641d84ce   
   From: mailbox@dmitry-kazakov.de   
      
   On Wed, 15 Oct 2008 08:27:25 -0700 (PDT), bakim wrote:   
      
   > 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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