does not matter
whether this water fell at 15 or 16 October, again assuming that the time
is not an input. The laws of physics do not change with the calendar.
--
Regards,
Dmitry A. Kazakovhttp://www.dmitry-kazakov.de
|
Dear Sir,
I appreciate at your opinion related to the problem. I could
understand that rainfall for a particular event/day has a specific
value, but the values of rainfall get changed as time changed. For
example, the amount of rain falling in a certain area for yesterday
is 10 mm and today is 30 mm. Hence, temporally the rainfall has an
influence on other spatial variables on landscape i.e. for that
particular location, all variables which are varied spatially doesnot
changed in small time interval. For all variables which vaired
spatially, a membership function can be assigned considering the
expert knowlege and their interaction between them. For rainfall, the
range of values i.e. lower support and upper support to define the
fuzzy sets are temporal in nature ( rainfall value for past 100 days;
min:0 max: 150 mm; hence the range is (0,100) to define the membership
and assess the fuzzy sets). On the contary, other variables like slope
is in spatial domain ( slope value for the region range from 0 to 45,
(0,45)). My problem was whether Fuzzy set and membership function that
represent in temporal domain and that in spatial domain can be put
together to develop a Fuzzy rule based system. Its a kind of Spatio-
Temporal concept as far as i understand from literature. Whether this
kind of Spatio-temporal concept can be introduce/implement with Rule
based fuzzy modeling.
With Best Regards
Bakim |
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Dmitry A. Kazakov
Guest
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| Posted: Thu Oct 16, 2008 8:25 am Post subject: Re: Ideas to incorporate/integrate both the spatial and temp |
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On Wed, 15 Oct 2008 08:27:25 -0700 (PDT), bakim wrote:
| Quote: | I appreciate at your opinion related to the problem. I could
understand that rainfall for a particular event/day has a specific
value, but the values of rainfall get changed as time changed. For
example, the amount of rain falling in a certain area for yesterday
is 10 mm and today is 30 mm. Hence, temporally the rainfall has an
influence on other spatial variables on landscape i.e. for that
particular location, all variables which are varied spatially doesnot
changed in small time interval. For all variables which vaired
spatially, a membership function can be assigned considering the
expert knowlege and their interaction between them. For rainfall, the
range of values i.e. lower support and upper support to define the
fuzzy sets are temporal in nature ( rainfall value for past 100 days;
min:0 max: 150 mm; hence the range is (0,100) to define the membership
and assess the fuzzy sets). On the contary, other variables like slope
is in spatial domain ( slope value for the region range from 0 to 45,
(0,45)). My problem was whether Fuzzy set and membership function that
represent in temporal domain and that in spatial domain can be put
together to develop a Fuzzy rule based system. Its a kind of Spatio-
Temporal concept as far as i understand from literature.
|
I see. It means that the input is *not* rainfall.
When you start defining a fuzzy set, the first question to ask yourself is
what is the domain of. A fuzzy set of rainfall has the domain of
dimensioned real numbers measured in meters (the measure of rainfall).
Formally:
L -> [0,1] (here L is in meters: m^3 / m^2)
Now, if you want to bring time into the picture, then it is not a rainfall,
but a distribution of over some time interval. In this case the fuzzy set
is:
L x T -> [0,1]
I.e. its membership function is defined over the Cartesian product of
rainfall and time. It tells for given rainfall value and given time how is
it possible (or other truth value) that it rained that much at that time.
Similarly you can add spatial data:
L x L x L x T -> [0,1]
First L is rainfall, the second two L is the coordinates, T is time. The
meaning is how is it possible that it rained that much at the spot (X,Y) at
the time T.
Now, of course, if you want to deploy some machine learning or else
manually define a classifier (set of rules) based on such data, you
certainly will have a difficult problem that any representative statistics
in such model will be extremely huge. In short it likely won't work.
So before you start you probably have to cluster your data into sets of
significantly lesser dimensions. For example, the space L x L could be
split into areas of interests so that L x L were replaced to N (a set of
linguistic variables describing areas). In fuzzy approach these areas
itself can have fuzzy margins and overlapping. Same can be done with T. For
example, linguistic variables Day, Night, Dawn etc. Of course clustering
may involve all three components. I.e. you can have linguistic variables
like "typical rainfall in London in spring." I think you have got the idea.
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de |
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