The heightened values of CRP (measured in
milligrams per liter) are discerned in levels
1 = “almost normal” for CRP < 10,
2 = “heightened” if 10
≤ CRP ≤ 20,
3 = “very heightened” if 20
≤ CRP ≤ 25,
4 = “dangerously heightened” for CRP > 25.
The age borders are decided as
1 = “not advanced for surgery” if “age” < 60,
2 = ”advanced for surgery” if 60 ≤ ”age” ≤ 80,
3 = “dangerous for surgery” if “age” > 80.
Suppose that in a seventy-year-old patient the
CRP-value is measured to be 18.
Due to (4) and (10) sets P
1
, P
2
and their
intersection are expressed as
)}25.0),3,4((
),...,5.0),2,3((),...,1),1,1{((
)},34.0,3(),66.0,2(),1,1{(
)},25.0,4(),5.0,3(),75.0,2(),1,1{(
21
2
1
=∩
=
=
PP
P
P
(14)
while P
1
`, P
2
` and their cut are computed, with
respect to (3) and (9), as
)}5.0),3,4((
),...,75.0),2,3((),...,66.0),1,1{((
)},66.0,3(),1,2(),66.0,1{(
)},5.0,4(),75.0,3(),1,2(),75.0,1{(
21
2
1
=
′
∩
′
=
′
=
′
PP
P
P
(15)
provided that X
1
= {1,2,3,4} and X
2
= {1,2,3}.
Matrix R, found in compliance with (11), is
expanded as a two-dimensional table
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
25.075.075.0
5.015.0
15.00
)3,4(
)2,3(
)1,1(
741
""
##
""
##
""
#
#
""
R
LLL
.
(16)
We in6sert R given by (16) and
∩
21
PP
determined by (15) in (12) in order to estimate
)}.66.0,(),715.0,(),88.0,(),84.0,(
),72.0,(),715.0,(),66.0,{(`
7654
321
LLLL
LLLQ =
(17)
The largest membership degree in (17) points out
chance L
5
= “promising” for a result of the operation
on the elderly patient whose CRP-index is evaluated
on the second growth level.
5 CONCLUSIONS
We have adapted approximate reasoning as a
deductive algorithm to introduce the idea of
evaluating the operation chance for patients with
heightened values of biological indices in cancer
diseases.
The formulas of membership functions in data
sets have been expanded by applying a formal
mathematical design invented by the author. The
data sets involve parametric families of functions,
which allow preparing a computer program. We
have tested a large sample of patient data to get the
results mostly converging to the physicians’
prognoses. This confirms reliability of the system.
ACKNOWLEDGEMENTS
The author thanks the Blekinge Research Board in
Karlskrona – Sweden for the grant funding this
research. The author is grateful to Medicine
Professor Henrik Forssell for all helpful hints made
in the subject of cancer surgery.
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