JOURNAL OF COMPUTING, VOLUME 2, ISSUE 5, MAY 2010, ISSN 2151-9617 HTTPS://SITES.GOOGLE.COM/SITE/JOURNALOFCOMPUTING/ WWW.JOURNALOFCOMPUTING.ORG 111 complex mappings involving fuzzy set theory exist. In this case, a component of b(j), say b(i,j), often represents the membership function for a fuzzy description of the severity of problem j. 

The membership function reflect the painfulness of or blueness of symptoms such as headache and cyanosis. Fuzzy sets such as these are pertinent to the determination of symptom severity levels. Thus for this problem case, the function of the mapping in Eq. (17) becomes δ (b(j)) = δ [ b(1,j), b(2,j), ……., b(k,j) ] r 
………(19) This mapping can thus involve functions of fuzzy and non-fuzzy sets. Many times, only the membership function of a fuzzy set, µA(c), is needed to determine the severity of a symptom. In such cases the eq.(19) reduces to δ(b(j)) = µA(c), 
……………………………………….(20) 
 or δ (b(j)) = g(µA(c)) 
where g is a simple function of fuzzy sets and other problem factors. Thus fuzzy set theory is highly useful in characterizing the severity levels of non-binary symptoms. 

3.3 **SIGNS OBSERVED UPON PHYSICAL EXAMINATION** 
Most models in the literature [ex. 1-3,5,911,13,14] either fail to include a description for severity level or simply equated symptoms with signs. We attempt to correct this deficiency by more precisely modeling varying levels of sign severity. For the diseases under consideration, let 
The _increases_ under consideration, let = {signs of disease j},j = N (21) $\phi$ = U $\phi$j where j =...0
3,.....…n 
 
In matrix form, let S = [ s(1), s(2),… . . ., s(f)] ...........................(22) 
where f is the cardinality of Ф, and s(j)  [0, 1], 
j = 1, 2, . . . f. 
Thus, s(j) reflects the severity of sign j in the patient. If the sign corresponding to s(j) is assumed 
to be binary, then s(j)  {0, 1}. 
Let D denotes a matrix of observables, in which 
 d(1,1) d(1,2) …. d(1,f)   d(2,1) d(2,2) …. d(2,f)   D = ………………………   ……………………...   d(e,1) d(e,2) …. d(e,f)   . .  with e is the number of elements in largest set of   
observables. An entry of the matrix is denoted by 
d (i,j) ….……………(24) with i  I (index for 
each set of observables), and j = 1, 2, ……… 
f. Each column of matrix D, say d(j), corresponds to the set of observables for sign j. The 
severity of sign j, is represented thus 
$$\mathbf{d}({\dot{\mathbf{i}}})$$
Ψ (b(j)) d(j) ――> s(j) 
.........................................(25) 
This mapping, as was the case in determining symptom severity, may or may not involve fuzzy sets. The function Ψ is usually very similar in nature to the function δ used to map patient information into symptoms in Eq. (17). Nonfuzzy mappings exist when only location factors are pertinent to severity determination. If other factors exist, they often involve the use of fuzzy sets. For example, severity aspects of a systolic heart murmur may involve fuzzy sets with regard to the loudness and quality of the sound. Specific functional relationships of Ψ(d(j)) are omitted since the general structures are similar to those presented in Eqs. (19) and (20). 

3.4 **RESULTS OF CLINICAL AND DIAGNOSTIC** 
TESTS 
 
Consider the set Tt of possible test results of test t. The elements of this set Tt may be discrete or 
continuous. Fuzzy set theory is introduced in an 
attempt to transform these test results in to a proper perspective and scale. For each test t, a 
fuzzy set Γt is created to represent the 'abnormality' of the possible test results. Tt. The membership function, reflection the degree of abnormality, must be determined for each set Γt t 
= 1, 2, 3,…..k., where k equals the number of tests preformed on the patient. Let rt Є Tt. The 
degree of abnormality of this test result is reflected by the membership function μΓt ( rt) where 
For the k tests performed on a given patient, let 
 μΓt ( rt) rt ――> z(t)  ……………………………(26)  and z(t)  [0,1]. 
Z = [ z(1) z(2) . . . z(k) ] ………………(27) 
represent the test results evaluated via fuzzy set theory. Any test result can be mapped into the [0, 1] continuum using this theory, so k is the 
number of tests performed. The degree of membership is thus a function of a single variable, 
where 
$$\mu\Gamma t(r t)=\left\{\begin{array}{l l l}{{0,}}&{{\quad}}&{{\mathrm{for}\quad r t<260}}\\ {{\frac{r t}{340}\,\cdot\,\frac{26}{34}}}&{{\quad}}&{{\mathrm{for}\quad260\leq r t\leq600}}\\ {{1}}&{{\quad}}&{{\mathrm{for}\quad r t>600}}\end{array}\right.$$
…………………….....(28) 
The result of test t, rt may possess defining aspects so that rt ={ r1, r2,……….rtn } ……………………...(29) 