Environmental Engineering Reference
In-Depth Information
(1)
Where are: X- finite set of all consideration objects; k- total number of
objects
a) Forming vectors x= (x
1
,......., x
m
) of all initial quality needed to the full
assessment of investigated objects quality.
First, it is presumed, that complex objects are identified with vectors:
x(j)=(x
1
(j),........,x
m
(j))),
(2)
i=1,.....,m; j = (1,......,k),
k-number of objects under investigation
where x
i
(j) is a value of 'i'-th initial parameter x
i
for 'j'-th complex object (an
element of all real numbers of set E1). Component x
i
(j) of vector x(j) refer to
as value of initial quality(indicator) x
i
of object x(j). The finite set of objects
shows the base for all fuzzy sets.
The initial quality of objects can be defined by vector:
x(j)=(x
1
(j),......,x
m
(j))
(3)
It is supposed that each value of vector x
i
is necessary and the total value of
quality vector is sufficient for a fixed quality of the object, respectively for the
sustainability assessment of configured object over set of indices.
b) Forming of vectors of specific quality q=(q
1
,......., q
m
)
Quality of the objects x(j), j = 1,...., k, is defined by a number of specific
quality q
1
,....,q
m
where each of them being a function of corresponding
attribute (or initial parameters of vector):
q
i
= q
i
(x(i), i = 1,...m;
where m is number of specific quality
(4)
