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Table 3.17
(
continued
)
0,272 0,502 0,794 0,562 0,502 0,502 0,562 0,517 0,502 0,562 0,562 0,562 1,000 0,562 0,562 0,502 0,562
0,272 0,502 0,562 0,566 0,502 0,502 0,566 0,517 0,502 0,566 0,566 0,566 0,562 1,000 0,620 0,502 0,566
0,272 0,502 0,562 0,566 0,502 0,502 0,566 0,517 0,502 0,566 0,566 0,566 0,562 0,620 1,000 0,502 0,566
0,272 0,635 0,502 0,502 0,548 0,548 0,502 0,502 0,635 0,502 0,502 0,502 0,502 0,502 0,502 1,000 0,502
0,272 0,502 0,562 0,660 0,502 0,502 0,660 0,517 0,502 0,660 0,660 0,660 0,562 0,566 0,566 0,502 1,000
As one can see from Table 3.14 and Table3.15, fuzzy relations
R
and
R
defined by matrixes of pairwise similarity and pairwise consistency, accordingly,
are not transitive, therefore their transitive closures
R
which are
R
and
2
1
R
are
R
and
similarity relations, are constructed. Elements of relations matrixes
1
2
provided in Table 3.16 and Table 3.17, accordingly.
Fuzzinesses of similarity relations are
ˆ
1
ˆ
2
,
. As known [15],
R
=
0
433
R
=
0
805
fuzziness degree of fuzzy relation
R
2
(
)
()
∑
ξ
R
=
μ
x
,
y
−
r
,
R
i
j
ij
n
⋅
m
i
,
j
(
)
⎧
0
μ
x
,
y
≤
0
R
i
j
r
=
where
⎩
⎨
(
)
ij
1
μ
x
,
y
>
0
R
i
j
R
, the decision to use the
Owing to higher fuzziness of similarity relation
2
R
for the further analysis was made. Based on the
decomposition theorem, all plant species were divided, under relation
similarity relation
1
R
, into
clusters of the similar species based on their state. Results of fuzzy clusterization
under similarity relation
1
R
, are provided in Table 3.18.
The results obtained allow concluding that the state of “European white birch”
plants essentially differs from the states of all other plant species. States of “Witch
elm” and “large-leaved linden” plants, and also states of “little-leaved linden” and
“Hungarian lilac” plants are similar to each other. Based on the states of other
plant species one can say with high confidence level that there is no similarity of
them.
1
