
## 3.2 Present Symptoms

Classical models begin the decision process with the symptoms already designated or severity levels determined. Let πi = the set of possible problems that might be observed or experienced by a patient with disease i, where i  N. Further, let π = U πi, i = 1, 2, 3,……, n ………...(8) where n is the cardinality of N. We note that π comprises the patient related problems that are encountered for all diseases under consideration. The elements of this set are not medically designated symptoms, but are patient descriptions such as dizziness, chest pain, and inability to breathe properly. Associated with each of these problems, q, (where q  π), is a set of factors ∆q. which are important to the medical designation and severity determination of problem q. Each problem profile set ∆q may have the following subsets of discrete information : 
JOURNAL OF COMPUTING, VOLUME 2, ISSUE 5, MAY 2010, ISSN 2151-9617 HTTPS://SITES.GOOGLE.COM/SITE/JOURNALOFCOMPUTING/ WWW.JOURNALOFCOMPUTING.ORG 110 existed in the patient's past, then the matrix V(j) 
must be determined. This matrix V(j) is then used to complete the patient history matrix H. for a specific patient and undiagnosed disease of disorder f(V(j))V(j) ――> h(j)……………………………(7) 
such that f (V(j))  I, I = {0, 1} and 1 ≤ j ≤ p. 

Therefore, a vector of symptoms V(j) is mapped 
(non-fuzzy) into the jth element of HA such that h(j) equals 0 or 1. The function f(V(j)) may be very simplistic in nature, or be similar to the function presented as the general diagnosis decision model. Using this mapping the past history matrix HA can be quantified for all possible elements h(j), 1 ≤ j ≤ p and is used later in developing the various diagnoses decision models. 

where i = 1, 2, 3, …., s and j = 1, 2, 3,……..,r. 

Here for a cell-element b(i, j) of this matrix B, j=1,2,3,……..,r,and 
………………………………………(13) i  I is the index for characteristics of the problem profile, and r = max I. 

For example, the ith row of this matrix might correspond to the location of problems j, and the jth column to the profile factors in the set ∆q with j 
= q. 

Clearly, the matrix B contains all the pertinent information obtained from the verbal physician - 
patient interaction during the initial interview. 

Once the information for B has been gained, the physician must medically designate the symptoms as well as the severity levels. From the set β of all possible medically designated symptoms under consideration, let us construct a matrix A 
such that A = [ a(1), a(2), a(3),…….,a(t) ] …………………(14) 
in which a(i)  [0,1] and t is the cardinality of β. 

The variable a(i) of the matrix A represents the severity of symptom i, with i Є β. If a symptom i is assumed to be dichotomous for the diseases under consideration then a(i)  {0, 1}………(15) 
with a(i) = 0,if symptom i is not related by the patient. 

 = 1, otherwise. 

Otherwise, the severity of the symptom is considered to be pertinent information and can be represented as a(i)  [0,1]. As a(i) approaches 1, the severity of symptom i increases while the severity of symptom i decreases as a(i) approaches 0. The mapping of patient related problems to medically designated symptoms can now be more precisely written in matrix from as δ (B) B ――> A ………………………………(16) 
In this matrix form, a given problem j may be mapped into one more entries of A. Let b(j), a column vector of matrix B, represent the problem j and its problem profile set ∆j. Then. 

δ (b(j)) b(j) ――> a(i) ………………(17) where j = 1, 2, . . . r; and i = 1, 2, . . ., t. 

 ∆q1 = {location of problem q} ∆q2 = {longevity of problem q} 
 ∆q3={continuity of problem q} ...................(9) 
 ∆q4 = {defining aspects of intermittent problem q} 
∆q5 = {specifics for severity determination of problem q : fuzzy descriptions}. where ∆q=∆q1U∆q2U∆q3U∆q4U∆q5 
....................................(10) 
Let ∆ = U ∆q , q = 1, 2. 3. …, r where r is the cardinality of the set π. 

If β is the collective set of medically designated symptoms for the disease under consideration, then f(π,∆)π――> β ……………………………...(11) 
Define a matrix B containing information obtained from the patient with regard to his problems π , 
and problem profiles ∆q as B. 

 B = matrix ( b(i,j) ), ........................................(12) 
Clearly, a(i) is binary, i.e. the map δ (b(j))  {0, 1}. For this case, the function δ is very simplistic and usually incorporates the presence or absence of a few factors, primarily those of location, in the problem profile. It is obvious that if c be the relative measure or description of the symptom severity, A be the fuzzy set evaluating severity descriptions. 

Then. 

 µA(c) = b(i,j) , iff a(i) does not belong to [0,1]. ……(18) 
If a(i) is not assumed to be binary, then more 