Biology Reference
In-Depth Information
Nonfuzzy set
Cool
Fuzzy set
Cool
100
100
0
0
50
60
70
50
60
70
Fuzzy Set and its Complement
Not Cool
Cool
Not Cool
100
50
0
50 60 70
Air Temperature (°F)
Fig. 5.6 Diagrammatic representations of
binary logic
and
fuzzy logic
. In standard logic, objects
belong to a set completely (100%) or not at all (0 %) (see
top left
). In fuzzy logic, objects belong to a
fuzzy set only to some degree (
top right
) and to the complement of the set to some other extent
(
bottom
), the sum of the partial memberships always summing up to unity. For example, the air
temperature of 50
F is 0%cool and 100%not cool; 55
F is 50% cool and 50% not cool; 60
Fis100%
cool and 0% not cool; 65
F is 50% cool and 50% not cool; and 70
F is 0% cool and 100% not cool
According to fuzzy/vague/multivalence theorists, including Peirce, Russell, Black,
Lukasiewicz, Zadeh, and Kosko (1993), words are fuzzy sets. The word “young” is
an example of the fuzzy set. I am neither “young” (0) or old (1) but both young (to a
degree of say 0.2) and old (to a degree of say 0.8). In other words I am both “young”
and “not-young” (i.e., old) at the same time to certain degrees. Similarly, it can be
suggested that the word “complementary” or “complementarity” is also a fuzzy set,
since what is complementary to some scholars may not be complementary to others.
For example, Kelso and EngstrØm list hundreds of complementary pairs in their
topic,
The Complementary Nature
(2006). Although their complementary pairs do
satisfy Bohr's definition of complementarity, Statement (5.16), they certainly do
not satisfy the definition of complementarity given in Sect.
2.3.3
, which is based on
three criteria of the complementarian logic:
1.
Exclusivity
(A and B are mutually exclusive)
2.
Essentiality
(A and B are both essential to account for C)
3.
Transcendentality
(C transcends the level where A and B have meanings)
