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In-Depth Information
X
Fig. 3.1
Membership functions of COSS term-set
“a state of European white birch
1
plants in the Boulevard Ring avenue”
The abundance of plants of
i
-th specie in the greenery of the Boulevard
Rin
g av
enue
w
hich was referred by experts to
l
-th level, is denoted with
1
i
a
(
)
i
=
1
17
;
l
=
1
7
. The data obtained are summarized in Ta
ble 3
.12.
B
ase
d on data of Table 3.12, seventeen COSS's
(
)
Y
i
=
1
17
with term-sets
X
(
)
=
i
were constructed using the method of § 2.2. The fuzzy numbers
corresponding to term-sets
1
7
X
are
T
-numbers or normal triangular numbers with
()
x
μ
, accordingly ( Table 3.13).
As an example, graphs of membership functions of COSS
membership functions
il
X
term-set are
shown in Fig. 3.1.
Using definitions of §3.1, paired comparative characteristics of states of various
plant species were defined. Elements of the pairwise similarity matrix are given in
Table 3.14.
Elements of the pairwise consistency matrix are summarized in Table 3.15.
The additive index (3.4) of general consistency of states of all plant
species is equal to 0.11 thus evidencing that states of plant species considerably
differ.
Fuzzy clusterization for 17 species of woody plants and brushwood, the states
of which are formalized above, was made. Fuzzy binary relations of similarity
over the set of the formalized states are constructed on the basis of matrixes of
pairwise similarity and pairwise consistency the elements which are provided in
Table 3.14 and Table3.15, accordingly.
