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Aggregation (decomposition) abstraction
helps us to construct concept by others concepts
depending on their decomposition or functional dependence:
E
i
PART_OF E
j
Transformation
is very similar to that of the aggregation, except that it contains a calculation
rule, which specifies how the values representing the occurrences of the defined concept are
derived from the values representing the defining concepts.
More in details we consider the example of analysis of water resources and the pollution of
sewage of the enterprise. The pollutants from the production are entering into the water in
some types of cases (Fig. 3). The initial task is always data gathering, resulting in a set of
observed findings.
A dynamically changing environment imposes time constraints. Many problems are to be
solved simultaneously. The values of the observed parameters may change dynamically,
depending on time and the events occurring. Solution of different problems is interfered
with one another. For instance, the high concentration of harmful material thrown out into
the air is related with the risk factors referring prevention of links that are of biological
significance and time-dependent, etc. Another essential aspect of such an application
domain is its spatial dimension. While in many other application domains the problems of
study are within a very precise and, usually, narrow frameworks. For instance, the
contamination problem of an enterprise (e.g. manufactory, firm, and plant) deals with
spatially varying phenomena of unbounded limits.
4.3 Formal representation of processes by E-nets
The E-nets (Evaluation nets) are the extension of Petri nets, and were introduced by (Noe,
Nutt 1973). The structure and behavioural logic of E-nets give new features in conceptual
modelling and imitation of domain processes and decision-making processes (Dzemydiene,
2001).
Apart from time evaluation property, E-nets have a much more complex mechanism for
description of transition work, some types of the basic transition structures, a detailing of
various operations with token parameters. In addition to Petri nets, two different types of
locations are introduced (peripheral and resolution locations).
The exceptional feature is the fact that the E-net transition can represent a sequence of
smaller operations with transition parameters connected with the processes.
It is possible to consider the E-net as a relation on
(E,M
0
,
,Q,
),
where
E
is a connected set
of locations over a set of permissible transition schemes,
E
is denoted by a four-tupple:
E=(L,P,R,A),
where
L
is a set of locations,
P
is the set of peripheral locations,
R
is a set of
resolution locations, A is a finite, non-empty set of transition declarations;
M
o
is an initial
marking of a net by tokens;
={
j}
is a set of token parameters;
Q
is a set of transition
procedures; is a set of procedures of resolution locations.
The E-net transition is denoted as
a
i
=(s
i,
t(a
i
),q
i
),
where s
i
is a transition scheme,
t(a
i
)
is a
transition time and
q
i
is a transition procedure.
The input locations
L
i
'
of the transition correspond to the pre-conditions of the activity
(represented by the transition in Fig. 4). The output locations
L
i
”
correspond to post-
conditions of the activity.
In order to represent the dynamic aspects of complex processes and their control in
changing environment it is impossible to restrict ourselves on the using only one temporal
parameter
t(a
i
)
which describes the delaying of the activity, i.e. the duration of transition.
The complex rules of transition firing are specified in the procedures of resolution locations
and express the rules of process determination.
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