Hello All, This is the history of the problem:
In a course on decision analysis with Stanford [1], Prof Ron Howard introduces a non-trivial decision problems called the Kim's party problem. The statement is that the teenager Kim want's to organize a party at her home. There are three choices of location - outdoors, porch and indoors. The choice depends on the weather conditions that can be sunny or rainy. Given the various prospects of location and weather, Kim comes up with her order of preference of the prospects as so: 1. Outdoors - Sunny 2. Porch - Sunny 3. Indoors - Rainy 4. Indoors - Sunny 5. Porch - Rainy 6. Outdoors - Rainy In an introductory paper on decision analysis[2], Prof Howard introduces the concept of a profit measure. For this I need to quantify the location (L vector), the weather (W vector) and a profit measure (F) that can generate for me the order above. So, with L =. l1 (outdoors), l2 (porch), l3 (indoors) & W =. w1 (sunny), w2 (rainy), we have 0: l1 F w1 (Outdoors - Sunny) 1: l1 F w2 (Outdoors - Rainy) 2: l2 F w1 (Porch - Sunny) 3: l2 F w2 (Porch - Rainy) 4: l3 F w1 (Indoors - Sunny) 5: l3 F w2 (Indoors - Rainy) and (l1 F w1) > (l2 F w1) > (l3 F w2) > (l3 F w1) > (l2 F w2) > (l1 F w2) This led me to formulate the problem which I asked. It is possible that in my translation to J, I might have erred - I apologize if that is the case. I proposed simple dyads like * or (x^2 - y^2) to illustrate the possibilities of functions that can be tested using a brute force test rig. After a few shots at this, I realized that my approach is naive and inefficient and so I proposed the problem to the J forum group. Once a Profit Measure is so described, I want to vary the parameters in the function to other combinations. This means that I cannot have a simple discrete function that matches at exactly these points. So, the question is a) Is there a continuous function that matches these values at the points? b) If there is a family of continuous functions that can work, is there a further characterization that can help in deciding among the alternatives? As I write this, I tend to agree that the problem is not defined well enough and may not admit further discussion. In any case, do share with me what you think. Regards, Yuva [1]: http://strategicdecisions.stanford.edu/courses/syllabus-decAnal.htm [2]: http://decision.stanford.edu/library/ronald-a.-howard/Decision%20Analysis-%20Applied%20Decision%20Theory.pdf/view On Thu, Feb 25, 2010 at 4:37 PM, Yuvaraj Athur Raghuvir < [email protected]> wrote: > Dear J Forum, > > I have an interesting problem for which I need more insights to proceed. > > I have to determine three unknowns: > (a) W where 2 = $W = w1, w2 > (b) L where 3 = $ L = l1 , l2 , l3 > (c) F a dyad that takes scalar inputs > > Such that > (6 1 5 2 3 4) -: \:; L F"0 0/ W NB. the order of values is known. > > For example, > F =: * > (6 1 5 2 3 4) -: \:; L F"0 0/ W [W =. 3 9 [L =. 20 16 12 > 0 > > I designed a test that is essentially a blind brute force on the inputs > assuming F is given: > F =: 4 : 'x^2 - y^2' NB. for example > odometer =: #: i.@(*/) > test =: 3 : 0 > n =. y > w =. odometer n,n > l =. odometer n,n,n > NB. I get a length error if I use bigger inputs. So chunking into 100's > for_i. i. 100 %~ {. $l do. > for_j. i. 100 %~ {. $w do. > b =. ('' -: I. (6 1 5 2 3 4) -:"1 1 (>@[ \:@,"_1@:(F"0 0/"1 1) >@])/ > (_100{.(100*>:i){. l);(_100{.(100*>:j){. w)) > smoutput i,j > if. b<1 do. break. [smoutput 'found it';i;j end. > end. > end. > '' > ) > > I am not convinced that I can find a solution this way since the functional > forms are far too many to be tried out notwithstanding my other assumptions. > > > Any suggestions? > > Regards, > Yuva > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
